AI Email Edit

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  AI nationalism

  AI nationalism is the idea that nations should develop and control their own artificial intelligence technologies to advance their own interests and ensure technological sovereignty. This concept is gaining traction globally, leading countries to implement new laws, form strategic alliances, and invest significantly in domestic AI capabilities. == Global trends and national strategies == In 2018, British technology investor Ian Hogarth published an influential essay titled AI Nationalism. He argued that as AI gains more power and its economic and military significance expands, governments will take measures to bolster their own domestic AI industries, and predicted that the advancement of machine learning systems would lead to what he termed "AI nationalism." He anticipated that this rise in AI would accelerate a global arms race, resulting in more closed economies, restrictions on foreign acquisitions, and limitations on the movement of talent. Hogarth predicted that AI policy would become a central focus of government agendas. He also criticized Britain’s approach to AI strategy, citing the sale of London-based DeepMind—one of the leading AI laboratories, acquired by Google for a relatively modest £400 million in 2014—as a significant misstep. AI nationalism is chiefly reflected in the escalating rhetoric of an artificial intelligence arms race, portraying AI development as a zero-sum game where the winner gains significant economic, political, and military advantages. This mindset, as highlighted in a 2017 Pentagon report, warns that sharing AI technology could erode technological supremacy and enhance rivals' capabilities. The winner-takes-all mentality of AI nationalism poses risks including unsafe AI development, increased geopolitical tension, and potential military aggression (such as cyberattacks or targeting AI professionals). Several countries, including Canada, France, and India, have formulated national strategies to advance their positions in AI. In the United States, a leading player in the global AI arena, trade policies have been enacted to restrict China's access to critical microchips, reflecting a strategic effort to maintain a technological edge. The United States’ National Security Commission on Artificial Intelligence (NSCAI) frames AI development as a critical aspect of a broader technology competition crucial for national success. It emphasizes the need to outpace China in AI to maintain strategic advantage, reflecting AI nationalism by linking geopolitical power directly to advancements in AI. France has seen notable governmental support for local AI startups, particularly those specializing in language technologies that cater to French and other non-English languages. In Saudi Arabia, Crown Prince Mohammed bin Salman is investing billions in AI research and development. The country has actively collaborated with major technology firms such as Amazon, IBM, and Microsoft to establish itself as a prominent AI hub. == Historical and cultural context == AI nationalism is seen as deeply connected to historical racism and imperialism. It is viewed not merely as a technological competition but as a contest over racial and civilizational superiority. Historically, technological achievements were often used to justify colonialism and racial hierarchies, with Western societies perceiving their advancements as evidence of superiority. In the context of AI, this historical context continues to shape views on intelligence and development. Some argue that AI nationalism reinforces the idea of fundamental civilizational divides, especially between the Western world and China. This perspective often frames China's progress in AI as a direct challenge to Western values, presenting the AI competition as a struggle over values. AI nationalism is said to draw from long-standing anti-Asian stereotypes, such as the "Yellow Peril," which portray Asian nations as threats to Western civilization. This viewpoint links Asian technological advances with dehumanization and artificiality, reflecting persistent anxieties about China's growing role in the global tech landscape. == Implications == AI nationalism is seen as a component of a broader trend towards the fragmentation of the internet, where digital services are increasingly influenced by local regulations and national interests. This shift is creating a new technological landscape in which the impact of artificial intelligence on individuals' lives can vary significantly depending on their geographic location. J. Paul Goode argues that AI nationalism may exacerbate existing societal divisions by promoting the development of systems that embed cultural biases, thereby privileging certain groups while disadvantaging others.

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  Calibration (statistics)

  There are two main uses of the term calibration in statistics that denote special types of statistical inference problems. Calibration can mean a reverse process to regression, where instead of a future dependent variable being predicted from known explanatory variables, a known observation of the dependent variables is used to predict a corresponding explanatory variable; procedures in statistical classification to determine class membership probabilities which assess the uncertainty of a given new observation belonging to each of the already established classes. In addition, calibration is used in statistics with the usual general meaning of calibration. For example, model calibration can be also used to refer to Bayesian inference about the value of a model's parameters, given some data set, or more generally to any type of fitting of a statistical model. As Philip Dawid puts it, "a forecaster is well calibrated if, for example, of those events to which he assigns a probability 30 percent, the long-run proportion that actually occurs turns out to be 30 percent." == In classification == Calibration in classification means transforming classifier scores into class membership probabilities. An overview of calibration methods for two-class and multi-class classification tasks is given by Gebel (2009). A classifier might separate the classes well, but be poorly calibrated, meaning that the estimated class probabilities are far from the true class probabilities. In this case, a calibration step may help improve the estimated probabilities. A variety of metrics exist that are aimed to measure the extent to which a classifier produces well-calibrated probabilities. Foundational work includes the Expected Calibration Error (ECE). Into the 2020s, variants include the Adaptive Calibration Error (ACE) and the Test-based Calibration Error (TCE), which address limitations of the ECE metric that may arise when classifier scores concentrate on narrow subset of the [0,1] range. A 2020s advancement in calibration assessment is the introduction of the Estimated Calibration Index (ECI). The ECI extends the concepts of the Expected Calibration Error (ECE) to provide a more nuanced measure of a model's calibration, particularly addressing overconfidence and underconfidence tendencies. Originally formulated for binary settings, the ECI has been adapted for multiclass settings, offering both local and global insights into model calibration. This framework aims to overcome some of the theoretical and interpretative limitations of existing calibration metrics. Through a series of experiments, Famiglini et al. demonstrate the framework's effectiveness in delivering a more accurate understanding of model calibration levels and discuss strategies for mitigating biases in calibration assessment. An online tool has been proposed to compute both ECE and ECI. The following univariate calibration methods exist for transforming classifier scores into class membership probabilities in the two-class case: Assignment value approach, see Garczarek (2002) Bayes approach, see Bennett (2002) Isotonic regression, see Zadrozny and Elkan (2002) Platt scaling (a form of logistic regression), see Lewis and Gale (1994) and Platt (1999) Bayesian Binning into Quantiles (BBQ) calibration, see Naeini, Cooper, Hauskrecht (2015) Beta calibration, see Kull, Filho, Flach (2017) === In probability prediction and forecasting === In prediction and forecasting, a Brier score is sometimes used to assess prediction accuracy of a set of predictions, specifically that the magnitude of the assigned probabilities track the relative frequency of the observed outcomes. Philip E. Tetlock employs the term "calibration" in this sense in his 2015 book Superforecasting. This differs from accuracy and precision. For example, as expressed by Daniel Kahneman, "if you give all events that happen a probability of .6 and all the events that don't happen a probability of .4, your discrimination is perfect but your calibration is miserable". In meteorology, in particular, as concerns weather forecasting, a related mode of assessment is known as forecast skill. == In regression == The calibration problem in regression is the use of known data on the observed relationship between a dependent variable and an independent variable to make estimates of other values of the independent variable from new observations of the dependent variable. This can be known as "inverse regression"; there is also sliced inverse regression. The following multivariate calibration methods exist for transforming classifier scores into class membership probabilities in the case with classes count greater than two: Reduction to binary tasks and subsequent pairwise coupling, see Hastie and Tibshirani (1998) Dirichlet calibration, see Gebel (2009) === Example === One example is that of dating objects, using observable evidence such as tree rings for dendrochronology or carbon-14 for radiometric dating. The observation is caused by the age of the object being dated, rather than the reverse, and the aim is to use the method for estimating dates based on new observations. The problem is whether the model used for relating known ages with observations should aim to minimise the error in the observation, or minimise the error in the date. The two approaches will produce different results, and the difference will increase if the model is then used for extrapolation at some distance from the known results.

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  Wolfram Mathematica

  Wolfram Mathematica (also known as Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram, and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in Mathematica. Mathematica 1.0 was released on June 23, 1988 in Champaign, Illinois and Santa Clara, California. Mathematica's Wolfram Language is fundamentally based on Lisp; for example, the Mathematica command Most is identically equal to the Lisp command butlast. == Notebook interface == Mathematica is split into two parts: the kernel and the front end. The kernel interprets expressions (Wolfram Language code) and returns result expressions, which can then be displayed by the front end. The original front end, designed by Theodore Gray in 1988, consists of a notebook interface and allows the creation and editing of notebook documents that can contain code, plaintext, images, and graphics. Code development is also supported through support in a range of standard integrated development environment (IDE) including Eclipse, IntelliJ IDEA, Atom, Vim, Visual Studio Code and Git. The Mathematica Kernel also includes a command line front end. Other interfaces include JMath, based on GNU Readline and WolframScript which runs self-contained Mathematica programs (with arguments) from the UNIX command line. == High-performance computing == Capabilities for high-performance computing were extended with the introduction of packed arrays in version 4 (1999) and sparse matrices (version 5, 2003), and by adopting the GNU Multiple Precision Arithmetic Library to evaluate high-precision arithmetic. Version 5.2 (2005) added automatic multi-threading when computations are performed on multi-core computers. This release included CPU-specific optimized libraries. In addition Mathematica is supported by third party specialist acceleration hardware such as ClearSpeed. In 2002, gridMathematica was introduced to allow user level parallel programming on heterogeneous clusters and multiprocessor systems and in 2008 parallel computing technology was included in all Mathematica licenses including support for grid technology such as Windows HPC Server 2008, Microsoft Compute Cluster Server and Sun Grid. Support for CUDA and OpenCL GPU hardware was added in 2010. == Extensions == As of Version 14, there are 6,602 built-in functions and symbols in the Wolfram Language. Stephen Wolfram announced the launch of the Wolfram Function Repository in June 2019 as a way for the public Wolfram community to contribute functionality to the Wolfram Language. There are currently more than 3000 functions contributed as Resource Functions. In addition to the Wolfram Function Repository, there is a Wolfram Data Repository with computable data and the Wolfram Neural Net Repository for machine learning. Wolfram Mathematica is the basis of the Combinatorica package, which adds discrete mathematics functionality in combinatorics and graph theory to the program. == Connections to other applications, programming languages, and services == Communication with other applications can be done using a protocol called Wolfram Symbolic Transfer Protocol (WSTP). It allows communication between the Wolfram Mathematica kernel and the front end and provides a general interface between the kernel and other applications. Wolfram Research freely distributes a developer kit for linking applications written in the programming language C to the Mathematica kernel through WSTP using J/Link., a Java program that can ask Mathematica to perform computations. Similar functionality is achieved with .NET /Link, but with .NET programs instead of Java programs. Other languages that connect to Mathematica include Haskell, AppleScript, Racket, Visual Basic, Python, and Clojure. Mathematica supports the generation and execution of Modelica models for systems modeling and connects with Wolfram System Modeler. Links are also available to many third-party software packages and APIs. Mathematica can also capture real-time data from a variety of sources and can read and write to public blockchains (Bitcoin, Ethereum, and ARK). It supports import and export of over 220 data, image, video, sound, computer-aided design (CAD), geographic information systems (GIS), document, and biomedical formats. In 2019, support was added for compiling Wolfram Language code to LLVM. Version 12.3 of the Wolfram Language added support for Arduino. == Computable data == Mathematica is also integrated with Wolfram Alpha, an online answer engine that provides additional data, some of which is kept updated in real time, for users who use Mathematica with an internet connection. Some of the data sets include astronomical, chemical, geopolitical, language, biomedical, airplane, and weather data, in addition to mathematical data (such as knots and polyhedra). == Reception == BYTE in 1989 listed Mathematica as among the "Distinction" winners of the BYTE Awards, stating that it "is another breakthrough Macintosh application ... it could enable you to absorb the algebra and calculus that seemed impossible to comprehend from a textbook". Mathematica has been criticized for being closed source. Wolfram Research claims keeping Mathematica closed source is central to its business model and the continuity of the software.

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  Mathematics of neural networks in machine learning

  An artificial neural network (ANN) or neural network combines biological principles with advanced statistics to solve problems in domains such as pattern recognition and game-play. ANNs adopt the basic model of neuron analogues connected to each other in a variety of ways. == Structure == === Neuron === A neuron with label j {\displaystyle j} receiving an input p j ( t ) {\displaystyle p_{j}(t)} from predecessor neurons consists of the following components: an activation a j ( t ) {\displaystyle a_{j}(t)} , the neuron's state, depending on a discrete time parameter, an optional threshold θ j {\displaystyle \theta _{j}} , which stays fixed unless changed by learning, an activation function f {\displaystyle f} that computes the new activation at a given time t + 1 {\displaystyle t+1} from a j ( t ) {\displaystyle a_{j}(t)} , θ j {\displaystyle \theta _{j}} and the net input p j ( t ) {\displaystyle p_{j}(t)} giving rise to the relation a j ( t + 1 ) = f ( a j ( t ) , p j ( t ) , θ j ) , {\displaystyle a_{j}(t+1)=f(a_{j}(t),p_{j}(t),\theta _{j}),} and an output function f out {\displaystyle f_{\text{out}}} computing the output from the activation o j ( t ) = f out ( a j ( t ) ) . {\displaystyle o_{j}(t)=f_{\text{out}}(a_{j}(t)).} Often the output function is simply the identity function. An input neuron has no predecessor but serves as input interface for the whole network. Similarly an output neuron has no successor and thus serves as output interface of the whole network. === Propagation function === The propagation function computes the input p j ( t ) {\displaystyle p_{j}(t)} to the neuron j {\displaystyle j} from the outputs o i ( t ) {\displaystyle o_{i}(t)} and typically has the form p j ( t ) = ∑ i o i ( t ) w i j . {\displaystyle p_{j}(t)=\sum _{i}o_{i}(t)w_{ij}.} === Bias === A bias term can be added, changing the form to the following: p j ( t ) = ∑ i o i ( t ) w i j + w 0 j , {\displaystyle p_{j}(t)=\sum _{i}o_{i}(t)w_{ij}+w_{0j},} where w 0 j {\displaystyle w_{0j}} is a bias. == Neural networks as functions == Neural network models can be viewed as defining a function that takes an input (observation) and produces an output (decision) f : X → Y {\displaystyle \textstyle f:X\rightarrow Y} or a distribution over X {\displaystyle \textstyle X} or both X {\displaystyle \textstyle X} and Y {\displaystyle \textstyle Y} . Sometimes models are intimately associated with a particular learning rule. A common use of the phrase "ANN model" is really the definition of a class of such functions (where members of the class are obtained by varying parameters, connection weights, or specifics of the architecture such as the number of neurons, number of layers or their connectivity). Mathematically, a neuron's network function f ( x ) {\displaystyle \textstyle f(x)} is defined as a composition of other functions g i ( x ) {\displaystyle \textstyle g_{i}(x)} , that can further be decomposed into other functions. This can be conveniently represented as a network structure, with arrows depicting the dependencies between functions. A widely used type of composition is the nonlinear weighted sum, where f ( x ) = K ( ∑ i w i g i ( x ) ) {\displaystyle \textstyle f(x)=K\left(\sum _{i}w_{i}g_{i}(x)\right)} , where K {\displaystyle \textstyle K} (commonly referred to as the activation function) is some predefined function, such as the hyperbolic tangent, sigmoid function, softmax function, or rectifier function. The important characteristic of the activation function is that it provides a smooth transition as input values change, i.e. a small change in input produces a small change in output. The following refers to a collection of functions g i {\displaystyle \textstyle g_{i}} as a vector g = ( g 1 , g 2 , … , g n ) {\displaystyle \textstyle g=(g_{1},g_{2},\ldots ,g_{n})} . This figure depicts such a decomposition of f {\displaystyle \textstyle f} , with dependencies between variables indicated by arrows. These can be interpreted in two ways. The first view is the functional view: the input x {\displaystyle \textstyle x} is transformed into a 3-dimensional vector h {\displaystyle \textstyle h} , which is then transformed into a 2-dimensional vector g {\displaystyle \textstyle g} , which is finally transformed into f {\displaystyle \textstyle f} . This view is most commonly encountered in the context of optimization. The second view is the probabilistic view: the random variable F = f ( G ) {\displaystyle \textstyle F=f(G)} depends upon the random variable G = g ( H ) {\displaystyle \textstyle G=g(H)} , which depends upon H = h ( X ) {\displaystyle \textstyle H=h(X)} , which depends upon the random variable X {\displaystyle \textstyle X} . This view is most commonly encountered in the context of graphical models. The two views are largely equivalent. In either case, for this particular architecture, the components of individual layers are independent of each other (e.g., the components of g {\displaystyle \textstyle g} are independent of each other given their input h {\displaystyle \textstyle h} ). This naturally enables a degree of parallelism in the implementation. Networks such as the previous one are commonly called feedforward, because their graph is a directed acyclic graph. Networks with cycles are commonly called recurrent. Such networks are commonly depicted in the manner shown at the top of the figure, where f {\displaystyle \textstyle f} is shown as dependent upon itself. However, an implied temporal dependence is not shown. == Backpropagation == Backpropagation training algorithms fall into three categories: steepest descent (with variable learning rate and momentum, resilient backpropagation); quasi-Newton (Broyden–Fletcher–Goldfarb–Shanno, one step secant); Levenberg–Marquardt and conjugate gradient (Fletcher–Reeves update, Polak–Ribiére update, Powell–Beale restart, scaled conjugate gradient). === Algorithm === Let N {\displaystyle N} be a network with e {\displaystyle e} connections, m {\displaystyle m} inputs and n {\displaystyle n} outputs. Below, x 1 , x 2 , … {\displaystyle x_{1},x_{2},\dots } denote vectors in R m {\displaystyle \mathbb {R} ^{m}} , y 1 , y 2 , … {\displaystyle y_{1},y_{2},\dots } vectors in R n {\displaystyle \mathbb {R} ^{n}} , and w 0 , w 1 , w 2 , … {\displaystyle w_{0},w_{1},w_{2},\ldots } vectors in R e {\displaystyle \mathbb {R} ^{e}} . These are called inputs, outputs and weights, respectively. The network corresponds to a function y = f N ( w , x ) {\displaystyle y=f_{N}(w,x)} which, given a weight w {\displaystyle w} , maps an input x {\displaystyle x} to an output y {\displaystyle y} . In supervised learning, a sequence of training examples ( x 1 , y 1 ) , … , ( x p , y p ) {\displaystyle (x_{1},y_{1}),\dots ,(x_{p},y_{p})} produces a sequence of weights w 0 , w 1 , … , w p {\displaystyle w_{0},w_{1},\dots ,w_{p}} starting from some initial weight w 0 {\displaystyle w_{0}} , usually chosen at random. These weights are computed in turn: first compute w i {\displaystyle w_{i}} using only ( x i , y i , w i − 1 ) {\displaystyle (x_{i},y_{i},w_{i-1})} for i = 1 , … , p {\displaystyle i=1,\dots ,p} . The output of the algorithm is then w p {\displaystyle w_{p}} , giving a new function x ↦ f N ( w p , x ) {\displaystyle x\mapsto f_{N}(w_{p},x)} . The computation is the same in each step, hence only the case i = 1 {\displaystyle i=1} is described. w 1 {\displaystyle w_{1}} is calculated from ( x 1 , y 1 , w 0 ) {\displaystyle (x_{1},y_{1},w_{0})} by considering a variable weight w {\displaystyle w} and applying gradient descent to the function w ↦ E ( f N ( w , x 1 ) , y 1 ) {\displaystyle w\mapsto E(f_{N}(w,x_{1}),y_{1})} to find a local minimum, starting at w = w 0 {\displaystyle w=w_{0}} . This makes w 1 {\displaystyle w_{1}} the minimizing weight found by gradient descent. == Learning pseudocode == To implement the algorithm above, explicit formulas are required for the gradient of the function w ↦ E ( f N ( w , x ) , y ) {\displaystyle w\mapsto E(f_{N}(w,x),y)} where the function is E ( y , y ′ ) = | y − y ′ | 2 {\displaystyle E(y,y')=|y-y'|^{2}} . The learning algorithm can be divided into two phases: propagation and weight update. === Propagation === Propagation involves the following steps: Propagation forward through the network to generate the output value(s) Calculation of the cost (error term) Propagation of the output activations back through the network using the training pattern target to generate the deltas (the difference between the targeted and actual output values) of all output and hidden neurons. === Weight update === For each weight: Multiply the weight's output delta and input activation to find the gradient of the weight. Subtract the ratio (percentage) of the weight's gradient from the weight. The learning rate is the ratio (percentage) that influences the speed and quality of learning. The greater the ratio, the faster the neuron trains, but the lower the ratio, the more accurat

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  Wilkinson's Grammar of Graphics

  The Grammar of Graphics (GoG) is a grammar-based system for representing graphics to provide grammatical constraints on the composition of data and information visualizations. A graphical grammar differs from a graphics pipeline as it focuses on semantic components such as scales and guides, statistical functions, coordinate systems, marks and aesthetic attributes. For example, a bar chart can be converted into a pie chart by specifying a polar coordinate system without any other change in graphical specification. The grammar of graphics concept was launched by Leland Wilkinson in 2001 (Wilkinson et al., 2001; Wilkinson, 2005) and graphical grammars have since been written in a variety of languages with various parameterisations and extensions. The major implementations of graphical grammars are nViZn created by a team at SPSS/IBM, followed by Polaris focusing on multidimensional relational databases which is commercialised as Tableau, a revised Layered Grammar of Graphics by Hadley Wickham in Ggplot2, and Vega-Lite which is a visualisation grammar with added interactivity. The grammar of graphics continues to evolve with alternate parameterisations, extensions, or new specifications. == Wilkinson's Grammar of Graphics == === Theory === Wilkinson conceived the seven elements of a graphics to be Variables: mapping of objects to values represented in a graphic Algebra: operations to combine variables and specify dimensions of graphs Geometry: creation of geometric graphs from variables Aesthetics: sensory attributes Statistics: functions to change the appearance and representation of graphs Scales: represent variables on measured dimensions Coordinates: mapping to coordinate systems With these, Wilkinson hypothesised that These seven constructs are orthogonal and virtually all known statistical charts can be generated relatively parsimoniously This computational system is not a taxonomy of charts and rather it describes the meaning of what we do when we construct statistical graphics. === Implementations === Wilkinson wrote SYSTAT, a statistical software package, in the early 1980s. This program was noted for its comprehensive graphics, including the first software implementation of the heatmap display now widely used among biologists. After his company grew to 50 employees, he sold it to SPSS in 1995. At SPSS, he assembled a team of graphics programmers who developed the nViZn platform that produces the visualizations in SPSS, Clementine, and other analytics products. While at Stanford, Tableau founders Hanrahan and Stolte, as well as Diane Tang, created the predecessor to Tableau, named Polaris. Polaris was a data visualization software tool, built with the support of a United States Department of Energy defense program, the Accelerated Strategic Computing Initiative (ASCI). The main differences between Wilkinson's system and Polaris are the use of SQL relational algebra for database services and using shelves instead of cross and nest operators. == Wickham's Layered Grammar of Graphics == === Theory === Hadley Wickham conceived an alternate parameterisation of the syntax Wilkinson had derived, creating a layered grammar of graphics which he implemented as ggplot2 for R (programming language) users. This added a hierarchy of defaults based around the idea of building up a graphic from multiple layers. Wickham conceived these elements to be: Defaults: consists of data and mapping Data: dataset Mapping: aesthetic mappings Layer: consists of data, mapping, geom, stat, and position Data: dataset, or inherit from defaults Mapping: aesthetic mappings, or inherit from defaults Geom: geometric object Stat: statistical transformation Position: position adjustment Scale: mapping of data to aesthetic attributes Coord: mapping of data to the plane of the plot Facet: split up the data === Reception === Wilkinson is generally positive on Wickham's parameterisation and implementation of ggplot2, praising its elegance and expressivity whilst claiming that his original Grammar of Graphics is capable of representing a wider range of statistical graphics. === Implementations === ggplot2 is the first implementation of a layered grammar of graphics in R and implementations in other programming languages have ensued. These include direct ports plotnine for Python, gramm for MATLAB, Lets-Plot for Kotlin and gadfly for Julia. Projects inspired by elements of Wickham's grammar include Vega-Lite which specifies plots in JSON and uses a JavaScript engine. Implementations for Python include Vega-Altair (built on top of Vega-Lite). == Vega-Lite: A Grammar of Interactive Graphics == === Theory === Vega-Lite combines ideas from Wilkinson's Grammar of Graphics and Wickham's Layered Grammar of Graphics with a composition algebra for layered and multi-view displays with a grammar of interaction. The Vega-Lite specification is instantiated in JSON and rendered by the lower-level Vega. The graphical grammar implemented by Vega-Lite is composed of the following: Unit: consists of data, transforms, mark-type and encoding Data: relational table consisting of records (rows) and named attributes (columns) Transforms: data transformations Mark-type: geometric object for visual encoding Encodings: mapping of data attributes to visual marks properties where each encoding consists of: Channel: e.g. colour, shape, size, or text Field: data attribute Data-type: e.g. nominal, ordinal, quantitative, or temporal Value: use a literal instead of a data-type Functions: e.g. binning, aggregation, and sorting Scale: maps from data domain to visual range Guide: axis or legend for visualising scale Composite Views: compose views from multiple unit specifications with operators: Layer: charts plotted on top of each other Hconcat/Vconcat: place views side-by-side Facet: subset data to produce a trellis plot Repeat: multiple plots similar to facet but with full data replication in each cell Interaction: selections identify the set of points a user is interested in manipulating, with components: Selection: get the minimal number of backing points Name: reference Type: how many backing values are stored Predicate: determine the set of selected points e.g. single, list, interval Domain|Range: store data domain or visual range Event: e.g. mouseover, mousedown, mouseup, Init: initialise with specific backing points Transforms: e.g. project, toggle, translate, zoom, and nearest Resolve: resolve selections to union or intersect ==== Implementations ==== Whilst Vega-Lite is the sole implementation of this graphics grammar specification with compilation to Vega, other implementations do create JSON files which can be interpreted by Vega-Lite. == Related projects == Ggplot2 is an R package for plotting Tableau Software (originally known as Polaris) is a commercial software built using the Grammar of Graphics nViZn built by Wilkinson. SYSTAT (statistics package) built by Wilkinson ggpy, ggplot for Python, but has not been updated since 20 November 2016 plotnine started as an effort to improve the scalability of ggplot for Python and is largely compatible with ggplot2 syntax. Plotly - Interactive, online ggplot2 graphs gramm, a plotting class for MATLAB inspired by ggplot2 gadfly, a system for plotting and visualization written in Julia, based largely on ggplot2 Chart::GGPlot - ggplot2 port in Perl, but has not been updated since 16 March 2023 The Lets-Plot for Python library includes a native backend and a Python API, which was mostly based on the ggplot2 package. Lets-Plot Kotlin API is an open-source plotting library for statistical data implemented using the Kotlin programming language, and is built on the principles of layered graphics first described in the Leland Wilkinson's work The Grammar of Graphics. ggplotnim, plotting library using the Nim programming language inspired by ggplot2. Vega and Vega-Lite are plotting libraries that use JSON to specify plots. Vega-Altair, a Python library built on top of Vega-Lite chart-parts - React-friendly Grammar of Graphics, but has not been updated since 10 Dec 2021 g2 - a JavaScript library

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  Bayesian hierarchical modeling

  Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the posterior distribution of model parameters using the Bayesian method. The sub-models combine to form the hierarchical model, and Bayes' theorem is used to integrate them with the observed data and account for all the uncertainty that is present. This integration enables calculation of updated posterior over the (hyper)parameters, effectively updating prior beliefs in light of the observed data. Frequentist statistics may yield conclusions seemingly incompatible with those offered by Bayesian statistics due to the Bayesian treatment of the parameters as random variables and its use of subjective information in establishing assumptions on these parameters. As the approaches answer different questions the formal results are not technically contradictory but the two approaches disagree over which answer is relevant to particular applications. Bayesians argue that relevant information regarding decision-making and updating beliefs cannot be ignored and that hierarchical modeling has the potential to overrule classical methods in applications where respondents give multiple observational data. Moreover, the model has proven to be robust, with the posterior distribution less sensitive to the more flexible hierarchical priors. Hierarchical modeling, as its name implies, retains nested data structure, and is used when information is available at several different levels of observational units. For example, in epidemiological modeling to describe infection trajectories for multiple countries, observational units are countries, and each country has its own time-based profile of daily infected cases. In decline curve analysis to describe oil or gas production decline curve for multiple wells, observational units are oil or gas wells in a reservoir region, and each well has each own time-based profile of oil or gas production rates (usually, barrels per month). Hierarchical modeling is used to devise computation based strategies for multiparameter problems. == Philosophy == Statistical methods and models commonly involve multiple parameters that can be regarded as related or connected in such a way that the problem implies a dependence of the joint probability model for these parameters. Individual degrees of belief, expressed in the form of probabilities, come with uncertainty. Amidst this is the change of the degrees of belief over time. As was stated by Professor José M. Bernardo and Professor Adrian F. Smith, "The actuality of the learning process consists in the evolution of individual and subjective beliefs about the reality." These subjective probabilities are more directly involved in the mind rather than the physical probabilities. Hence, it is with this need of updating beliefs that Bayesians have formulated an alternative statistical model which takes into account the prior occurrence of a particular event. == Bayes' theorem == The assumed occurrence of a real-world event will typically modify preferences between certain options. This is done by modifying the degrees of belief attached, by an individual, to the events defining the options. Suppose in a study of the effectiveness of cardiac treatments, with the patients in hospital j having survival probability θ j {\displaystyle \theta _{j}} , the survival probability will be updated with the occurrence of y, the event in which a controversial serum is created which, as believed by some, increases survival in cardiac patients. In order to make updated probability statements about θ j {\displaystyle \theta _{j}} , given the occurrence of event y, we must begin with a model providing a joint probability distribution for θ j {\displaystyle \theta _{j}} and y. This can be written as a product of the two distributions that are often referred to as the prior distribution P ( θ ) {\displaystyle P(\theta )} and the sampling distribution P ( y ∣ θ ) {\displaystyle P(y\mid \theta )} respectively: P ( θ , y ) = P ( θ ) P ( y ∣ θ ) {\displaystyle P(\theta ,y)=P(\theta )P(y\mid \theta )} Using the basic property of conditional probability, the posterior distribution will yield: P ( θ ∣ y ) = P ( θ , y ) P ( y ) = P ( y ∣ θ ) P ( θ ) P ( y ) {\displaystyle P(\theta \mid y)={\frac {P(\theta ,y)}{P(y)}}={\frac {P(y\mid \theta )P(\theta )}{P(y)}}} This equation, showing the relationship between the conditional probability and the individual events, is known as Bayes' theorem. This simple expression encapsulates the technical core of Bayesian inference which aims to deconstruct the probability, P ( θ ∣ y ) {\displaystyle P(\theta \mid y)} , relative to solvable subsets of its supportive evidence. == Exchangeability == The usual starting point of a statistical analysis is the assumption that the n values y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} are exchangeable. If no information – other than data y – is available to distinguish any of the θ j {\displaystyle \theta _{j}} 's from any others, and no ordering or grouping of the parameters can be made, one must assume symmetry of prior distribution parameters. This symmetry is represented probabilistically by exchangeability. Generally, it is useful and appropriate to model data from an exchangeable distribution as independently and identically distributed, given some unknown parameter vector θ {\displaystyle \theta } , with distribution P ( θ ) {\displaystyle P(\theta )} . === Finite exchangeability === For a fixed number n, the set y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} is exchangeable if the joint probability P ( y 1 , y 2 , … , y n ) {\displaystyle P(y_{1},y_{2},\ldots ,y_{n})} is invariant under permutations of the indices. That is, for every permutation π {\displaystyle \pi } or ( π 1 , π 2 , … , π n ) {\displaystyle (\pi _{1},\pi _{2},\ldots ,\pi _{n})} of (1, 2, …, n), P ( y 1 , y 2 , … , y n ) = P ( y π 1 , y π 2 , … , y π n ) . {\displaystyle P(y_{1},y_{2},\ldots ,y_{n})=P(y_{\pi _{1}},y_{\pi _{2}},\ldots ,y_{\pi _{n}}).} The following is an exchangeable, but not independent and identical (iid), example: Consider an urn with a red ball and a blue ball inside, with probability 1 2 {\displaystyle {\frac {1}{2}}} of drawing either. Balls are drawn without replacement, i.e. after one ball is drawn from the n {\displaystyle n} balls, there will be n − 1 {\displaystyle n-1} remaining balls left for the next draw. Let Y i = { 1 , if the i th ball is red , 0 , otherwise . {\displaystyle {\text{Let }}Y_{i}={\begin{cases}1,&{\text{if the }}i{\text{th ball is red}},\\0,&{\text{otherwise}}.\end{cases}}} The probability of selecting a red ball in the first draw and a blue ball in the second draw is equal to the probability of selecting a blue ball on the first draw and a red on the second, both of which are 1/2: P ( y 1 = 1 , y 2 = 0 ) = P ( y 1 = 0 , y 2 = 1 ) = 1 2 {\displaystyle P(y_{1}=1,y_{2}=0)=P(y_{1}=0,y_{2}=1)={\frac {1}{2}}} . This makes y 1 {\displaystyle y_{1}} and y 2 {\displaystyle y_{2}} exchangeable. But the probability of selecting a red ball on the second draw given that the red ball has already been selected in the first is 0. This is not equal to the probability that the red ball is selected in the second draw, which is 1/2: P ( y 2 = 1 ∣ y 1 = 1 ) = 0 ≠ P ( y 2 = 1 ) = 1 2 {\displaystyle P(y_{2}=1\mid y_{1}=1)=0\neq P(y_{2}=1)={\frac {1}{2}}} . Thus, y 1 {\displaystyle y_{1}} and y 2 {\displaystyle y_{2}} are not independent. If x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} are independent and identically distributed, then they are exchangeable, but the converse is not necessarily true. === Infinite exchangeability === Infinite exchangeability is the property that every finite subset of an infinite sequence y 1 {\displaystyle y_{1}} , y 2 , … {\displaystyle y_{2},\ldots } is exchangeable. For any n, the sequence y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} is exchangeable. == Hierarchical models == === Components === Bayesian hierarchical modeling makes use of two important concepts in deriving the posterior distribution, namely: Hyperparameters: parameters of the prior distribution Hyperpriors: distributions of Hyperparameters Suppose a random variable Y follows a normal distribution with parameter θ {\displaystyle \theta } as the mean and 1 as the variance, that is Y ∣ θ ∼ N ( θ , 1 ) {\displaystyle Y\mid \theta \sim N(\theta ,1)} . The tilde relation ∼ {\displaystyle \sim } can be read as "has the distribution of" or "is distributed as". Suppose also that the parameter θ {\displaystyle \theta } has a distribution given by a normal distribution with mean μ {\displaystyle \mu } and variance 1, i.e. θ ∣ μ ∼ N ( μ , 1 ) {\displaystyle \theta \mid \mu \sim N(\mu ,1)} . Furthermore, μ {\displaystyle \mu } follows another distribution given, for example, by the standard normal distribution, N ( 0 , 1 ) {\displaystyle {\text{N}}(0,1)} . The parameter μ {\dis

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  Random projection

  In mathematics and statistics, random projection is a technique used to reduce the dimensionality of a set of points which lie in Euclidean space. According to theoretical results, random projection preserves distances well, but empirical results are sparse. They have been applied to many natural language tasks under the name random indexing. == Dimensionality reduction == Dimensionality reduction, as the name suggests, is reducing the number of random variables using various mathematical methods from statistics and machine learning. Dimensionality reduction is often used to reduce the problem of managing and manipulating large data sets. Dimensionality reduction techniques generally use linear transformations in determining the intrinsic dimensionality of the manifold as well as extracting its principal directions. For this purpose there are various related techniques, including: principal component analysis, linear discriminant analysis, canonical correlation analysis, discrete cosine transform, random projection, etc. Random projection is a simple and computationally efficient way to reduce the dimensionality of data by trading a controlled amount of error for faster processing times and smaller model sizes. The dimensions and distribution of random projection matrices are controlled so as to approximately preserve the pairwise distances between any two samples of the dataset. == Method == The core idea behind random projection is given in the Johnson-Lindenstrauss lemma, which states that if points in a vector space are of sufficiently high dimension, then they may be projected into a suitable lower-dimensional space in a way which approximately preserves pairwise distances between the points with high probability. In random projection, the original d {\displaystyle d} -dimensional data is projected to a k {\displaystyle k} -dimensional subspace, by multiplying on the left by a random matrix R ∈ R k × d {\displaystyle R\in \mathbb {R} ^{k\times d}} . Using matrix notation: If X d × N {\displaystyle X_{d\times N}} is the original set of N d-dimensional observations, then X k × N R P = R k × d X d × N {\displaystyle X_{k\times N}^{RP}=R_{k\times d}X_{d\times N}} is the projection of the data onto a lower k-dimensional subspace. Random projection is computationally simple: form the random matrix "R" and project the d × N {\displaystyle d\times N} data matrix X onto K dimensions of order O ( d k N ) {\displaystyle O(dkN)} . If the data matrix X is sparse with about c nonzero entries per column, then the complexity of this operation is of order O ( c k N ) {\displaystyle O(ckN)} . === Orthogonal random projection === A unit vector can be orthogonally projected to a random subspace. Let u {\displaystyle u} be the original unit vector, and let v {\displaystyle v} be its projection. The norm-squared ‖ v ‖ 2 2 {\displaystyle \|v\|_{2}^{2}} has the same distribution as projecting a random point, uniformly sampled on the unit sphere, to its first k {\displaystyle k} coordinates. This is equivalent to sampling a random point in the multivariate gaussian distribution x ∼ N ( 0 , I d × d ) {\displaystyle x\sim {\mathcal {N}}(0,I_{d\times d})} , then normalizing it. Therefore, ‖ v ‖ 2 2 {\displaystyle \|v\|_{2}^{2}} has the same distribution as ∑ i = 1 k x i 2 ∑ i = 1 k x i 2 + ∑ i = k + 1 d x i 2 {\displaystyle {\frac {\sum _{i=1}^{k}x_{i}^{2}}{\sum _{i=1}^{k}x_{i}^{2}+\sum _{i=k+1}^{d}x_{i}^{2}}}} , which by the chi-squared construction of the Beta distribution, has distribution Beta ⁡ ( k / 2 , ( d − k ) / 2 ) {\displaystyle \operatorname {Beta} (k/2,(d-k)/2)} , with mean k / d {\displaystyle k/d} . We have a concentration inequality P r [ | ‖ v ‖ 2 − k d | ≥ ϵ k d ] ≤ 3 exp ⁡ ( − k ϵ 2 / 64 ) {\displaystyle Pr\left[\left|\|v\|_{2}-{\frac {k}{d}}\right|\geq \epsilon {\sqrt {\frac {k}{d}}}\right]\leq 3\exp \left(-k\epsilon ^{2}/64\right)} for any ϵ ∈ ( 0 , 1 ) {\displaystyle \epsilon \in (0,1)} . === Gaussian random projection === The random matrix R can be generated using a Gaussian distribution. The first row is a random unit vector uniformly chosen from S d − 1 {\displaystyle S^{d-1}} . The second row is a random unit vector from the space orthogonal to the first row, the third row is a random unit vector from the space orthogonal to the first two rows, and so on. In this way of choosing R, and the following properties are satisfied: Spherical symmetry: For any orthogonal matrix A ∈ O ( d ) {\displaystyle A\in O(d)} , RA and R have the same distribution. Orthogonality: The rows of R are orthogonal to each other. Normality: The rows of R are unit-length vectors. === More computationally efficient random projections === Achlioptas has shown that the random matrix can be sampled more efficiently. Either the full matrix can be sampled IID according to R i , j = 3 / k × { + 1 with probability 1 6 0 with probability 2 3 − 1 with probability 1 6 {\displaystyle R_{i,j}={\sqrt {3/k}}\times {\begin{cases}+1&{\text{with probability }}{\frac {1}{6}}\\0&{\text{with probability }}{\frac {2}{3}}\\-1&{\text{with probability }}{\frac {1}{6}}\end{cases}}} or the full matrix can be sampled IID according to R i , j = 1 / k × { + 1 with probability 1 2 − 1 with probability 1 2 {\displaystyle R_{i,j}={\sqrt {1/k}}\times {\begin{cases}+1&{\text{with probability }}{\frac {1}{2}}\\-1&{\text{with probability }}{\frac {1}{2}}\end{cases}}} Both are efficient for database applications because the computations can be performed using integer arithmetic. More related study is conducted in. It was later shown how to use integer arithmetic while making the distribution even sparser, having very few nonzeroes per column, in work on the Sparse JL Transform. This is advantageous since a sparse embedding matrix means being able to project the data to lower dimension even faster. === Random Projection with Quantization === Random projection can be further condensed by quantization (discretization), with 1-bit (sign random projection) or multi-bits. It is the building block of SimHash, RP tree, and other memory efficient estimation and learning methods. == Large quasiorthogonal bases == The Johnson-Lindenstrauss lemma states that large sets of vectors in a high-dimensional space can be linearly mapped in a space of much lower (but still high) dimension n with approximate preservation of distances. One of the explanations of this effect is the exponentially high quasiorthogonal dimension of n-dimensional Euclidean space. There are exponentially large (in dimension n) sets of almost orthogonal vectors (with small value of inner products) in n–dimensional Euclidean space. This observation is useful in indexing of high-dimensional data. Quasiorthogonality of large random sets is important for methods of random approximation in machine learning. In high dimensions, exponentially large numbers of randomly and independently chosen vectors from equidistribution on a sphere (and from many other distributions) are almost orthogonal with probability close to one. This implies that in order to represent an element of such a high-dimensional space by linear combinations of randomly and independently chosen vectors, it may often be necessary to generate samples of exponentially large length if we use bounded coefficients in linear combinations. On the other hand, if coefficients with arbitrarily large values are allowed, the number of randomly generated elements that are sufficient for approximation is even less than dimension of the data space. == Implementations == RandPro - An R package for random projection sklearn.random_projection - A module for random projection from the scikit-learn Python library Weka implementation [1]

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  Automated Pain Recognition

  Automated Pain Recognition (APR) is a method for objectively measuring pain and at the same time represents an interdisciplinary research area that comprises elements of medicine, psychology, psychobiology, and computer science. The focus is on computer-aided objective recognition of pain, implemented on the basis of machine learning. Automated pain recognition allows for the valid, reliable detection and monitoring of pain in people who are unable to communicate verbally. The underlying machine learning processes are trained and validated in advance by means of unimodal or multimodal body signals. Signals used to detect pain may include facial expressions or gestures and may also be of a (psycho-)physiological or paralinguistic nature. To date, the focus has been on identifying pain intensity, but visionary efforts are also being made to recognize the quality, site, and temporal course of pain. However, the clinical implementation of this approach is a controversial topic in the field of pain research. Critics of automated pain recognition argue that pain diagnosis can only be performed subjectively by humans. == Background == Pain diagnosis under conditions where verbal reporting is restricted - such as in verbally and/or cognitively impaired people or in patients who are sedated or mechanically ventilated - is based on behavioral observations by trained professionals. However, all known observation procedures (e.g., Zurich Observation Pain Assessment (ZOPA)); Pain Assessment in Advanced Dementia Scale (PAINAD) require a great deal of specialist expertise. These procedures can be made more difficult by perception- and interpretation-related misjudgments on the part of the observer. With regard to the differences in design, methodology, evaluation sample, and conceptualization of the phenomenon of pain, it is difficult to compare the quality criteria of the various tools. Even if trained personnel could theoretically record pain intensity several times a day using observation instruments, it would not be possible to measure it every minute or second. In this respect, the goal of automated pain recognition is to use valid, robust pain response patterns that can be recorded multimodally for a temporally dynamic, high-resolution, automated pain intensity recognition system. == Procedure == For automated pain recognition, pain-relevant parameters are usually recorded using non-invasive sensor technology, which captures data on the (physical) responses of the person in pain. This can be achieved with camera technology that captures facial expressions, gestures, or posture, while audio sensors record paralinguistic features. (Psycho-)physiological information such as muscle tone and heart rate can be collected via biopotential sensors (electrodes). Pain recognition requires the extraction of meaningful characteristics or patterns from the data collected. This is achieved using machine learning techniques that are able to provide an assessment of the pain after training (learning), e.g., "no pain," "mild pain," or "severe pain." == Parameters == Although the phenomenon of pain comprises different components (sensory discriminative, affective (emotional), cognitive, vegetative, and (psycho-)motor), automated pain recognition currently relies on the measurable parameters of pain responses. These can be divided roughly into the two main categories of "physiological responses" and "behavioral responses". === Physiological responses === In humans, pain almost always initiates autonomic nervous processes that are reflected measurably in various physiological signals. ==== Physiological signals ==== Measurements can include electrodermal activity (EDA, also skin conductance), electromyography (EMG), electrocardiogram (ECG), blood volume pulse (BVP), electroencephalogram (EEG), respiration, and body temperature, which are regulatory mechanisms of the sympathetic and parasympathetic systems. Physiological signals are mainly recorded using special non-invasive surface electrodes (for EDA, EMG, ECG, and EEG), a blood volume pulse sensor (BVP), a respiratory belt (respiration), and a thermal sensor (body temperature). Endocrinological and immunological parameters can also be recorded, but this requires measures that are somewhat invasive (e.g., blood sampling). === Behavioral responses === Behavioral responses to pain fulfil two functions: protection of the body (e.g., through protective reflexes) and external communication of the pain (e.g., as a cry for help). The responses are particularly evident in facial expressions, gestures, and paralinguistic features. ==== Facial expressions ==== Behavioral signals captured comprise facial expression patterns (expressive behavior), which are measured with the aid of video signals. Facial expression recognition is based on the everyday clinical observation that pain often manifests itself in the patient's facial expressions but that this is not necessarily always the case, since facial expressions can be inhibited through self-control. Despite the possibility that facial expressions may be influenced consciously, facial expression behavior represents an essential source of information for pain diagnosis and is thus also a source of information for automatic pain recognition. One advantage of video-based facial expression recognition is the contact-free measurement of the face, provided that it can be captured on video, which is not possible in every position (e.g., lying face down) or may be limited by bandages covering the face. Facial expression analysis relies on rapid, spontaneous, and temporary changes in neuromuscular activity that lead to visually detectable changes in the face. ==== Gestures ==== Gestures are also captured predominantly using non-contact camera technology. Motor pain responses vary and are strongly dependent on the type and cause of the pain. They range from abrupt protective reflexes (e.g., spontaneous retraction of extremities or doubling up) to agitation (pathological restlessness) and avoidance behavior (hesitant, cautious movements). ==== Paralinguistic features of language ==== Among other things, pain leads to nonverbal linguistic behavior that manifests itself in sounds such as sighing, gasping, moaning, whining, etc. Paralinguistic features are usually recorded using highly sensitive microphones. == Algorithms == After the recording, pre-processing (e.g., filtering), and extraction of relevant features, an optional information fusion can be performed. During this process, modalities from different signal sources are merged to generate new or more precise knowledge. The pain is classified using machine learning processes. The method chosen has a significant influence on the recognition rate and depends greatly on the quality and granularity of the underlying data. Similar to the field of affective computing, the following classifiers are currently being used: Support Vector Machine (SVM): The goal of an SVM is to find a clearly defined optimal hyperplane with the greatest minimal distance to two (or more) classes to be separated. The hyperplane acts as a decision function for classifying an unknown pattern. Random Forest (RF): RF is based on the composition of random, uncorrelated decision trees. An unknown pattern is judged individually by each tree and assigned to a class. The final classification of the patterns by the RF is then based on a majority decision. k-Nearest Neighbors (k-NN): The k-NN algorithm classifies an unknown object using the class label that most commonly classifies the k neighbors closest to it. Its neighbors are determined using a selected similarity measure (e.g., Euclidean distance, Jaccard coefficient, etc.). Artificial neural networks (ANNs): ANNs are inspired by biological neural networks and model their organizational principles and processes in a very simplified manner. Class patterns are learned by adjusting the weights of the individual neuronal connections. == Databases == In order to classify pain in a valid manner, it is necessary to create representative, reliable, and valid pain databases that are available to the machine learner for training. An ideal database would be sufficiently large and would consist of natural (not experimental), high-quality pain responses. However, natural responses are difficult to record and can only be obtained to a limited extent; in most cases they are characterized by suboptimal quality. The databases currently available therefore contain experimental or quasi-experimental pain responses, and each database is based on a different pain model. The following list shows a selection of the most relevant pain databases (last updated: April 2020): UNBC-McMaster Shoulder Pain BioVid Heat Pain EmoPain SenseEmotion X-ITE Pain

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  Spanner (database)

  Spanner is a distributed SQL database management and storage service developed by Google. It provides features such as global transactions, strongly consistent reads, and automatic multi-site replication and failover. Spanner is used in Google F1, the database for its advertising business Google Ads, as well as Gmail and Google Photos. == Features == Spanner stores large amounts of mutable structured data. Spanner allows users to perform arbitrary queries using SQL with relational data while maintaining strong consistency and high availability for that data with synchronous replication. Key features of Spanner: Transactions can be applied across rows, columns, tables, and databases within a Spanner universe. Clients can control the replication and placement of data using automatic multi-site replication and failover. Replication is synchronous and strongly consistent. Reads are strongly consistent and data is versioned to allow for stale reads: clients can read previous versions of data, subject to garbage collection windows. Supports a native SQL interface for reading and writing data. Support for Graph Query Language == History == Spanner was first described in 2012 for internal Google data centers. Spanner's SQL capability was added in 2017 and documented in a SIGMOD 2017 paper. It became available as part of Google Cloud Platform in 2017, under the name "Cloud Spanner". == Architecture == Spanner uses the Paxos algorithm as part of its operation to shard (partition) data across up to hundreds of servers. It makes heavy use of hardware-assisted clock synchronization using GPS clocks and atomic clocks to ensure global consistency. TrueTime is the brand name for Google's distributed cloud infrastructure, which provides Spanner with the ability to generate monotonically increasing timestamps in data centers around the world. Google's F1 SQL database management system (DBMS) is built on top of Spanner, replacing Google's custom MySQL variant.

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  Radial basis function kernel

  In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular, it is commonly used in support vector machine classification. The RBF kernel on two samples x , x ′ ∈ R k {\displaystyle \mathbf {x} ,\mathbf {x'} \in \mathbb {R} ^{k}} , represented as feature vectors in some input space, is defined as K ( x , x ′ ) = exp ⁡ ( − ‖ x − x ′ ‖ 2 2 σ 2 ) {\displaystyle K(\mathbf {x} ,\mathbf {x'} )=\exp \left(-{\frac {\|\mathbf {x} -\mathbf {x'} \|^{2}}{2\sigma ^{2}}}\right)} ‖ x − x ′ ‖ 2 {\displaystyle \textstyle \|\mathbf {x} -\mathbf {x'} \|^{2}} may be recognized as the squared Euclidean distance between the two feature vectors. σ {\displaystyle \sigma } is a free parameter. An equivalent definition involves a parameter γ = 1 2 σ 2 {\displaystyle \textstyle \gamma ={\tfrac {1}{2\sigma ^{2}}}} : K ( x , x ′ ) = exp ⁡ ( − γ ‖ x − x ′ ‖ 2 ) {\displaystyle K(\mathbf {x} ,\mathbf {x'} )=\exp(-\gamma \|\mathbf {x} -\mathbf {x'} \|^{2})} Since the value of the RBF kernel decreases with distance and ranges between zero (in the infinite-distance limit) and one (when x = x'), it has a ready interpretation as a similarity measure. The feature space of the kernel has an infinite number of dimensions; for σ = 1 {\displaystyle \sigma =1} , its expansion using the multinomial theorem is: exp ⁡ ( − 1 2 ‖ x − x ′ ‖ 2 ) = exp ⁡ ( 2 2 x ⊤ x ′ − 1 2 ‖ x ‖ 2 − 1 2 ‖ x ′ ‖ 2 ) = exp ⁡ ( x ⊤ x ′ ) exp ⁡ ( − 1 2 ‖ x ‖ 2 ) exp ⁡ ( − 1 2 ‖ x ′ ‖ 2 ) = ∑ j = 0 ∞ ( x ⊤ x ′ ) j j ! exp ⁡ ( − 1 2 ‖ x ‖ 2 ) exp ⁡ ( − 1 2 ‖ x ′ ‖ 2 ) = ∑ j = 0 ∞ ∑ n 1 + n 2 + ⋯ + n k = j exp ⁡ ( − 1 2 ‖ x ‖ 2 ) x 1 n 1 ⋯ x k n k n 1 ! ⋯ n k ! exp ⁡ ( − 1 2 ‖ x ′ ‖ 2 ) x ′ 1 n 1 ⋯ x ′ k n k n 1 ! ⋯ n k ! = ⟨ φ ( x ) , φ ( x ′ ) ⟩ {\displaystyle {\begin{alignedat}{2}\exp \left(-{\frac {1}{2}}\|\mathbf {x} -\mathbf {x'} \|^{2}\right)&=\exp \left({\frac {2}{2}}\mathbf {x} ^{\top }\mathbf {x'} -{\frac {1}{2}}\|\mathbf {x} \|^{2}-{\frac {1}{2}}\|\mathbf {x'} \|^{2}\right)\\[5pt]&=\exp \left(\mathbf {x} ^{\top }\mathbf {x'} \right)\exp \left(-{\frac {1}{2}}\|\mathbf {x} \|^{2}\right)\exp \left(-{\frac {1}{2}}\|\mathbf {x'} \|^{2}\right)\\[5pt]&=\sum _{j=0}^{\infty }{\frac {(\mathbf {x} ^{\top }\mathbf {x'} )^{j}}{j!}}\exp \left(-{\frac {1}{2}}\|\mathbf {x} \|^{2}\right)\exp \left(-{\frac {1}{2}}\|\mathbf {x'} \|^{2}\right)\\[5pt]&=\sum _{j=0}^{\infty }\quad \sum _{n_{1}+n_{2}+\dots +n_{k}=j}\exp \left(-{\frac {1}{2}}\|\mathbf {x} \|^{2}\right){\frac {x_{1}^{n_{1}}\cdots x_{k}^{n_{k}}}{\sqrt {n_{1}!\cdots n_{k}!}}}\exp \left(-{\frac {1}{2}}\|\mathbf {x'} \|^{2}\right){\frac {{x'}_{1}^{n_{1}}\cdots {x'}_{k}^{n_{k}}}{\sqrt {n_{1}!\cdots n_{k}!}}}\\[5pt]&=\langle \varphi (\mathbf {x} ),\varphi (\mathbf {x'} )\rangle \end{alignedat}}} φ ( x ) = exp ⁡ ( − 1 2 ‖ x ‖ 2 ) ( a ℓ 0 ( 0 ) , a 1 ( 1 ) , … , a ℓ 1 ( 1 ) , … , a 1 ( j ) , … , a ℓ j ( j ) , … ) {\displaystyle \varphi (\mathbf {x} )=\exp \left(-{\frac {1}{2}}\|\mathbf {x} \|^{2}\right)\left(a_{\ell _{0}}^{(0)},a_{1}^{(1)},\dots ,a_{\ell _{1}}^{(1)},\dots ,a_{1}^{(j)},\dots ,a_{\ell _{j}}^{(j)},\dots \right)} where ℓ j = ( k + j − 1 j ) {\displaystyle \ell _{j}={\tbinom {k+j-1}{j}}} , a ℓ ( j ) = x 1 n 1 ⋯ x k n k n 1 ! ⋯ n k ! | n 1 + n 2 + ⋯ + n k = j ∧ 1 ≤ ℓ ≤ ℓ j {\displaystyle a_{\ell }^{(j)}={\frac {x_{1}^{n_{1}}\cdots x_{k}^{n_{k}}}{\sqrt {n_{1}!\cdots n_{k}!}}}\quad |\quad n_{1}+n_{2}+\dots +n_{k}=j\wedge 1\leq \ell \leq \ell _{j}} == Approximations == Because support vector machines and other models employing the kernel trick do not scale well to large numbers of training samples or large numbers of features in the input space, several approximations to the RBF kernel (and similar kernels) have been introduced. Typically, these take the form of a function z that maps a single vector to a vector of higher dimensionality, approximating the kernel: ⟨ z ( x ) , z ( x ′ ) ⟩ ≈ ⟨ φ ( x ) , φ ( x ′ ) ⟩ = K ( x , x ′ ) {\displaystyle \langle z(\mathbf {x} ),z(\mathbf {x'} )\rangle \approx \langle \varphi (\mathbf {x} ),\varphi (\mathbf {x'} )\rangle =K(\mathbf {x} ,\mathbf {x'} )} where φ {\displaystyle \textstyle \varphi } is the implicit mapping embedded in the RBF kernel. === Fourier random features === One way to construct such a z is to randomly sample from the Fourier transformation of the kernel φ ( x ) = 1 D [ cos ⁡ ⟨ w 1 , x ⟩ , sin ⁡ ⟨ w 1 , x ⟩ , … , cos ⁡ ⟨ w D , x ⟩ , sin ⁡ ⟨ w D , x ⟩ ] T {\displaystyle \varphi (x)={\frac {1}{\sqrt {D}}}[\cos \langle w_{1},x\rangle ,\sin \langle w_{1},x\rangle ,\ldots ,\cos \langle w_{D},x\rangle ,\sin \langle w_{D},x\rangle ]^{T}} where w 1 , . . . , w D {\displaystyle w_{1},...,w_{D}} are independent samples from the normal distribution N ( 0 , σ − 2 I ) {\displaystyle N(0,\sigma ^{-2}I)} . Theorem: E ⁡ [ ⟨ φ ( x ) , φ ( y ) ⟩ ] = e ‖ x − y ‖ 2 / ( 2 σ 2 ) . {\displaystyle \operatorname {E} [\langle \varphi (x),\varphi (y)\rangle ]=e^{\|x-y\|^{2}/(2\sigma ^{2})}.} Proof: It suffices to prove the case of D = 1 {\displaystyle D=1} . Use the trigonometric identity cos ⁡ ( a − b ) = cos ⁡ ( a ) cos ⁡ ( b ) + sin ⁡ ( a ) sin ⁡ ( b ) {\displaystyle \cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)} , the spherical symmetry of Gaussian distribution, then evaluate the integral ∫ − ∞ ∞ cos ⁡ ( k x ) e − x 2 / 2 2 π d x = e − k 2 / 2 . {\displaystyle \int _{-\infty }^{\infty }{\frac {\cos(kx)e^{-x^{2}/2}}{\sqrt {2\pi }}}dx=e^{-k^{2}/2}.} Theorem: Var ⁡ [ ⟨ φ ( x ) , φ ( y ) ⟩ ] = O ( D − 1 ) {\displaystyle \operatorname {Var} [\langle \varphi (x),\varphi (y)\rangle ]=O(D^{-1})} . (Appendix A.2). === Nyström method === Another approach uses the Nyström method to approximate the eigendecomposition of the Gram matrix K, using only a random sample of the training set.

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  Joseph Nechvatal

  Joseph Nechvatal (born January 15, 1951) is an American post-conceptual digital artist and art theoretician who creates computer-assisted paintings and computer animations, often using custom computer viruses. == Life and work == Joseph Nechvatal was born in Chicago. He studied fine art and philosophy at Southern Illinois University Carbondale, Cornell University, and Columbia University. He earned a Doctor of Philosophy in Philosophy of Art and Technology at the Planetary Collegium at University of Wales, Newport and has taught art theory and art history at the School of Visual Arts. He has had many solo exhibitions and is one of five artists that art historian Patrick Frank examines in his 2024 book Art of the 1980s: As If the Digital Mattered. His work in the late 1970s and early 1980s chiefly consisted of postminimal gray palimpsest-like drawings that were often photo-mechanically enlarged. Beginning in 1979 he became associated with the artist group Colab, organized the Public Arts International/Free Speech series, and helped established the non-profit group ABC No Rio. In 1983 he co-founded the avant-garde electronic art music audio project Tellus Audio Cassette Magazine. In 1984, Nechvatal began work on an opera called XS: The Opera Opus (1984-6) with the no wave musical composer Rhys Chatham. He began using computers and robotics to make post-conceptual paintings in 1986 and later, in his signature work, began to employ self-created computer viruses. From 1991 to 1993, he was artist-in-residence at the Louis Pasteur Atelier in Arbois, France and at the Saline Royale/Ledoux Foundation's computer lab. There he worked on The Computer Virus Project, his first artistic experiment with computer viruses and computer virus animation. He exhibited computer-robotic paintings at Documenta 8 in 1987. In 2002 he extended his experimentation into viral artificial life through a collaboration with the programmer Stephane Sikora of music2eye in a work called the Computer Virus Project II. Nechvatal has also created a noise music work called viral symphOny, a collaborative sound symphony created by using his computer virus software at the Institute for Electronic Arts at Alfred University. In 2021 Pentiments released Nechvatal's retrospective audio cassette called Selected Sound Works (1981-2021) and in 2022 his The Viral Tempest, a double vinyl LP of new audio work. In 2025, he joined the roster of artists/musicians at Table of the Elements with two CD/book releases: Selected Sound Works (1981-2021) and The Marriage of Orlando and Artaud, Even. From 1999 to 2013, Nechvatal taught art theories of immersive virtual reality and the viractual at the School of Visual Arts in New York City (SVA). A book of his collected essays entitled Towards an Immersive Intelligence: Essays on the Work of Art in the Age of Computer Technology and Virtual Reality (1993–2006) was published by Edgewise Press in 2009. Also in 2009, his virtual reality art theory and art history book Immersive Ideals / Critical Distances was published. In 2011, his book Immersion Into Noise was published by Open Humanities Press in conjunction with the University of Michigan Library's Scholarly Publishing Office. Nechvatal has also published three books with Punctum Books: Minóy (noise music—ed.—2014), Destroyer of Naivetés (poetry—2015), and Styling Sagaciousness (poetry—2022). In 2023 his art theory cybersex farce novella venus©~Ñ~vibrator, even was published by Orbis Tertius Press The Joseph Nechvatal archive is housed at The Fales Library Downtown Collection at the NYU Special Collections Library in New York City. === Viractualism === Viractualism is an art theory concept developed by Nechvatal in 1999 from Ph.D. research Nechvatal conducted at the Planetary Collegium at University of Wales, Newport. There he developed his concept of the viractual, which strives to create an interface between the actual and the virtual.

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  Vapnik–Chervonenkis dimension

  In Vapnik–Chervonenkis theory, the Vapnik–Chervonenkis (VC) dimension is a measure of the size (capacity, complexity, expressive power, richness, or flexibility) of a class of sets. The notion can be extended to classes of binary functions. It is defined as the cardinality of the largest set of points that the function class can shatter—that is, for which all possible binary labelings can be realized by some function in the class. It was originally defined by Vladimir Vapnik and Alexey Chervonenkis. Informally, the capacity of a classification model is related to how complicated it can be. For example, consider the thresholding of a high-degree polynomial: if the polynomial evaluates above zero, that point is classified as positive, otherwise as negative. A high-degree polynomial can be wiggly, so that it can fit a given set of training points well. Such a polynomial has a high capacity. A much simpler alternative is to threshold a linear function. This function may not fit the training set well, because it has a low capacity. This notion of capacity is made rigorous below. == Definitions == === VC dimension of a set-family === Let C = { C } C ∈ C {\displaystyle {\mathcal {C}}=\{C\}_{C\in {\mathcal {C}}}} be a family of sets (also called set family, collection of sets or set of sets) and X {\displaystyle X} a set. Their intersection is defined as the following set family: C ∩ X := { C ∩ X ∣ C ∈ C } . {\displaystyle {\mathcal {C}}\cap X:=\{C\cap X\mid C\in {\mathcal {C}}\}.} Here typically X {\displaystyle X} and each C ∈ C {\displaystyle C\in {\mathcal {C}}} are subsets of a big "universe" of possibilities U {\displaystyle U} where intersection takes place. We say that a set X {\displaystyle X} is shattered by C {\displaystyle {\mathcal {C}}} if P ( X ) = C ∩ X {\displaystyle {\mathcal {P}}(X)={\mathcal {C}}\cap X} i.e. the set of intersections contains (hence is equal to) all the subsets of X {\displaystyle X} . For finite sets X {\displaystyle X} this is equivalent to | C ∩ X | = 2 | X | . {\displaystyle |{\mathcal {C}}\cap X|=2^{|X|}.} The VC dimension D {\displaystyle D} of C {\displaystyle {\mathcal {C}}} is the cardinality of the largest set that is shattered by C {\displaystyle {\mathcal {C}}} . If arbitrarily large sets can be shattered, the VC dimension of C {\displaystyle {\mathcal {C}}} is ∞ {\displaystyle \infty } . === VC dimension of a classification model === A binary classification model f {\displaystyle f} with some parameter vector θ {\displaystyle \theta } is said to shatter a set of generally positioned data points ( x 1 , x 2 , … , x n ) {\displaystyle (x_{1},x_{2},\ldots ,x_{n})} if, for every assignment of labels to those points, there exists a θ {\displaystyle \theta } such that the model f {\displaystyle f} makes no errors when evaluating that set of data points. The VC dimension of a model f {\displaystyle f} is the maximum number of points that can be arranged so that f {\displaystyle f} shatters them. More formally, it is the maximum cardinal D {\displaystyle D} such that there exists a generally positioned data point set of cardinality D {\displaystyle D} that can be shattered by f {\displaystyle f} . == Examples == f {\displaystyle f} is a constant classifier (with no parameters); Its VC dimension is 0 since it cannot shatter even a single point. In general, the VC dimension of a finite classification model, which can return at most 2 d {\displaystyle 2^{d}} different classifiers, is at most d {\displaystyle d} (this is an upper bound on the VC dimension; the Sauer–Shelah lemma gives a lower bound on the dimension). f {\displaystyle f} is a single-parametric threshold classifier on real numbers; i.e., for a certain threshold θ {\displaystyle \theta } , the classifier f θ {\displaystyle f_{\theta }} returns 1 if the input number is larger than θ {\displaystyle \theta } and 0 otherwise. The VC dimension of f {\displaystyle f} is 1 because: (a) It can shatter a single point. For every point x {\displaystyle x} , a classifier f θ {\displaystyle f_{\theta }} labels it as 0 if θ > x {\displaystyle \theta >x} and labels it as 1 if θ < x {\displaystyle \theta x + 2 {\displaystyle \theta >x+2} , as (1,0) if θ ∈ [ x − 4 , x − 2 ) {\displaystyle \theta \in [x-4,x-2)} , as (1,1) if θ ∈ [ x − 2 , x ] {\displaystyle \theta \in [x-2,x]} , and as (0,1) if θ ∈ ( x , x + 2 ] {\displaystyle \theta \in (x,x+2]} . (b) It cannot shatter any set of three points. For every set of three numbers, if the smallest and the largest are labeled 1, then the middle one must also be labeled 1, so not all labelings are possible. f {\displaystyle f} is a straight line as a classification model on points in a two-dimensional plane (this is the model used by a perceptron). The line should separate positive data points from negative data points. There exist sets of 3 points that can indeed be shattered using this model (any 3 points that are not collinear can be shattered). However, no set of 4 points can be shattered: by Radon's theorem, any four points can be partitioned into two subsets with intersecting convex hulls, so it is not possible to separate one of these two subsets from the other. Thus, the VC dimension of this particular classifier is 3. It is important to remember that while one can choose any arrangement of points, the arrangement of those points cannot change when attempting to shatter for some label assignment. Note, only 3 of the 23 = 8 possible label assignments are shown for the three points. f {\displaystyle f} is a single-parametric sine classifier, i.e., for a certain parameter θ {\displaystyle \theta } , the classifier f θ {\displaystyle f_{\theta }} returns 1 if the input number x {\displaystyle x} has sin ⁡ ( θ x ) > 0 {\displaystyle \sin(\theta x)>0} and 0 otherwise. The VC dimension of f {\displaystyle f} is infinite, since it can shatter any finite subset of the set { 2 − m ∣ m ∈ N } {\displaystyle \{2^{-m}\mid m\in \mathbb {N} \}} . == Uses == === In statistical learning theory === The VC dimension can predict a probabilistic upper bound on the test error of a classification model. Vapnik proved that the probability of the test error (i.e., risk with 0–1 loss function) distancing from an upper bound (on data that is drawn i.i.d. from the same distribution as the training set) is given by: Pr ( test error ⩽ training error + 1 N [ D ( log ⁡ ( 2 N D ) + 1 ) − log ⁡ ( η 4 ) ] ) = 1 − η , {\displaystyle \Pr \left({\text{test error}}\leqslant {\text{training error}}+{\sqrt {{\frac {1}{N}}\left[D\left(\log \left({\tfrac {2N}{D}}\right)+1\right)-\log \left({\tfrac {\eta }{4}}\right)\right]}}\,\right)=1-\eta ,} where D {\displaystyle D} is the VC dimension of the classification model, 0 < η ⩽ 1 {\displaystyle 0<\eta \leqslant 1} , and N {\displaystyle N} is the size of the training set (restriction: this formula is valid when D ≪ N {\displaystyle D\ll N} . When D {\displaystyle D} is larger, the test-error may be much higher than the training-error. This is due to overfitting). The VC dimension also appears in sample-complexity bounds. A space of binary functions with VC dimension D {\displaystyle D} can be learned with: N = Θ ( D + ln ⁡ 1 δ ε 2 ) {\displaystyle N=\Theta \left({\frac {D+\ln {1 \over \delta }}{\varepsilon ^{2}}}\right)} samples, where ε {\displaystyle \varepsilon } is the learning error and δ {\displaystyle \delta } is the failure probability. Thus, the sample-complexity is a linear function of the VC dimension of the hypothesis space. === In computational geometry === The VC dimension is one of the critical parameters in the size of ε-nets, which determines the complexity of approximation algorithms based on them; range sets without finite VC dimension may not have finite ε-nets at all. == Bounds == The VC dimension of the dual set-family of C {\displaystyle {\mathcal {C}}} is strictly less than 2 vc ⁡ ( C ) + 1 {\displaystyle 2^{\operatorname {vc} ({\mathcal {C}})+1}} , and this is best possible. The VC dimension of a finite set-family C {\displaystyle {\mathcal {C}}} is at most log 2 ⁡ | C | {\displaystyle \log _{2}|{\mathcal {C}}|} . This is because | C ∩ X | ≤ | X | {\displaystyle |{\mathcal {C}}\cap X|\leq |X|} by definition. Given a set-fa

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  Virtual assistant

  A virtual assistant (VA) is a software agent that can perform a range of tasks or services for a user based on user input, such as commands or questions, including verbal ones. Such technologies often incorporate chatbot capabilities to streamline task execution. The interaction may be via text, graphical interface, or voice, as some virtual assistants are able to interpret human speech and respond via synthesized voices. In many cases, users can ask their virtual assistants questions, control home automation devices and media playback, and manage other basic tasks such as email, to-do lists, and calendars – all with verbal commands. In recent years, prominent virtual assistants for direct consumer use have included Apple Siri, Amazon Alexa, Google Assistant (Gemini), Microsoft Copilot and Samsung Bixby. Also, companies in various industries often incorporate some kind of virtual assistant technology into their customer service or support. Into the 2020s, the emergence of artificial intelligence based chatbots, such as ChatGPT, has brought increased capability and interest to the field of virtual assistant products and services. == History == === Experimental decades: 1910s–1980s === Radio Rex was the first voice-activated toy, patented in 1916 and released in 1922. It was a wooden toy in the shape of a dog that would come out of its house when its name is called. In 1952, Bell Labs presented "Audrey", the Automatic Digit Recognition machine. It occupied a six-foot-high relay rack, consumed substantial power, had streams of cables and exhibited the myriad maintenance problems associated with complex vacuum-tube circuitry. It could recognize the fundamental units of speech, phonemes. It was limited to the accurate recognition of digits spoken by designated talkers. It could therefore be used for voice dialing, but in most cases, push-button dialing was cheaper and faster, rather than speaking the consecutive digits. Another early tool which was enabled to perform digital speech recognition was the IBM Shoebox voice-activated calculator, presented to the general public during the 1962 Seattle World's Fair after its initial market launch in 1961. This early computer, developed almost 20 years before the introduction of the first IBM Personal Computer in 1981, was able to recognize 16 spoken words and the digits 0 to 9. The first natural language processing computer program or the chatbot ELIZA was developed by MIT professor Joseph Weizenbaum in the 1960s. It was created to "demonstrate that the communication between man and machine was superficial". ELIZA used pattern matching and substitution methodology into scripted responses to simulate conversation, which gave an illusion of understanding on the part of the program. Weizenbaum's own secretary reportedly asked Weizenbaum to leave the room so that she and ELIZA could have a real conversation. Weizenbaum was surprised by this, later writing: "I had not realized ... that extremely short exposures to a relatively simple computer program could induce powerful delusional thinking in quite normal people. This gave name to the ELIZA effect, the tendency to unconsciously assume computer behaviors are analogous to human behaviors; that is, anthropomorphisation, a phenomenon present in human interactions with virtual assistants. The next milestone in the development of voice recognition technology was achieved in the 1970s at the Carnegie Mellon University in Pittsburgh, Pennsylvania with substantial support of the United States Department of Defense and its DARPA agency, funded five years of a Speech Understanding Research program, aiming to reach a minimum vocabulary of 1,000 words. Companies and academia including IBM, Carnegie Mellon University (CMU) and Stanford Research Institute took part in the program. The result was "Harpy", it mastered about 1000 words, the vocabulary of a three-year-old and it could understand sentences. It could process speech that followed pre-programmed vocabulary, pronunciation, and grammar structures to determine which sequences of words made sense together, and thus reducing speech recognition errors. In 1986, Tangora was an upgrade of the Shoebox, it was a voice recognizing typewriter. Named after the world's fastest typist at the time, it had a vocabulary of 20,000 words and used prediction to decide the most likely result based on what was said in the past. IBM's approach was based on a hidden Markov model, which adds statistics to digital signal processing techniques. The method makes it possible to predict the most likely phonemes to follow a given phoneme. Still each speaker had to individually train the typewriter to recognize their voice, and pause between each word. In 1983, Gus Searcy invented the "Butler in a Box", an electronic voice home controller system. === Birth of smart virtual assistants: 1990s–2010s === In the 1990s, digital speech recognition technology became a feature of the personal computer with IBM, Philips and Lernout & Hauspie fighting for customers. Much later the market launch of the first smartphone IBM Simon in 1994 laid the foundation for smart virtual assistants as we know them today. In 1997, Dragon's NaturallySpeaking software could recognize and transcribe natural human speech without pauses between each word into a document at a rate of 100 words per minute. A version of Naturally Speaking is still available for download and it is still used today, for instance, by many doctors in the US and the UK to document their medical records. In 2001 Colloquis publicly launched SmarterChild, on platforms like AIM and MSN Messenger. While entirely text-based SmarterChild was able to play games, check the weather, look up facts, and converse with users to an extent. The first modern digital virtual assistant installed on a smartphone was Siri, which was introduced as a feature of the iPhone 4S on 4 October 2011. Apple Inc. developed Siri following the 2010 acquisition of Siri Inc., a spin-off of SRI International, which is a research institute financed by DARPA and the United States Department of Defense. Its aim was to aid in tasks such as sending a text message, making phone calls, checking the weather or setting up an alarm. Over time, it has developed to provide restaurant recommendations, search the internet, and provide driving directions. In November 2014, Amazon announced Alexa alongside the Echo. In 2016, Salesforce debuted Einstein, developed from a set of technologies underlying the Salesforce platform. Einstein was replaced by Agentforce, an agentic AI, in September 2024. In April 2017 Amazon released a service for building conversational interfaces for any type of virtual assistant or interface. === Large Language Models: 2020s-present === In the 2020s, artificial intelligence (AI) systems like ChatGPT have gained popularity for their ability to generate human-like responses to text-based conversations. In February 2020, Microsoft introduced its Turing Natural Language Generation (T-NLG), which was then the "largest language model ever published at 17 billion parameters." On November 30, 2022, ChatGPT was launched as a prototype and quickly garnered attention for its detailed responses and articulate answers across many domains of knowledge. The advent of ChatGPT and its introduction to the wider public increased interest and competition in the space. In February 2023, Google began introducing an experimental service called "Bard" which is based on its LaMDA program to generate text responses to questions asked based on information gathered from the web. While ChatGPT and other generalized chatbots based on the latest generative AI are capable of performing various tasks associated with virtual assistants, there are also more specialized forms of such technology that are designed to target more specific situations or needs. == Method of interaction == Virtual assistants work via: Text, including: online chat (especially in an instant messaging application or other application ), SMS text, e-mail or other text-based communication channel, for example Conversica's intelligent virtual assistants for business. Voice: for example with Amazon Alexa on Amazon Echo devices, Siri on an iPhone, Google Assistant on Google-enabled Android devices, or Bixby on Samsung devices. Images: some assistants, such as Google Assistant (which includes Google Lens) and Bixby on the Samsung Galaxy series, have the added capability of performing image processing to recognize objects in images. Many virtual assistants are accessible via multiple methods, offering versatility in how users can interact with them, whether through chat, voice commands, or other integrated technologies. Virtual assistants use natural language processing (NLP) to match user text or voice input to executable commands. Some continually learn using artificial intelligence techniques including machine learning and ambient intelligence. To activate a virtual assistant u

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  SqueezeNet

  SqueezeNet is a deep neural network for image classification released in 2016. SqueezeNet was developed by researchers at DeepScale, University of California, Berkeley, and Stanford University. In designing SqueezeNet, the authors' goal was to create a smaller neural network with fewer parameters while achieving competitive accuracy. Their best-performing model achieved the same accuracy as AlexNet on ImageNet classification, but has a size 510x less than it. == Version history == SqueezeNet was originally released on February 22, 2016. This original version of SqueezeNet was implemented on top of the Caffe deep learning software framework. Shortly thereafter, the open-source research community ported SqueezeNet to a number of other deep learning frameworks. On February 26, 2016, Eddie Bell released a port of SqueezeNet for the Chainer deep learning framework. On March 2, 2016, Guo Haria released a port of SqueezeNet for the Apache MXNet framework. On June 3, 2016, Tammy Yang released a port of SqueezeNet for the Keras framework. In 2017, companies including Baidu, Xilinx, Imagination Technologies, and Synopsys demonstrated SqueezeNet running on low-power processing platforms such as smartphones, FPGAs, and custom processors. As of 2018, SqueezeNet ships "natively" as part of the source code of a number of deep learning frameworks such as PyTorch, Apache MXNet, and Apple CoreML. In addition, third party developers have created implementations of SqueezeNet that are compatible with frameworks such as TensorFlow. Below is a summary of frameworks that support SqueezeNet. == Relationship to other networks == === AlexNet === SqueezeNet was originally described in SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size. AlexNet is a deep neural network that has 240 MB of parameters, and SqueezeNet has just 5 MB of parameters. This small model size can more easily fit into computer memory and can more easily be transmitted over a computer network. However, it's important to note that SqueezeNet is not a "squeezed version of AlexNet." Rather, SqueezeNet is an entirely different DNN architecture than AlexNet. What SqueezeNet and AlexNet have in common is that both of them achieve approximately the same level of accuracy when evaluated on the ImageNet image classification validation dataset. === Model compression === Model compression (e.g. quantization and pruning of model parameters) can be applied to a deep neural network after it has been trained. In the SqueezeNet paper, the authors demonstrated that a model compression technique called Deep Compression can be applied to SqueezeNet to further reduce the size of the parameter file from 5 MB to 500 KB. Deep Compression has also been applied to other DNNs, such as AlexNet and VGG. == Variants == Some of the members of the original SqueezeNet team have continued to develop resource-efficient deep neural networks for a variety of applications. A few of these works are noted in the following table. As with the original SqueezeNet model, the open-source research community has ported and adapted these newer "squeeze"-family models for compatibility with multiple deep learning frameworks. In addition, the open-source research community has extended SqueezeNet to other applications, including semantic segmentation of images and style transfer.

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  Relation network

  A relation network (RN) is an artificial neural network component with a structure that can reason about relations among objects. An example category of such relations is spatial relations (above, below, left, right, in front of, behind). RNs can infer relations, they are data efficient, and they operate on a set of objects without regard to the objects' order. == History == In June 2017, DeepMind announced the first relation network. It claimed that the technology had achieved "superhuman" performance on multiple question-answering problem sets. == Design == RNs constrain the functional form of a neural network to capture the common properties of relational reasoning. These properties are explicitly added to the system, rather than established by learning just as the capacity to reason about spatial, translation-invariant properties is explicitly part of convolutional neural networks (CNN). The data to be considered can be presented as a simple list or as a directed graph whose nodes are objects and whose edges are the pairs of objects whose relationships are to be considered. The RN is a composite function: R N ( O ) = f ϕ ( ∑ i , j g θ ( o i , o j , q ) ) , {\displaystyle RN\left(O\right)=f_{\phi }\left(\sum _{i,j}g_{\theta }\left(o_{i},o_{j},q\right)\right),} where the input is a set of "objects" O = { o 1 , o 2 , . . . , o n } , o i ∈ R m {\displaystyle O=\left\lbrace o_{1},o_{2},...,o_{n}\right\rbrace ,o_{i}\in \mathbb {R} ^{m}} is the ith object, and fφ and gθ are functions with parameters φ and θ, respectively and q is the question. fφ and gθ are multilayer perceptrons, while the 2 parameters are learnable synaptic weights. RNs are differentiable. The output of gθ is a "relation"; therefore, the role of gθ is to infer any ways in which two objects are related. Image (128x128 pixel) processing is done with a 4-layer CNN. Outputs from the CNN are treated as the objects for relation analysis, without regard for what those "objects" explicitly represent. Questions were processed with a long short-term memory network.

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