AI For Students Pros And Cons

AI For Students Pros And Cons — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Hierarchical control system

  A hierarchical control system (HCS) is a form of control system in which a set of devices and governing software is arranged in a hierarchical tree. When the links in the tree are implemented by a computer network, then that hierarchical control system is also a form of networked control system. == Overview == A human-built system with complex behavior is often organized as a hierarchy. For example, a command hierarchy has among its notable features the organizational chart of superiors, subordinates, and lines of organizational communication. Hierarchical control systems are organized similarly to divide the decision making responsibility. Each element of the hierarchy is a linked node in the tree. Commands, tasks and goals to be achieved flow down the tree from superior nodes to subordinate nodes, whereas sensations and command results flow up the tree from subordinate to superior nodes. Nodes may also exchange messages with their siblings. The two distinguishing features of a hierarchical control system are related to its layers. Each higher layer of the tree operates with a longer interval of planning and execution time than its immediately lower layer. The lower layers have local tasks, goals, and sensations, and their activities are planned and coordinated by higher layers which do not generally override their decisions. The layers form a hybrid intelligent system in which the lowest, reactive layers are sub-symbolic. The higher layers, having relaxed time constraints, are capable of reasoning from an abstract world model and performing planning. A hierarchical task network is a good fit for planning in a hierarchical control system. Besides artificial systems, an animal's control systems are proposed to be organized as a hierarchy. In perceptual control theory, which postulates that an organism's behavior is a means of controlling its perceptions, the organism's control systems are suggested to be organized in a hierarchical pattern as their perceptions are constructed so. == Control system structure == The accompanying diagram is a general hierarchical model which shows functional manufacturing levels using computerised control of an industrial control system. Referring to the diagram; Level 0 contains the field devices such as flow and temperature sensors, and final control elements, such as control valves Level 1 contains the industrialised Input/Output (I/O) modules, and their associated distributed electronic processors. Level 2 contains the supervisory computers, which collate information from processor nodes on the system, and provide the operator control screens. Level 3 is the production control level, which does not directly control the process, but is concerned with monitoring production and monitoring targets Level 4 is the production scheduling level. == Applications == === Manufacturing, robotics and vehicles === Among the robotic paradigms is the hierarchical paradigm in which a robot operates in a top-down fashion, heavy on planning, especially motion planning. Computer-aided production engineering has been a research focus at NIST since the 1980s. Its Automated Manufacturing Research Facility was used to develop a five layer production control model. In the early 1990s DARPA sponsored research to develop distributed (i.e. networked) intelligent control systems for applications such as military command and control systems. NIST built on earlier research to develop its Real-Time Control System (RCS) and Real-time Control System Software which is a generic hierarchical control system that has been used to operate a manufacturing cell, a robot crane, and an automated vehicle. In November 2007, DARPA held the Urban Challenge. The winning entry, Tartan Racing employed a hierarchical control system, with layered mission planning, motion planning, behavior generation, perception, world modelling, and mechatronics. === Artificial intelligence === Subsumption architecture is a methodology for developing artificial intelligence that is heavily associated with behavior based robotics. This architecture is a way of decomposing complicated intelligent behavior into many "simple" behavior modules, which are in turn organized into layers. Each layer implements a particular goal of the software agent (i.e. system as a whole), and higher layers are increasingly more abstract. Each layer's goal subsumes that of the underlying layers, e.g. the decision to move forward by the eat-food layer takes into account the decision of the lowest obstacle-avoidance layer. Behavior need not be planned by a superior layer, rather behaviors may be triggered by sensory inputs and so are only active under circumstances where they might be appropriate. Reinforcement learning has been used to acquire behavior in a hierarchical control system in which each node can learn to improve its behavior with experience. James Albus, while at NIST, developed a theory for intelligent system design named the Reference Model Architecture (RMA), which is a hierarchical control system inspired by RCS. Albus defines each node to contain these components. Behavior generation is responsible for executing tasks received from the superior, parent node. It also plans for, and issues tasks to, the subordinate nodes. Sensory perception is responsible for receiving sensations from the subordinate nodes, then grouping, filtering, and otherwise processing them into higher level abstractions that update the local state and which form sensations that are sent to the superior node. Value judgment is responsible for evaluating the updated situation and evaluating alternative plans. World Model is the local state that provides a model for the controlled system, controlled process, or environment at the abstraction level of the subordinate nodes. At its lowest levels, the RMA can be implemented as a subsumption architecture, in which the world model is mapped directly to the controlled process or real world, avoiding the need for a mathematical abstraction, and in which time-constrained reactive planning can be implemented as a finite-state machine. Higher levels of the RMA however, may have sophisticated mathematical world models and behavior implemented by automated planning and scheduling. Planning is required when certain behaviors cannot be triggered by current sensations, but rather by predicted or anticipated sensations, especially those that come about as result of the node's actions.

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  Isotropic position

  In the fields of machine learning, the theory of computation, and random matrix theory, a probability distribution over vectors is said to be in isotropic position if its covariance matrix is proportional to the identity matrix. == Formal definitions == Let D {\textstyle D} be a distribution over vectors in the vector space R n {\textstyle \mathbb {R} ^{n}} . Then D {\textstyle D} is in isotropic position if, for vector v {\textstyle v} sampled from the distribution, E v v T = I d . {\displaystyle \mathbb {E} \,vv^{\mathsf {T}}=\mathrm {Id} .} A set of vectors is said to be in isotropic position if the uniform distribution over that set is in isotropic position. In particular, every orthonormal set of vectors is isotropic. As a related definition, a convex body K {\textstyle K} in R n {\textstyle \mathbb {R} ^{n}} is called isotropic if it has volume | K | = 1 {\textstyle |K|=1} , center of mass at the origin, and there is a constant α > 0 {\textstyle \alpha >0} such that ∫ K ⟨ x , y ⟩ 2 d x = α 2 | y | 2 , {\displaystyle \int _{K}\langle x,y\rangle ^{2}dx=\alpha ^{2}|y|^{2},} for all vectors y {\textstyle y} in R n {\textstyle \mathbb {R} ^{n}} ; here | ⋅ | {\textstyle |\cdot |} stands for the standard Euclidean norm.

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  Video Super Resolution

  RTX Video Super Resolution (RTX VSR) is a video scaling feature by Nvidia. It was released on February 28, 2023. == History == The feature was first unveiled during CES 2023 as RTX Video Super Resolution. It uses the on-board Tensor Cores to upscale browser video content in real time. Video Super Resolution was initially only available on RTX 30 and 40 series GPUs, while support for 20 series GPUs was added afterwards; it is now available on all Nvidia RTX-branded GPUs. The feature supports input resolutions from 360p to 1440p and a max output of 4K and comes without support for HDR content although that could be likely added in the future. Nvidia released RTX Video Super Resolution 1.5 with improved video quality and RTX 20 series support on October 17, 2023. == Reception == According to ComputerBase, although "the algorithm is not yet working flawlessly", the feature is "overall recommendable".

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  Action model learning

  Action model learning (sometimes abbreviated action learning) is an area of machine learning concerned with the creation and modification of a software agent's knowledge about the effects and preconditions of the actions that can be executed within its environment. This knowledge is usually represented in a logic-based action description language and used as input for automated planners. Learning action models is important when goals change. When an agent acted for a while, it can use its accumulated knowledge about actions in the domain to make better decisions. Thus, learning action models differs from reinforcement learning. It enables reasoning about actions instead of expensive trials in the world. Action model learning is a form of inductive reasoning, where new knowledge is generated based on the agent's observations. The usual motivation for action model learning is the fact that manual specification of action models for planners is often a difficult, time-consuming, and error-prone task (especially in complex environments). == Action models == Given a training set E {\displaystyle E} consisting of examples e = ( s , a , s ′ ) {\displaystyle e=(s,a,s')} , where s , s ′ {\displaystyle s,s'} are observations of a world state from two consecutive time steps t , t ′ {\displaystyle t,t'} and a {\displaystyle a} is an action instance observed in time step t {\displaystyle t} , the goal of action model learning in general is to construct an action model ⟨ D , P ⟩ {\displaystyle \langle D,P\rangle } , where D {\displaystyle D} is a description of domain dynamics in action description formalism like STRIPS, ADL or PDDL and P {\displaystyle P} is a probability function defined over the elements of D {\displaystyle D} . However, many state of the art action learning methods assume determinism and do not induce P {\displaystyle P} . In addition to determinism, individual methods differ in how they deal with other attributes of domain (e.g. partial observability or sensoric noise). == Action learning methods == === State of the art === Recent action learning methods take various approaches and employ a wide variety of tools from different areas of artificial intelligence and computational logic. As an example of a method based on propositional logic, we can mention SLAF (Simultaneous Learning and Filtering) algorithm, which uses agent's observations to construct a long propositional formula over time and subsequently interprets it using a satisfiability (SAT) solver. Another technique, in which learning is converted into a satisfiability problem (weighted MAX-SAT in this case) and SAT solvers are used, is implemented in ARMS (Action-Relation Modeling System). Two mutually similar, fully declarative approaches to action learning were based on logic programming paradigm Answer Set Programming (ASP) and its extension, Reactive ASP. In another example, bottom-up inductive logic programming approach was employed. Several different solutions are not directly logic-based. For example, the action model learning using a perceptron algorithm or the multi level greedy search over the space of possible action models. In the older paper from 1992, the action model learning was studied as an extension of reinforcement learning. Nonetheless, further algorithms can be found that operate under different assumptions: FAMA can work even when some observations are missing, and it produces a general (lifted) planning model. It treats learning an action model like a planning problem, making sure the learned model matches the observations given. NOLAM can learn general action models even from noisy or imperfect data. LOCM focuses only on the order of actions in the data, ignoring any details about the states between those actions. The family of safe action model (SAM) learning methods create models that guarantee any plans made with them will actually work in the real world. There's also an extension called N-SAM that can learn action models with numeric conditions and effects. Additionally, numeric action models like N-SAM can be used to improve reinforcement learning (RL) performance through the RAMP algorithm. === Literature === Most action learning research papers are published in journals and conferences focused on artificial intelligence in general (e.g. Journal of Artificial Intelligence Research (JAIR), Artificial Intelligence, Applied Artificial Intelligence (AAI) or AAAI conferences). Despite mutual relevance of the topics, action model learning is usually not addressed in planning conferences like the International Conference on Automated Planning and Scheduling (ICAPS).

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  Luminance HDR

  Luminance HDR, formerly Qtpfsgui, is graphics software used for the creation and manipulation of high-dynamic-range images. Released under the terms of the GPL, it is available for Linux, Microsoft Windows, and Mac OS X (Intel only). Luminance HDR supports several High Dynamic Range (HDR) as well as Low Dynamic Range (LDR) file formats. == Functionality == Prerequisite of HDR photography are several narrow-range digital images with different exposures. Luminance HDR combines these images and calculates a high-contrast image. In order to view this image on a regular computer monitor, Luminance HDR can convert it into a displayable LDR image format using a variety of methods, such as tone mapping. Currently fifteen different tone mapping operators (algorithms) are available, each one with its tunable parameters. Different image processing techniques can be applied to the generated HDR images, such as resizing, cropping, rotating and a number of projective transformations. The software also provides batch processing functionality for creating HDR images and for tone mapping them in a non-interactive way. A module for copying Exif data among sets of images is also provided. For users who prefers the command line, a non-GUI, non-graphical interface is also available on all supported platforms. A common problem with HDR photography is that images need to be aligned exactly. If the subject is static, this can be achieved using a tripod or a stable surface on which the camera is placed. In the case of image data that does not align exactly, an automatic alignment can be performed using a tool provided by the Hugin project. If this automation doesn't provide the desired result, the user may improve it manually. == Supported formats == HDR images are images with a high dynamic range and, using Luminance HDR, they can be created as well as edited. The following HDR graphic formats are supported: OpenEXR Radiance HDR Tag Image File Format (TIFF) Format: 16 Bit, 32 Bit (Float) and LogLuv Raw PFS native Luminance HDR can create an HDR image from several LDR images and tonemap an HDR into an LDR. The following LDR formats are supported: JPG PNG Portable Pixmap (PPM) Portable Bitmap (PBM) TIFF (8 Bit)

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  Similarity learning

  Similarity learning is an area of supervised machine learning in artificial intelligence. It is closely related to regression and classification, but the goal is to learn a similarity function that measures how similar or related two objects are. It has applications in ranking, in recommendation systems, visual identity tracking, face verification, and speaker verification. == Learning setup == There are four common setups for similarity and metric distance learning. Regression similarity learning In this setup, pairs of objects are given ( x i 1 , x i 2 ) {\displaystyle (x_{i}^{1},x_{i}^{2})} together with a measure of their similarity y i ∈ R {\displaystyle y_{i}\in R} . The goal is to learn a function that approximates f ( x i 1 , x i 2 ) ∼ y i {\displaystyle f(x_{i}^{1},x_{i}^{2})\sim y_{i}} for every new labeled triplet example ( x i 1 , x i 2 , y i ) {\displaystyle (x_{i}^{1},x_{i}^{2},y_{i})} . This is typically achieved by minimizing a regularized loss min W ∑ i l o s s ( w ; x i 1 , x i 2 , y i ) + r e g ( w ) {\displaystyle \min _{W}\sum _{i}loss(w;x_{i}^{1},x_{i}^{2},y_{i})+reg(w)} . Classification similarity learning Given are pairs of similar objects ( x i , x i + ) {\displaystyle (x_{i},x_{i}^{+})} and non similar objects ( x i , x i − ) {\displaystyle (x_{i},x_{i}^{-})} . An equivalent formulation is that every pair ( x i 1 , x i 2 ) {\displaystyle (x_{i}^{1},x_{i}^{2})} is given together with a binary label y i ∈ { 0 , 1 } {\displaystyle y_{i}\in \{0,1\}} that determines if the two objects are similar or not. The goal is again to learn a classifier that can decide if a new pair of objects is similar or not. Ranking similarity learning Given are triplets of objects ( x i , x i + , x i − ) {\displaystyle (x_{i},x_{i}^{+},x_{i}^{-})} whose relative similarity obey a predefined order: x i {\displaystyle x_{i}} is known to be more similar to x i + {\displaystyle x_{i}^{+}} than to x i − {\displaystyle x_{i}^{-}} . The goal is to learn a function f {\displaystyle f} such that for any new triplet of objects ( x , x + , x − ) {\displaystyle (x,x^{+},x^{-})} , it obeys f ( x , x + ) > f ( x , x − ) {\displaystyle f(x,x^{+})>f(x,x^{-})} (contrastive learning). This setup assumes a weaker form of supervision than in regression, because instead of providing an exact measure of similarity, one only has to provide the relative order of similarity. For this reason, ranking-based similarity learning is easier to apply in real large-scale applications. Locality sensitive hashing (LSH) Hashes input items so that similar items map to the same "buckets" in memory with high probability (the number of buckets being much smaller than the universe of possible input items). It is often applied in nearest neighbor search on large-scale high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. A common approach for learning similarity is to model the similarity function as a bilinear form. For example, in the case of ranking similarity learning, one aims to learn a matrix W that parametrizes the similarity function f W ( x , z ) = x T W z {\displaystyle f_{W}(x,z)=x^{T}Wz} . When data is abundant, a common approach is to learn a siamese network – a deep network model with parameter sharing. == Metric learning == Similarity learning is closely related to distance metric learning. Metric learning is the task of learning a distance function over objects. A metric or distance function has to obey four axioms: non-negativity, identity of indiscernibles, symmetry and subadditivity (or the triangle inequality). In practice, metric learning algorithms ignore the condition of identity of indiscernibles and learn a pseudo-metric. When the objects x i {\displaystyle x_{i}} are vectors in R d {\displaystyle R^{d}} , then any matrix W {\displaystyle W} in the symmetric positive semi-definite cone S + d {\displaystyle S_{+}^{d}} defines a distance pseudo-metric of the space of x through the form D W ( x 1 , x 2 ) 2 = ( x 1 − x 2 ) ⊤ W ( x 1 − x 2 ) {\displaystyle D_{W}(x_{1},x_{2})^{2}=(x_{1}-x_{2})^{\top }W(x_{1}-x_{2})} . When W {\displaystyle W} is a symmetric positive definite matrix, D W {\displaystyle D_{W}} is a metric. Moreover, as any symmetric positive semi-definite matrix W ∈ S + d {\displaystyle W\in S_{+}^{d}} can be decomposed as W = L ⊤ L {\displaystyle W=L^{\top }L} where L ∈ R e × d {\displaystyle L\in R^{e\times d}} and e ≥ r a n k ( W ) {\displaystyle e\geq rank(W)} , the distance function D W {\displaystyle D_{W}} can be rewritten equivalently D W ( x 1 , x 2 ) 2 = ( x 1 − x 2 ) ⊤ L ⊤ L ( x 1 − x 2 ) = ‖ L ( x 1 − x 2 ) ‖ 2 2 {\displaystyle D_{W}(x_{1},x_{2})^{2}=(x_{1}-x_{2})^{\top }L^{\top }L(x_{1}-x_{2})=\|L(x_{1}-x_{2})\|_{2}^{2}} . The distance D W ( x 1 , x 2 ) 2 = ‖ x 1 ′ − x 2 ′ ‖ 2 2 {\displaystyle D_{W}(x_{1},x_{2})^{2}=\|x_{1}'-x_{2}'\|_{2}^{2}} corresponds to the Euclidean distance between the transformed feature vectors x 1 ′ = L x 1 {\displaystyle x_{1}'=Lx_{1}} and x 2 ′ = L x 2 {\displaystyle x_{2}'=Lx_{2}} . Many formulations for metric learning have been proposed. Some well-known approaches for metric learning include learning from relative comparisons, which is based on the triplet loss, large margin nearest neighbor, and information theoretic metric learning (ITML). In statistics, the covariance matrix of the data is sometimes used to define a distance metric called Mahalanobis distance. == Applications == Similarity learning is used in information retrieval for learning to rank, in face verification or face identification, and in recommendation systems. Also, many machine learning approaches rely on some metric. This includes unsupervised learning such as clustering, which groups together close or similar objects. It also includes supervised approaches like K-nearest neighbor algorithm which rely on labels of nearby objects to decide on the label of a new object. Metric learning has been proposed as a preprocessing step for many of these approaches. == Scalability == Metric and similarity learning scale quadratically with the dimension of the input space, as can easily see when the learned metric has a bilinear form f W ( x , z ) = x T W z {\displaystyle f_{W}(x,z)=x^{T}Wz} . Scaling to higher dimensions can be achieved by enforcing a sparseness structure over the matrix model, as done with HDSL, and with COMET. == Software == metric-learn is a free software Python library which offers efficient implementations of several supervised and weakly-supervised similarity and metric learning algorithms. The API of metric-learn is compatible with scikit-learn. OpenMetricLearning is a Python framework to train and validate the models producing high-quality embeddings. == Further information == For further information on this topic, see the surveys on metric and similarity learning by Bellet et al. and Kulis.

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  Hierarchical navigable small world

  Hierarchical navigable small world (HNSW) is an algorithm for approximate nearest neighbor search. It is used to find items that are similar to a query item in a large collection, without comparing the query with every item one by one. The algorithm is commonly used for searching vector data. In these systems, an item such as a document, image, song, or user profile is represented by a list of numbers called a vector. Items with similar vectors are treated as similar according to the model that produced the vectors. HNSW provides a way to search these vectors quickly, especially in large datasets. HNSW stores vectors in a graph. Each vector is a node, and links connect it to some nearby vectors. The graph has several layers: upper layers contain fewer nodes and act like a rough map, while the bottom layer contains all nodes and gives a more detailed view. A search starts in an upper layer, follows links toward nodes that are closer to the query, and then repeats the process in lower layers until it finds a set of likely nearest neighbors. == Background == The nearest neighbor search problem asks which items in a dataset are closest to a query item. A direct search can compare the query with every item in the dataset, but this becomes slow when the dataset is large. Exact search methods based on spatial trees, such as the k-d tree and R-tree, can also become less effective for high-dimensional data, a problem often associated with the curse of dimensionality. Approximate nearest neighbor methods trade some exactness for speed or lower resource use. Instead of always guaranteeing the exact closest item, they try to return close items quickly. Other approximate methods include locality-sensitive hashing and product quantization. HNSW builds on research into small-world networks and navigable graphs. In a small-world graph, most nodes can be reached from other nodes through a short chain of links. In a navigable graph, a search procedure can use local information to move toward a target. Jon Kleinberg's work on navigation in small-world networks is an important example of this research area. Later work studied ways to add links that make graphs easier to navigate greedily. The HNSW algorithm extends earlier navigable small world methods for similarity search by adding a hierarchy of graph layers. This hierarchy helps the algorithm find a good region of the graph before doing a more detailed search in the bottom layer. == Algorithm == HNSW is based on a proximity graph. In this graph, nearby vectors are connected by edges. The algorithm uses these edges to move through the dataset, rather than scanning every vector. The graph is hierarchical. Every vector appears in the bottom layer. Some vectors are also placed in higher layers, with fewer vectors appearing as the layers go upward. The upper layers allow long-range movement across the dataset, while the lower layers allow a more detailed search near promising candidates. A typical search proceeds as follows: The search begins from an entry point in the highest layer. At each step, the algorithm looks at neighboring nodes and moves to a neighbor that is closer to the query. When it cannot find a closer neighbor in that layer, it moves down to the next layer. In the bottom layer, it explores a wider set of candidate nodes and returns the nearest candidates found. This search strategy is often described as greedy navigation. The algorithm repeatedly chooses locally better nodes, using the graph structure to approach the query point. == Construction and parameters == The HNSW graph is built incrementally. When a new vector is inserted, the algorithm assigns it a maximum layer, searches for nearby existing nodes, and connects the new node to selected neighbors in each layer where it appears. Implementations usually expose parameters that control the trade-off between speed, accuracy, memory use, and construction time. A higher number of graph connections can improve recall but requires more memory. A larger search candidate list can improve accuracy but makes queries slower. A larger construction candidate list can improve the quality of the graph but makes index building slower. Because HNSW is approximate, its results are not always identical to a full exact search. Its practical performance depends on the dataset, distance measure, implementation, and parameter settings. Benchmarking studies have found HNSW-based libraries to be strong performers among approximate nearest neighbor methods, although worst-case performance can differ from performance on common benchmark datasets. == Use in vector search systems == HNSW is used as an index in systems that store and search high-dimensional vectors. These systems include vector databases, search engines, and database extensions. Typical uses include semantic search, recommender systems, image similarity search, and retrieval-augmented generation. Several software projects implement or support HNSW. Libraries include hnswlib, which is associated with the original HNSW authors, and FAISS. Database and search systems that document HNSW support include Apache Lucene, Chroma, ClickHouse, DuckDB, MariaDB, Milvus, pgvector, Qdrant, and Redis.

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  Graphics processing unit

  A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being present either as a component on a discrete graphics card or embedded on motherboards, mobile phones, personal computers, workstations, and game consoles. GPUs are increasingly being used for artificial intelligence (AI) processing due to linear algebra acceleration, which is also used extensively in graphics processing. Although there is no single definition of the term, and it may be used to describe any video display system, in modern use a GPU includes the ability to internally perform the calculations needed for various graphics tasks, like rotating and scaling 3D images, and often the additional ability to run custom programs known as shaders. This contrasts with earlier graphics controllers known as video display controllers which had no internal calculation capabilities, or blitters, which performed only basic memory movement operations. The modern GPU emerged during the 1990s, adding the ability to perform operations like drawing lines and text without CPU help, and later adding 3D functionality. Graphics functions are generally independent and this lends these tasks to being implemented on separate calculation engines. Modern GPUs include hundreds, or thousands, of calculation units. This made them useful for non-graphic calculations involving embarrassingly parallel problems due to their parallel structure. The ability of GPUs to rapidly perform vast numbers of calculations has led to their adoption in diverse fields including artificial intelligence (AI) where they excel at handling data-intensive and computationally demanding tasks. Other non-graphical uses include the training of neural networks and cryptocurrency mining. == History == === 1960s === Dedicated 3D graphics hardware dates back to graphic terminals such as the Adage AGT-30 from 1967 with analog matrix processors. In 1969 Evans & Sutherland (E&S) introduced the Line Drawing System-1 (LDS-1), which was the first all-digital system to provide matrix multiplication. Also in 1969, the low-cost graphics terminal IMLAC PDS-1 was introduced. It later saw use as an early 3D gaming machine with the likes of Maze War. === 1970s === In professional hardware, in 1972 PLATO IV system becomes operational at the University of Illinois Urbana-Champaign. Between around 1973 and 1978, several networked multiplayer wireframe 3D games are implemented and popularized by users of the system. Also in 1972, the E&S Continuous Tone 1 (CT1) "Watkins box" system (consisting of an E&S LDS-2 and Shaded Picture System) is delivered to Case Western Reserve University. It offered the first real-time Gouraud shading. In 1975, a joint effort between Evans & Sutherland Computer Corporation and the University of Utah's computer graphics department results in the first ever MOSFET video framebuffer, capable of color and smooth shading. E&S Continuous Tone 3 (CT3) system was delivered in 1977 to Lufthansa for pilot training using computer simulation. It was the first graphics system capable of real-time texture mapping. Ikonas made graphics systems with 8- and 24-bit graphics and 3D acceleration in the late 70s. Arcade system boards have used specialized 2D graphics circuits since the 1970s. In early video game hardware, RAM for frame buffers was expensive, so video chips composited data together as the display was being scanned out on the monitor. A specialized barrel shifter circuit helped the CPU animate the framebuffer graphics for various 1970s arcade video games from Midway and Taito, such as Gun Fight (1975), Sea Wolf (1976), and Space Invaders (1978). The Namco Galaxian arcade system in 1979 used specialized graphics hardware that supported RGB color, multi-colored sprites, and tilemap backgrounds. The Galaxian hardware was widely used during the golden age of arcade video games, by game companies such as Namco, Centuri, Gremlin, Irem, Konami, Midway, Nichibutsu, Sega, and Taito. The Atari 2600 in 1977 used a video shifter called the Television Interface Adaptor. Atari 8-bit computers (1979) had ANTIC, a video processor which interpreted instructions describing a "display list"—the way the scan lines map to specific bitmapped or character modes and where the memory is stored (so there did not need to be a contiguous frame buffer). 6502 machine code subroutines could be triggered on scan lines by setting a bit on a display list instruction. ANTIC also supported smooth vertical and horizontal scrolling independent of the CPU. === 1980s === In the 1980s significant advancements were made in professional 3D graphics hardware. Perhaps most impactful was the 1981 development of the Geometry Engine, a VLSI vector processor ASIC designed by Jim Clark and Marc Hannah at Stanford University. This processor is the forerunner of modern tensor cores and other similar processors marketed for graphics and AI. The Geometry Engine went on to be used in Silicon Graphics workstations for many years. Silicon Graphics's first product, shipped in November 1983, was the IRIS 1000, a terminal with hardware-accelerated 3D graphics based on the Geometry Engine. The Geometry Engine was capable of approximately 6 million operations per second. The 1981 NEC μPD7220 was the first implementation of a personal computer graphics display processor as a single large-scale integration (LSI) integrated circuit chip. This enabled the design of low-cost, high-performance video graphics cards such as those from Number Nine Visual Technology. It became the best-known GPU until the mid-1980s. It was the first fully integrated VLSI (very large-scale integration) metal–oxide–semiconductor (NMOS) graphics display processor for PCs, supported up to 1024×1024 resolution, and laid the foundations for the PC graphics market. It was used in a number of graphics cards and was licensed for clones such as the Intel 82720, the first of Intel's graphics processing units. The Williams Electronics arcade games Robotron: 2084, Joust, Sinistar, and Bubbles, all released in 1982, contain custom blitter chips for operating on 16-color bitmaps. In 1984, Hitachi released the ARTC HD63484, the first major CMOS graphics processor for personal computers. The ARTC could display up to 4K resolution when in monochrome mode. It was used in a number of graphics cards and terminals during the late 1980s. In 1985, the Amiga was released with a custom graphics chip called Agnus including a blitter for bitmap manipulation, line drawing, and area fill. It also included a coprocessor with its own simple instruction set, that was capable of manipulating graphics hardware registers in sync with the video beam (e.g. for per-scanline palette switches, sprite multiplexing, and hardware windowing), or driving the blitter. Also in 1985, IBM released the Professional Graphics Controller, designed by later to be Nvidia co-founder Curtis Priem, which was a rudimentary 3D card with 640 × 480 256-color graphics which used a dedicated CPU to draw graphics independently of the main system. It was used as the basis of cards by a number of makers (including Matrox) and its analog RGB signaling led directly to the VGA video standard. Priem later in the 80s worked on the influential Sun Microsystems GX (also known as cgsix) accelerated 2D graphics card. In 1986, Texas Instruments released the TMS34010, the first fully programmable graphics processor. It could run general-purpose code but also had a graphics-oriented instruction set. During 1990–1992, this chip became the basis of the Texas Instruments Graphics Architecture ("TIGA") Windows accelerator cards. Following in 1987, the IBM 8514 graphics system was released. It was one of the first video cards for IBM PC compatibles that implemented fixed-function 2D primitives in electronic hardware. Sharp's X68000, released in 1987, used a custom graphics chipset with a 65,536 color palette and hardware support for sprites, scrolling, and multiple playfields. It served as a development machine for Capcom's CP System arcade board. Fujitsu's FM Towns computer, released in 1989, had support for a 16,777,216 color palette. For context, IBM also introduced its Video Graphics Array (VGA) display system in 1987, with a maximum resolution of 640 × 480 pixels. Unlike 8514/A, VGA had no hardware acceleration features. In November 1988, NEC Home Electronics announced its creation of the Video Electronics Standards Association (VESA) to develop and promote a Super VGA (SVGA) computer display standard as a successor to VGA. Super VGA enabled graphics display resolutions up to 800 × 600 pixels, a 56% increase. In 1988 SGI sold IRIS workstation graphics with 10-12 Geometry Engines and introduced the IrisVision add-in board for IBM MicroChannel bus (RS/6000) based on the Geometry Engine as well. In 1988 as well, the first dedicated polygonal 3D graphics boards in arcade machines were introduced wit

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  Digital supply chain security

  Digital supply chain security refers to efforts to enhance cyber security within the supply chain. It is a subset of supply chain security and is focused on the management of cyber security requirements for information technology systems, software and networks, which are driven by threats such as cyber-terrorism, malware, data theft and the advanced persistent threat (APT). Typical supply chain cyber security activities for minimizing risks include buying only from trusted vendors, disconnecting critical machines from outside networks, and educating users on the threats and protective measures they can take. The acting deputy undersecretary for the National Protection and Programs Directorate for the United States Department of Homeland Security, Greg Schaffer, stated at a hearing that he is aware that there are instances where malware has been found on imported electronic and computer devices sold within the United States. == Examples of supply chain cyber security threats == Network or computer hardware that is delivered with malware installed on it already. Malware that is inserted into software or hardware (by various means) Vulnerabilities in software applications and networks within the supply chain that are discovered by malicious hackers Counterfeit computer hardware == Related U.S. government efforts == Comprehensive National Cyber Initiative Defense Procurement Regulations: Noted in section 806 of the National Defense Authorization Act International Strategy for Cyberspace: White House lays out for the first time the U.S.’s vision for a secure and open Internet. The strategy outlines three main themes: diplomacy, development and defense. Diplomacy: The strategy sets out to “promote an open, interoperable, secure and reliable information and communication infrastructure” by establishing norms of acceptable state behavior built through consensus among nations. Development: Through this strategy the government seeks to “facilitate cybersecurity capacity-building abroad, bilaterally and through multilateral organizations.” The objective is to protect the global IT infrastructure and to build closer international partnerships to sustain open and secure networks. Defense: The strategy calls out that the government “will ensure that the risks associated with attacking or exploiting our networks vastly outweigh the potential benefits” and calls for all nations to investigate, apprehend and prosecute criminals and non-state actors who intrude and disrupt network systems. == Related government efforts around the world == Common Criteria offers with Evaluation Assurance Level(EAL) 4 an opportunity to evaluate all relevant aspects of the digital supply chain security like the product, the development environment, IT systems security, the processes in human resource, physical security and with the module ALC_FLR.3 (Systematic Flaw Remediation) also security update processes and methods even by physical site visits. EAL 4 is mutually recognized in countries that signed the SOGIS-MRA and up to ELA 2 in countries the signed the CCRA but including ALC_FRL.3. Russia: Russia has had non-disclosed functionality certification requirements for several years and has recently initiated the National Software Platform effort based on open-source software. This reflects the apparent desire for national autonomy, reducing dependence on foreign suppliers. India: Recognition of supply chain risk in its draft National Cybersecurity Strategy. Rather than targeting specific products for exclusion, it is considering Indigenous Innovation policies, giving preferences to domestic ITC suppliers in order to create a robust, globally competitive national presence in the sector. China: Deriving from goals in the 11th Five Year Plan (2006–2010), China introduced and pursued a mix of security-focused and aggressive Indigenous Innovation policies. China is requiring an indigenous innovation product catalog be used for its government procurement and implementing a Multi-level Protection Scheme (MLPS) which requires (among other things) product developers and manufacturers to be Chinese citizens or legal persons, and product core technology and key components must have independent Chinese or indigenous intellectual property rights. == Private sector efforts == SLSA (Supply-chain Levels for Software Artifacts) is an end-to-end framework for ensuring the integrity of software artifacts throughout the software supply chain. The requirements are inspired by Google’s internal "Binary Authorization for Borg" that has been in use for the past 8+ years and that is mandatory for all of Google's production workloads. The goal of SLSA is to improve the state of the industry, particularly open source, to defend against the most pressing integrity threats. With SLSA, consumers can make informed choices about the security posture of the software they consume. == Other references == Financial Sector Information Sharing and Analysis Center International Strategy for Cyberspace (from the White House) NSTIC SafeCode Whitepaper Archived 2013-10-21 at the Wayback Machine Trusted Technology Forum and the Open Trusted Technology Provider Standard (O-TTPS) Archived 2012-01-03 at the Wayback Machine Cyber Supply Chain Security Solution Malware Implants in Firmware Supply Chain in the Software Era INFORMATION AND COMMUNICATIONS TECHNOLOGY SUPPLY CHAIN RISK MANAGEMENT TASK FORCE: INTERIM REPORT

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  NASA AI Assisted-Air Quality Monitoring Project

  The NASA Expert-System Ion Trap Mass Spectrometer (ES-ITMS) Project was a public-private partnership to develop an artificial intelligence assisted, air quality monitoring system and was qualified for use on the Space Shuttle. The partnership was also the first cost and intellectual property shared public-partnership implemented by NASA, which used the commercial Research and Development Limited Partnership (RDLP) model that had been adopted by the Reagan Administration for Department of Defense semiconductor development, and recommended for use by NASA for space commercialization. The project partners included NASA, the University of Florida and Finnigan MAT Corporation, was organized and administered by the NASA Joint Enterprise Institute (subsequently NASA Joint Sponsored Program) and ran from 1988 through 1990. The partnership concluded final testing in 1991, generating four patents, expert system software and application protocol reports. The system was space qualified for use on the Shuttle and elements of the ES-ITMS system were integrated into the product Improvements for Finnigan MAT corporation. The success of the partnership lead NASA to create a pilot program to develop partnership business models as an ongoing management practice. == Purpose and objectives == The need to monitor air quality in confined spaces represented an increasing challenge for NASA's planned space missions and private sector facility managers facing the increased scrutiny of possible air contaminants. Up to the early 1980's, air quality monitors generally required large spaces and human technicians to interpret readings. This created a need for miniaturized air quality monitors that could generate reliable and accurate analytic results without on-site technician presence. NASA initiated projects to develop..."mobile and/or portable mass spectrometers" that evaluated the "tradeoff between instrumentation capabilities and space, weight and power considerations." NASA selected a "commercial ITMS instrument capable of generating electron ionization, chemical ionization and mass spectrometry data", to develop a linked expert system to accomplish analysis without human intervention. The commercial instrumentation was from Finnigan MAT corporation while the scientific expertise to support expert system development was available at the University of Florida. The project managers at NASA Ames created a single, integrated project using the RDLP model with objectives to: Develop AI/expert system software for instrument control (NASA's role) Expand sensitivity, selectivity and speed of the spectrometer (Univ Florida role) Expand the spectrometer analytic capability and automate the screening (Finnigan role) == Membership == The partnership included seven specialists from five member organizations: Federal Government National Aeronautics and Space Administration (NASA) NASA Ames Research Center (ARC) NASA Kennedy Space Center (KSC) Commercial Finnigan MAT Corporation (Thermo-Fisher Scientific) TGS Technology, Inc. Research Management University of Florida == Organization, management and administration == The technical project was organized into two development teams, one located in at the NASA Ames Research Center covering expert systems and analytic capabilities and one in Florida covering improved sensitivity and testing. The partnership management and administration was provided by a non-profit, partnership support organization: the Joint Enterprise Institute operating through San Francisco State University Foundation (SFSUF) with a NASA employee liaison, Syed Shariq. == Public-private partnership == The partnership structure was as a prototype test of a pilot NASA program to develop public-private partnership business models. The pilot program was known as the NASA Joint Sponsored Research Program (JSRP), which operated as the NASA Joint Enterprise Institute between 1988 and 1991. The partnership was the first public-private, research and development partnership implemented by NASA in response to national policy shifts to increase technology transfer and space commercialization. The partnership structure included a two year technology development and testing plan that cost $610,000, of which NASA funded $310,000, Finnigan $175,000 and the University of Florida $95,000. == Results and commercialization == The project generated patents (4), software (2) and application protocol reports (8). NASA gained use of the patents and jointly development software while Finnigan received commercial utilization rights. The results were commercialized within eighteen months of project completion. == Recognition == NASA recognized the project as a space qualified instrument. Its achievements were reported to the NASA Administrator, directly leading to establishment of the agency-wide Joint Sponsored Research Program.

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  Spreading activation

  Spreading activation is a method for searching associative networks, biological and artificial neural networks, or semantic networks. The search process is initiated by labeling a set of source nodes (e.g. concepts in a semantic network) with weights or "activation" and then iteratively propagating or "spreading" that activation out to other nodes linked to the source nodes. Most often these "weights" are real values that decay as activation propagates through the network. When the weights are discrete this process is often referred to as marker passing. Activation may originate from alternate paths, identified by distinct markers, and terminate when two alternate paths reach the same node. However brain studies show that several different brain areas play an important role in semantic processing. Spreading activation in semantic networks as a model were invented in cognitive psychology to model the fan out effect. Spreading activation can also be applied in information retrieval, by means of a network of nodes representing documents and terms contained in those documents. == Cognitive psychology == As it relates to cognitive psychology, spreading activation is the theory of how the brain iterates through a network of associated ideas to retrieve specific information. The spreading activation theory presents the array of concepts within our memory as cognitive units, each consisting of a node and its associated elements or characteristics, all connected together by edges. A spreading activation network can be represented schematically, in a sort of web diagram with shorter lines between two nodes meaning the ideas are more closely related and will typically be associated more quickly to the original concept. In memory psychology, the spreading activation model holds that people organize their knowledge of the world based on their personal experiences, which in turn form the network of ideas that is the person's knowledge of the world. When a word (the target) is preceded by an associated word (the prime) in word recognition tasks, participants seem to perform better in the amount of time that it takes them to respond. For instance, subjects respond faster to the word "doctor" when it is preceded by "nurse" than when it is preceded by an unrelated word like "carrot". This semantic priming effect with words that are close in meaning within the cognitive network has been seen in a wide range of tasks given by experimenters, ranging from sentence verification to lexical decision and naming. As another example, if the original concept is "red" and the concept "vehicles" is primed, they are much more likely to say "fire engine" instead of something unrelated to vehicles, such as "cherries". If instead "fruits" was primed, they would likely name "cherries" and continue on from there. The activation of pathways in the network has everything to do with how closely linked two concepts are by meaning, as well as how a subject is primed. == Algorithm == A directed graph is populated by Nodes[ 1...N ] each having an associated activation value A [ i ] which is a real number in the range [0.0 ... 1.0]. A Link[ i, j ] connects source node[ i ] with target node[ j ]. Each edge has an associated weight W [ i, j ] usually a real number in the range [0.0 ... 1.0]. Parameters: Firing threshold F, a real number in the range [0.0 ... 1.0] Decay factor D, a real number in the range [0.0 ... 1.0] Steps: Initialize the graph setting all activation values A [ i ] to zero. Set one or more origin nodes to an initial activation value greater than the firing threshold F. A typical initial value is 1.0. For each unfired node [ i ] in the graph having an activation value A [ i ] greater than the node firing threshold F: For each Link [ i, j ] connecting the source node [ i ] with target node [ j ], adjust A [ j ] = A [ j ] + (A [ i ] W [ i, j ] D) where D is the decay factor. If a target node receives an adjustment to its activation value so that it would exceed 1.0, then set its new activation value to 1.0. Likewise maintain 0.0 as a lower bound on the target node's activation value should it receive an adjustment to below 0.0. Once a node has fired it may not fire again, although variations of the basic algorithm permit repeated firings and loops through the graph. Nodes receiving a new activation value that exceeds the firing threshold F are marked for firing on the next spreading activation cycle. If activation originates from more than one node, a variation of the algorithm permits marker passing to distinguish the paths by which activation is spread over the graph The procedure terminates when either there are no more nodes to fire or in the case of marker passing from multiple origins, when a node is reached from more than one path. Variations of the algorithm that permit repeated node firings and activation loops in the graph, terminate after a steady activation state, with respect to some delta, is reached, or when a maximum number of iterations is exceeded. == Examples ==

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  80 Million Tiny Images

  80 Million Tiny Images is a dataset intended for training machine-learning systems constructed by Antonio Torralba, Rob Fergus, and William T. Freeman in a collaboration between MIT and New York University. It was published in 2008. The dataset has size 760 GB. It contains 79,302,017 32×32-pixel color images, scaled down from images scraped from the World Wide Web over 8 months. The images are classified into 75,062 classes. Each class is a non-abstract noun in WordNet. Images may appear in more than one class. The dataset was motivated by non-parametric models of neural activations in the visual cortex upon seeing images. The CIFAR-10 dataset uses a subset of the images in this dataset, but with independently generated labels, as the original labels were not reliable. The CIFAR-10 set has 6000 examples of each of 10 classes, and the CIFAR-100 set has 600 examples of each of 100 non-overlapping classes. == Construction == It was first reported in a technical report in April 2007, during the middle of the construction process, when there were only 73 million images. The full dataset was published in 2008. They began with all 75,846 non-abstract nouns in WordNet, and then for each of these nouns, they scraped 7 image search engines: Altavista, Ask.com, Flickr, Cydral, Google, Picsearch, and Webshots. After 8 months of scraping, they obtained 97,245,098 images. Since they did not have enough storage, they downsized the images to 32×32 as they were scraped. After gathering, they removed images with zero variance and intra-word duplicate images, resulting in the final dataset. Out of the 75,846 nouns, only 75,062 classes had any results, so the other nouns did not appear in the final dataset. The number of images per noun follows a Zipf-like distribution, with 1056 images per noun on average. To prevent a few nouns taking up too many images, they put an upper bound of at most 3000 images per noun. == Retirement == The 80 Million Tiny Images dataset was retired from use by its creators in 2020, after a paper by researchers Abeba Birhane and Vinay Prabhu found that some of the labeling of several publicly available image datasets, including 80 Million Tiny Images, contained racist and misogynistic slurs which were causing models trained on them to exhibit racial and sexual bias. The dataset also contained offensive images. Following the release of the paper, the dataset's creators removed the dataset from distribution, and requested that other researchers not use it for further research and to delete their copies of the dataset.

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  Kernel density estimation

  In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy. == Definition == Let x = ( x 1 , x 2 , x 3 , . . . ) {\displaystyle \mathbf {x} =\left(x_{1},x_{2},x_{3},...\right)} be independent and identically distributed samples drawn from some univariate distribution with an unknown density f at any given point x. We are interested in estimating the shape of this function f. Its kernel density estimator is f ^ h ( x ) = 1 n ∑ i = 1 n K h ( x − x i ) = 1 n h ∑ i = 1 n K ( x − x i h ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}K_{h}(x-x_{i})={\frac {1}{nh}}\sum _{i=1}^{n}K{\left({\frac {x-x_{i}}{h}}\right)},} where K is the kernel — a non-negative function — and h > 0 is a smoothing parameter called the bandwidth or simply width. A kernel with subscript h is called the scaled kernel and defined as Kh(x) = ⁠1/h⁠ K(⁠x/h⁠). Intuitively one wants to choose h as small as the data will allow; however, there is always a trade-off between the bias of the estimator and its variance. The choice of bandwidth is discussed in more detail below. A range of kernel functions are commonly used: uniform, triangular, biweight, triweight, Epanechnikov (parabolic), normal, and others. The Epanechnikov kernel is optimal in a mean square error sense, though the loss of efficiency is small for the kernels listed previously. Due to its convenient mathematical properties, the normal kernel is often used, which means K(x) = ϕ(x), where ϕ is the standard normal density function. The kernel density estimator then becomes f ^ h ( x ) = 1 n ∑ i = 1 n 1 h 2 π exp ⁡ ( − ( x − x i ) 2 2 h 2 ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}{\frac {1}{h{\sqrt {2\pi }}}}\exp \left({\frac {-(x-x_{i})^{2}}{2h^{2}}}\right),} where h {\displaystyle h} is the standard deviation of the sample x {\displaystyle \mathbf {x} } . The construction of a kernel density estimate finds interpretations in fields outside of density estimation. For example, in thermodynamics, this is equivalent to the amount of heat generated when heat kernels (the fundamental solution to the heat equation) are placed at each data point locations xi. Similar methods are used to construct discrete Laplace operators on point clouds for manifold learning (e.g. diffusion map). == Example == Kernel density estimates are closely related to histograms, but can be endowed with properties such as smoothness or continuity by using a suitable kernel. The diagram below based on these 6 data points illustrates this relationship: For the histogram, first, the horizontal axis is divided into sub-intervals or bins which cover the range of the data: In this case, six bins each of width 2. Whenever a data point falls inside this interval, a box of height 1/12 is placed there. If more than one data point falls inside the same bin, the boxes are stacked on top of each other. For the kernel density estimate, normal kernels with a standard deviation of 1.5 (indicated by the red dashed lines) are placed on each of the data points xi. The kernels are summed to make the kernel density estimate (solid blue curve). The smoothness of the kernel density estimate (compared to the discreteness of the histogram) illustrates how kernel density estimates converge faster to the true underlying density for continuous random variables. == Bandwidth selection == The bandwidth of the kernel is a free parameter which exhibits a strong influence on the resulting estimate. To illustrate its effect, we take a simulated random sample from the standard normal distribution (plotted at the blue spikes in the rug plot on the horizontal axis). The grey curve is the true density (a normal density with mean 0 and variance 1). In comparison, the red curve is undersmoothed since it contains too many spurious data artifacts arising from using a bandwidth h = 0.05, which is too small. The green curve is oversmoothed since using the bandwidth h = 2 obscures much of the underlying structure. The black curve with a bandwidth of h = 0.337 is considered to be optimally smoothed since its density estimate is close to the true density. An extreme situation is encountered in the limit h → 0 {\displaystyle h\to 0} (no smoothing), where the estimate is a sum of n delta functions centered at the coordinates of analyzed samples. In the other extreme limit h → ∞ {\displaystyle h\to \infty } the estimate retains the shape of the used kernel, centered on the mean of the samples (completely smooth). The most common optimality criterion used to select this parameter is the expected L2 risk function, also termed the mean integrated squared error: MISE ⁡ ( h ) = E [ ∫ ( f ^ h ( x ) − f ( x ) ) 2 d x ] {\displaystyle \operatorname {MISE} (h)=\operatorname {E} \!\left[\int \!{\left({\hat {f}}\!_{h}(x)-f(x)\right)}^{2}dx\right]} Under weak assumptions on f and K, (f is the, generally unknown, real density function), MISE ⁡ ( h ) = AMISE ⁡ ( h ) + o ( ( n h ) − 1 + h 4 ) {\displaystyle \operatorname {MISE} (h)=\operatorname {AMISE} (h)+{\mathcal {o}}{\left((nh)^{-1}+h^{4}\right)}} where o is the little o notation, and n the sample size (as above). The AMISE is the asymptotic MISE, i. e. the two leading terms, AMISE ⁡ ( h ) = R ( K ) n h + 1 4 m 2 ( K ) 2 h 4 R ( f ″ ) {\displaystyle \operatorname {AMISE} (h)={\frac {R(K)}{nh}}+{\frac {1}{4}}m_{2}(K)^{2}h^{4}R(f'')} where R ( g ) = ∫ g ( x ) 2 d x {\textstyle R(g)=\int g(x)^{2}\,dx} for a function g, m 2 ( K ) = ∫ x 2 K ( x ) d x {\textstyle m_{2}(K)=\int x^{2}K(x)\,dx} and f ″ {\displaystyle f''} is the second derivative of f {\displaystyle f} and K {\displaystyle K} is the kernel. The minimum of this AMISE is the solution to this differential equation ∂ ∂ h AMISE ⁡ ( h ) = − R ( K ) n h 2 + m 2 ( K ) 2 h 3 R ( f ″ ) = 0 {\displaystyle {\frac {\partial }{\partial h}}\operatorname {AMISE} (h)=-{\frac {R(K)}{nh^{2}}}+m_{2}(K)^{2}h^{3}R(f'')=0} or h AMISE = R ( K ) 1 / 5 m 2 ( K ) 2 / 5 R ( f ″ ) 1 / 5 n − 1 / 5 = C n − 1 / 5 {\displaystyle h_{\operatorname {AMISE} }={\frac {R(K)^{1/5}}{m_{2}(K)^{2/5}R(f'')^{1/5}}}n^{-1/5}=Cn^{-1/5}} Neither the AMISE nor the hAMISE formulas can be used directly since they involve the unknown density function f {\displaystyle f} or its second derivative f ″ {\displaystyle f''} . To overcome that difficulty, a variety of automatic, data-based methods have been developed to select the bandwidth. Several review studies have been undertaken to compare their efficacies, with the general consensus that the plug-in selectors and cross validation selectors are the most useful over a wide range of data sets. Substituting any bandwidth h which has the same asymptotic order n−1/5 as hAMISE into the AMISE gives that AMISE(h) = O(n−4/5), where O is the big O notation. It can be shown that, under weak assumptions, there cannot exist a non-parametric estimator that converges at a faster rate than the kernel estimator. Note that the n−4/5 rate is slower than the typical n−1 convergence rate of parametric methods. If the bandwidth is not held fixed, but is varied depending upon the location of either the estimate (balloon estimator) or the samples (pointwise estimator), this produces a particularly powerful method termed adaptive or variable bandwidth kernel density estimation. Bandwidth selection for kernel density estimation of heavy-tailed distributions is relatively difficult. === A rule-of-thumb bandwidth estimator === If Gaussian basis functions are used to approximate univariate data, and the underlying density being estimated is Gaussian, the optimal choice for h (that is, the bandwidth that minimises the mean integrated squared error) is: h = ( 4 σ ^ 5 3 n ) 1 / 5 ≈ 1.06 σ ^ n − 1 / 5 , {\displaystyle h={\left({\frac {4{\hat {\sigma }}^{5}}{3n}}\right)}^{1/5}\approx 1.06\,{\hat {\sigma }}\,n^{-1/5},} An h {\displaystyle h} value is considered more robust when it improves the fit for long-tailed and skewed distributions or for bimodal mixture distributions. This is often done empirically by replacing the standard deviation σ ^ {\displaystyle {\hat {\sigma }}} by the parameter A {\displaystyle A} below: A = min ( σ ^ , I Q R 1.34 ) {\displaystyle A=\min \left({\hat {\sigma }},{\frac {\mathrm {IQR} }{1.34}}\right)} where IQR is the

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  Learnable function class

  In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms. == Definition == === Background === Let Ω = X × Y = { ( x , y ) } {\displaystyle \Omega ={\mathcal {X}}\times {\mathcal {Y}}=\{(x,y)\}} be the sample space, where y {\displaystyle y} are the labels and x {\displaystyle x} are the covariates (predictors). F = { f : X ↦ Y } {\displaystyle {\mathcal {F}}=\{f:{\mathcal {X}}\mapsto {\mathcal {Y}}\}} is a collection of mappings (functions) under consideration to link x {\displaystyle x} to y {\displaystyle y} . L : Y × Y ↦ R {\displaystyle L:{\mathcal {Y}}\times {\mathcal {Y}}\mapsto \mathbb {R} } is a pre-given loss function (usually non-negative). Given a probability distribution P ( x , y ) {\displaystyle P(x,y)} on Ω {\displaystyle \Omega } , define the expected risk I P ( f ) {\displaystyle I_{P}(f)} to be: I P ( f ) = ∫ L ( f ( x ) , y ) d P ( x , y ) {\displaystyle I_{P}(f)=\int L(f(x),y)dP(x,y)} The general goal in statistical learning is to find the function in F {\displaystyle {\mathcal {F}}} that minimizes the expected risk. That is, to find solutions to the following problem: f ^ = arg ⁡ min f ∈ F I P ( f ) {\displaystyle {\hat {f}}=\arg \min _{f\in {\mathcal {F}}}I_{P}(f)} But in practice the distribution P {\displaystyle P} is unknown, and any learning task can only be based on finite samples. Thus we seek instead to find an algorithm that asymptotically minimizes the empirical risk, i.e., to find a sequence of functions { f ^ n } n = 1 ∞ {\displaystyle \{{\hat {f}}_{n}\}_{n=1}^{\infty }} that satisfies lim n → ∞ P ( I P ( f ^ n ) − inf f ∈ F I P ( f ) > ϵ ) = 0 {\displaystyle \lim _{n\rightarrow \infty }\mathbb {P} (I_{P}({\hat {f}}_{n})-\inf _{f\in {\mathcal {F}}}I_{P}(f)>\epsilon )=0} One usual algorithm to find such a sequence is through empirical risk minimization. === Learnable function class === We can make the condition given in the above equation stronger by requiring that the convergence is uniform for all probability distributions. That is: The intuition behind the more strict requirement is as such: the rate at which sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} converges to the minimizer of the expected risk can be very different for different P ( x , y ) {\displaystyle P(x,y)} . Because in real world the true distribution P {\displaystyle P} is always unknown, we would want to select a sequence that performs well under all cases. However, by the no free lunch theorem, such a sequence that satisfies (1) does not exist if F {\displaystyle {\mathcal {F}}} is too complex. This means we need to be careful and not allow too "many" functions in F {\displaystyle {\mathcal {F}}} if we want (1) to be a meaningful requirement. Specifically, function classes that ensure the existence of a sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} that satisfies (1) are known as learnable classes. It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies (1). Thus in these settings not only do we know that the problem posed by (1) is solvable, we also immediately have an algorithm that gives the solution. == Interpretations == If the true relationship between y {\displaystyle y} and x {\displaystyle x} is y ∼ f ∗ ( x ) {\displaystyle y\sim f^{}(x)} , then by selecting the appropriate loss function, f ∗ {\displaystyle f^{}} can always be expressed as the minimizer of the expected loss across all possible functions. That is, f ∗ = arg ⁡ min f ∈ F ∗ I P ( f ) {\displaystyle f^{}=\arg \min _{f\in {\mathcal {F}}^{}}I_{P}(f)} Here we let F ∗ {\displaystyle {\mathcal {F}}^{}} be the collection of all possible functions mapping X {\displaystyle {\mathcal {X}}} onto Y {\displaystyle {\mathcal {Y}}} . f ∗ {\displaystyle f^{}} can be interpreted as the actual data generating mechanism. However, the no free lunch theorem tells us that in practice, with finite samples we cannot hope to search for the expected risk minimizer over F ∗ {\displaystyle {\mathcal {F}}^{}} . Thus we often consider a subset of F ∗ {\displaystyle {\mathcal {F}}^{}} , F {\displaystyle {\mathcal {F}}} , to carry out searches on. By doing so, we risk that f ∗ {\displaystyle f^{}} might not be an element of F {\displaystyle {\mathcal {F}}} . This tradeoff can be mathematically expressed as In the above decomposition, part ( b ) {\displaystyle (b)} does not depend on the data and is non-stochastic. It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to put enough restrictions on F {\displaystyle {\mathcal {F}}} will cause it to be not learnable, and part ( a ) {\displaystyle (a)} will not stochastically converge to 0. This is the well-known overfitting problem in statistics and machine learning literature. == Example: Tikhonov regularization == A good example where learnable classes are used is the so-called Tikhonov regularization in reproducing kernel Hilbert space (RKHS). Specifically, let F ∗ {\displaystyle {\mathcal {F^{}}}} be an RKHS, and | | ⋅ | | 2 {\displaystyle ||\cdot ||_{2}} be the norm on F ∗ {\displaystyle {\mathcal {F^{}}}} given by its inner product. It is shown in that F = { f : | | f | | 2 ≤ γ } {\displaystyle {\mathcal {F}}=\{f:||f||_{2}\leq \gamma \}} is a learnable class for any finite, positive γ {\displaystyle \gamma } . The empirical minimization algorithm to the dual form of this problem is arg ⁡ min f ∈ F ∗ { ∑ i = 1 n L ( f ( x i ) , y i ) + λ | | f | | 2 } {\displaystyle \arg \min _{f\in {\mathcal {F}}^{}}\left\{\sum _{i=1}^{n}L(f(x_{i}),y_{i})+\lambda ||f||_{2}\right\}} This was first introduced by Tikhonov to solve ill-posed problems. Many statistical learning algorithms can be expressed in such a form (for example, the well-known ridge regression). The tradeoff between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in (2) is geometrically more intuitive with Tikhonov regularization in RKHS. We can consider a sequence of { F γ } {\displaystyle \{{\mathcal {F}}_{\gamma }\}} , which are essentially balls in F ∗ {\displaystyle {\mathcal {F^{}}}} with centers at 0. As γ {\displaystyle \gamma } gets larger, F γ {\displaystyle {\mathcal {F}}_{\gamma }} gets closer to the entire space, and ( b ) {\displaystyle (b)} is likely to become smaller. However we will also suffer smaller convergence rates in ( a ) {\displaystyle (a)} . The way to choose an optimal γ {\displaystyle \gamma } in finite sample settings is usually through cross-validation. == Relationship to empirical process theory == Part ( a ) {\displaystyle (a)} in (2) is closely linked to empirical process theory in statistics, where the empirical risk { ∑ i = 1 n L ( y i , f ( x i ) ) , f ∈ F } {\displaystyle \{\sum _{i=1}^{n}L(y_{i},f(x_{i})),f\in {\mathcal {F}}\}} are known as empirical processes. In this field, the function class F {\displaystyle {\mathcal {F}}} that satisfies the stochastic convergence are known as uniform Glivenko–Cantelli classes. It has been shown that under certain regularity conditions, learnable classes and uniformly Glivenko-Cantelli classes are equivalent. Interplay between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in statistics literature is often known as the bias-variance tradeoff. However, note that in the authors gave an example of stochastic convex optimization for General Setting of Learning where learnability is not equivalent with uniform convergence.

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  Agentive logic

  Agentive logic (also called the logic of action or logic of agency) is the field of philosophical logic and logic in computer science that studies formal representations of agents, their actions, and their abilities. An agentive logic in the narrower sense is a formal system whose primitive operators express that an agent does something, can do something, or sees to it that something is the case. Agentive logics generalise modal logic by adding modalities indexed to agents and to actions. Typical examples include: STIT logics (from sees to it that) with operators of the form [ i s t i t : φ ] {\displaystyle [i\ {\mathsf {stit}}:\varphi ]} meaning that agent i {\displaystyle i} sees to it that φ {\displaystyle \varphi } holds; dynamic logics of action with program-like modalities [ α ] φ {\displaystyle [\alpha ]\varphi } and ⟨ α ⟩ φ {\displaystyle \langle \alpha \rangle \varphi } meaning, roughly, that after every (respectively, some) execution(s) of action α {\displaystyle \alpha } , φ {\displaystyle \varphi } holds; logics with explicit agentive operators such as "can do", "brings about", or "is able to ensure". Agentive logics are used in action theory in philosophy, in the semantics of natural language, in the theory of program verification, and in artificial intelligence, where they underpin formalisms for reasoning about actions, planning, and intelligent agents. == Terminology and scope == The adjective agentive derives from the Latin agens ("one who acts") and originally referred to the grammatical agent of a verb. In logical contexts it designates operators or predicates whose primary argument position is an agent rather than a proposition alone, for example A i φ {\displaystyle A_{i}\varphi } ("agent i {\displaystyle i} does φ {\displaystyle \varphi } ") or C i φ {\displaystyle C_{i}\varphi } ("agent i {\displaystyle i} can bring about φ {\displaystyle \varphi } "). In contemporary literature, agentive logic is sometimes used narrowly for formal reconstructions of St. Anselm's modal account of facere ("to do"). More broadly, the term is used interchangeably with logic of action or logic of agency to cover a family of modal and dynamic logics designed to capture the structure of action and choice. == Historical background == === Medieval and early modern roots === Medieval logicians already explored analogies between modalities of action and alethic modalities such as possibility and necessity, for instance, in discussions of obligation and power. An influential early agentive analysis is due to St. Anselm (11th century), who treated "doing φ {\displaystyle \varphi } " as a kind of modal operator on propositions, anticipating later modal logics of agency. Modern reconstructions of Anselm's theory show that the resulting "agentive logic" can be modelled with neighbourhood semantics and satisfies a recognisable square of opposition. === Modern logic of action === Modern study of the logic of action began in the mid-20th century, parallel to developments in deontic logic and tense logic. Early systems were proposed by Georg Henrik von Wright, Stig Kanger, and others, often motivated by questions about norms and responsibility. From the 1960s onward, two largely independent but eventually converging traditions emerged: a branching-time tradition, culminating in STIT logics, emphasising agents' choices among possible futures; and dynamic logics of programs and actions, developed within computer science to reason about program execution. In the 1990s and 2000s, action logics were further developed in connection with knowledge representation, planning, and multi-agent systems in AI, and with dynamic and update semantics in linguistics. == Core ideas == Despite their diversity, most agentive logics share some general themes: Agents are treated as explicit indices of modal operators, as in [ i d o e s ] φ {\displaystyle [i\ {\mathsf {does}}]\varphi } or C i φ {\displaystyle C_{i}\varphi } . Actions are represented either implicitly, via changes between possible worlds along an accessibility relation, or explicitly, as terms denoting primitive and composite actions. Choice and ability are captured by modalities describing what an agent can ensure, usually relative to assumptions about the environment and other agents. Formal properties such as closure under composition, interaction between different agents, and connections to obligation (what an agent ought to do) and knowledge (what an agent knows how to do) are investigated. == STIT logics == STIT ("sees to it that") logics, originating in work by Nuel Belnap and collaborators, treat agency in a branching-time framework. A STIT model consists of a partially ordered set of moments with a tree-like structure, sets of histories (maximal branches through the tree), and for each agent at each moment, a partition of the histories through that moment representing the choices available to the agent. Intuitively, an agent's action at a moment determines which equivalence class (choice cell) of histories becomes actual; a formula [ i s t i t : φ ] {\displaystyle [i\ {\mathsf {stit}}:\varphi ]} is true at a history–moment pair if φ {\displaystyle \varphi } holds on all histories in the choice cell corresponding to the agent's current action. Different STIT operators have been distinguished, notably: the Chellas STIT operator, often written [ i c s t i t : φ ] {\displaystyle [i\ {\mathsf {cstit}}:\varphi ]} , which requires only that the agent's choice guarantees φ {\displaystyle \varphi } ; and the deliberative STIT operator, [ i d s t i t : φ ] {\displaystyle [i\ {\mathsf {dstit}}:\varphi ]} , which additionally requires that φ {\displaystyle \varphi } is not already historically necessary. STIT frameworks have been extended with group agency operators, temporal modalities, epistemic operators, and deontic operators to study responsibility, collective action, and obligations under indeterminism. == Dynamic logics of action == Dynamic logic was originally developed to reason about the behaviour of computer programs, treating program execution as a kind of action. In propositional dynamic logic (PDL), action terms α , β , … {\displaystyle \alpha ,\beta ,\dots } denote abstract programs or actions, and formulas of the form [ α ] φ {\displaystyle [\alpha ]\varphi } and ⟨ α ⟩ φ {\displaystyle \langle \alpha \rangle \varphi } express that all, respectively some, terminating executions of α {\displaystyle \alpha } lead to states where φ {\displaystyle \varphi } holds. From the standpoint of agentive logic, dynamic logic provides: a language for building complex actions from primitives via sequencing, choice, and iteration (e.g., α ; β {\displaystyle \alpha ;\beta } , α ∪ β {\displaystyle \alpha \cup \beta } , α ∗ {\displaystyle \alpha ^{}} ); a Kripke semantics in which actions correspond to labelled accessibility relations; and proof systems (such as Hoare logic and weakest precondition calculi) for reasoning about the correctness of action sequences. Extensions such as concurrent dynamic logic add operators for parallel composition, allowing reasoning about interacting processes and concurrent actions. John-Jules Ch. Meyer and others have argued that dynamic logic is a natural base for logics of agents, by adding modalities for knowledge, belief, and ability on top of the action modalities. Dynamic logics have also been applied to normative reasoning, yielding dynamic deontic logics where actions are related to obligations and permissions, and to dynamic epistemic logics in which information-changing actions such as announcements are modelled as programs. == Situation calculus and other action formalisms == In artificial intelligence, reasoning about action and change is often based on first-order languages that explicitly represent situations, events, and fluents (time-varying properties). The best known is situation calculus, introduced by John McCarthy and developed extensively by Raymond Reiter. In such formalisms: action terms name primitive actions; a function symbol (often d o {\displaystyle {\mathsf {do}}} ) maps an action and a situation to a successor situation; and axioms describe which fluents hold in which situations and how actions change them. Reiter's successor state axioms give compact specifications of how each fluent changes under all actions, and precondition axioms specify when actions are possible. Related formalisms include the event calculus and fluent calculus, which provide alternative ways of representing events and their effects. While these systems are often first-order rather than modal, they are closely related to agentive logics: their action terms and transition structures can be seen as providing models for dynamic or STIT-style modalities, and conversely, dynamic logics can be used as abstract specification languages for such AI formalisms. == Ability, agency, and related modalities == Many agentive logics introduce explicit operators for ability or "can-do"

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