Types of neural networks (NN) include a family of techniques. The simplest types have static components, including number of units, number of layers, unit weights and topology. Dynamic NNs evolve via learning. Some types allow/require learning to be "supervised" by the operator, while others operate independently. Some types operate purely in hardware, while others are purely software and run on general purpose computers. The main types are: Transformers: these use attention to analyze every token in the input stream against every other token in the stream. That technique has enabled neural networks to reach the general public via chatbots, code generators and many other forms. Convolutional neural networks (CNN): a FNN that uses kernels and regularization to evade problems in prior generations of NNs. They are typically used to analyze visual and other two-dimensional data. Generative adversarial networks set networks (of varying structure) against each other, each trying to push the other(s) to produce better results such as winning a game or to deceive the opponent about the authenticity of an input. == Feedforward == In feedforward neural networks the information moves from the input to output directly in every layer. There can be hidden layers with or without cycles/loops to sequence inputs. Feedforward networks can be constructed with various types of units, such as binary McCulloch–Pitts neurons, the simplest of which is the perceptron. Continuous neurons, frequently with sigmoidal activation, are used in the context of backpropagation. == Group method of data handling == The Group Method of Data Handling (GMDH) features fully automatic structural and parametric model optimization. The node activation functions are Kolmogorov–Gabor polynomials that permit additions and multiplications. It uses a deep multilayer perceptron with eight layers. It is a supervised learning network that grows layer by layer, where each layer is trained by regression analysis. Useless items are detected using a validation set, and pruned through regularization. The size and depth of the resulting network depends on the task. == Autoencoder == An autoencoder, autoassociator or Diabolo network is similar to the multilayer perceptron (MLP) – with an input layer, an output layer and one or more hidden layers connecting them. However, the output layer has the same number of units as the input layer. Its purpose is to reconstruct its own inputs (instead of emitting a target value). Therefore, autoencoders are unsupervised learning models. An autoencoder is used for unsupervised learning of efficient codings, typically for the purpose of dimensionality reduction and for learning generative models of data. == Probabilistic == A probabilistic neural network (PNN) is a four-layer feedforward neural network. The layers are Input, hidden pattern, hidden summation, and output. In the PNN algorithm, the parent probability distribution function (PDF) of each class is approximated by a Parzen window and a non-parametric function. Then, using PDF of each class, the class probability of a new input is estimated and Bayes’ rule is employed to allocate it to the class with the highest posterior probability. It was derived from the Bayesian network and a statistical algorithm called Kernel Fisher discriminant analysis. It is used for classification and pattern recognition. == Time delay == A time delay neural network (TDNN) is a feedforward architecture for sequential data that recognizes features independent of sequence position. In order to achieve time-shift invariance, delays are added to the input so that multiple data points (points in time) are analyzed together. It usually forms part of a larger pattern recognition system. It has been implemented using a perceptron network whose connection weights were trained with back propagation (supervised learning). == Convolutional == A convolutional neural network (CNN, or ConvNet or shift invariant or space invariant) is a class of deep network, composed of one or more convolutional layers with fully connected layers (matching those in typical ANNs) on top. It uses tied weights and pooling layers. In particular, max-pooling. It is often structured via Fukushima's convolutional architecture. They are variations of multilayer perceptrons that use minimal preprocessing. This architecture allows CNNs to take advantage of the 2D structure of input data. Its unit connectivity pattern is inspired by the organization of the visual cortex. Units respond to stimuli in a restricted region of space known as the receptive field. Receptive fields partially overlap, over-covering the entire visual field. Unit response can be approximated mathematically by a convolution operation. CNNs are suitable for processing visual and other two-dimensional data. They have shown superior results in both image and speech applications. They can be trained with standard backpropagation. CNNs are easier to train than other regular, deep, feed-forward neural networks and have many fewer parameters to estimate. Capsule Neural Networks (CapsNet) add structures called capsules to a CNN and reuse output from several capsules to form more stable (with respect to various perturbations) representations. Examples of applications in computer vision include DeepDream and robot navigation. They have wide applications in image and video recognition, recommender systems and natural language processing. == Deep stacking network == A deep stacking network (DSN) (deep convex network) is based on a hierarchy of blocks of simplified neural network modules. It was introduced in 2011 by Deng and Yu. It formulates the learning as a convex optimization problem with a closed-form solution, emphasizing the mechanism's similarity to stacked generalization. Each DSN block is a simple module that is easy to train by itself in a supervised fashion without backpropagation for the entire blocks. Each block consists of a simplified multi-layer perceptron (MLP) with a single hidden layer. The hidden layer h has logistic sigmoidal units, and the output layer has linear units. Connections between these layers are represented by weight matrix U; input-to-hidden-layer connections have weight matrix W. Target vectors t form the columns of matrix T, and the input data vectors x form the columns of matrix X. The matrix of hidden units is H = σ ( W T X ) {\displaystyle {\boldsymbol {H}}=\sigma ({\boldsymbol {W}}^{T}{\boldsymbol {X}})} . Modules are trained in order, so lower-layer weights W are known at each stage. The function performs the element-wise logistic sigmoid operation. Each block estimates the same final label class y, and its estimate is concatenated with original input X to form the expanded input for the next block. Thus, the input to the first block contains the original data only, while downstream blocks' input adds the output of preceding blocks. Then learning the upper-layer weight matrix U given other weights in the network can be formulated as a convex optimization problem: min U T f = ‖ U T H − T ‖ F 2 , {\displaystyle \min _{U^{T}}f=\|{\boldsymbol {U}}^{T}{\boldsymbol {H}}-{\boldsymbol {T}}\|_{F}^{2},} which has a closed-form solution. Unlike other deep architectures, such as DBNs, the goal is not to discover the transformed feature representation. The structure of the hierarchy of this kind of architecture makes parallel learning straightforward, as a batch-mode optimization problem. In purely discriminative tasks, DSNs outperform conventional DBNs. === Tensor deep stacking networks === This architecture is a DSN extension. It offers two important improvements: it uses higher-order information from covariance statistics, and it transforms the non-convex problem of a lower-layer to a convex sub-problem of an upper-layer. TDSNs use covariance statistics in a bilinear mapping from each of two distinct sets of hidden units in the same layer to predictions, via a third-order tensor. While parallelization and scalability are not considered seriously in conventional DNNs, all learning for DSNs and TDSNs is done in batch mode, to allow parallelization. Parallelization allows scaling the design to larger (deeper) architectures and data sets. The basic architecture is suitable for diverse tasks such as classification and regression. == Physics-informed == Such a neural network is designed for the numerical solution of mathematical equations, such as differential, integral, delay, fractional and others. As input parameters, PINN accepts variables (spatial, temporal, and others), transmits them through the network block. At the output, it produces an approximate solution and substitutes it into the mathematical model, considering the initial and boundary conditions. If the solution does not satisfy the required accuracy, one uses the backpropagation and rectify the solution. Besides PINN, other architectures have been developed to produce surrogate models for scientific comput
Grammar checker
A grammar checker, in computing terms, is a program, or part of a program, that attempts to verify written text for grammatical correctness. Grammar checkers are most often implemented as a feature of a larger program, such as a word processor, but are also available as a stand-alone application that can be activated from within programs that work with editable text. The implementation of a grammar checker makes use of natural language processing. == History == The earliest "grammar checkers" were programs that checked for punctuation and style inconsistencies, rather than a complete range of possible grammatical errors. The first system was called Writer's Workbench, and was a set of writing tools included with Unix systems as far back as the 1970s. The whole Writer's Workbench package included several separate tools to check for various writing problems. The "diction" tool checked for wordy, trite, clichéd or misused phrases in a text. The tool would output a list of questionable phrases and provide suggestions for improving the writing. The "style" tool analyzed the writing style of a given text. It performed a number of readability tests on the text and output the results, and gave some statistical information about the sentences of the text. Aspen Software of Albuquerque, New Mexico released the earliest version of a diction and style checker for personal computers, Grammatik, in 1981. Grammatik was first available for a Radio Shack - TRS-80, and soon had versions for CP/M and the IBM PC. Reference Software International of San Francisco, California, acquired Grammatik in 1985. Development of Grammatik continued, and it became an actual grammar checker that could detect writing errors beyond simple style checking. Other early diction and style checking programs included Punctuation & Style, Correct Grammar, RightWriter and PowerEdit. While all the earliest programs started as simple diction and style checkers, all eventually added various levels of language processing, and developed some level of true grammar checking capability. Until 1992, grammar checkers were sold as add-on programs. There were a large number of different word processing programs available at that time, with WordPerfect and Microsoft Word the top two in market share. In 1992, Microsoft decided to add grammar checking as a feature of Word, and licensed CorrecText, a grammar checker from Houghton Mifflin that had not yet been marketed as a standalone product. WordPerfect answered Microsoft's move by acquiring Reference Software, and the direct descendant of Grammatik is still included with WordPerfect. As of 2019, grammar checkers are built into systems like Google Docs, browser extensions like Grammarly and Qordoba, desktop applications like Ginger, free and open-source software like LanguageTool, and text editor plugins like those available from WebSpellChecker Software. == Technical issues == The earliest writing style programs checked for wordy, trite, clichéd, or misused phrases in a text. This process was based on simple pattern matching. The heart of the program was a list of many hundreds or thousands of phrases that are considered poor writing by many experts. The list of questionable phrases included alternative wording for each phrase. The checking program would simply break text into sentences, check for any matches in the phrase dictionary, flag suspect phrases and show an alternative. These programs could also perform some mechanical checks. For example, they would typically flag doubled words, doubled punctuation, some capitalization errors, and other simple mechanical mistakes. True grammar checking is more complex. While a programming language has a very specific syntax and grammar, this is not so for natural languages. One can write a somewhat complete formal grammar for a natural language, but there are usually so many exceptions in real usage that a formal grammar is of minimal help in writing a grammar checker. One of the most important parts of a natural language grammar checker is a dictionary of all the words in the language, along with the part of speech of each word. The fact that a natural word may be used as any one of several parts of speech (such as "free" being used as an adjective, adverb, noun, or verb) greatly increases the complexity of any grammar checker. A grammar checker will find each sentence in a text, look up each word in the dictionary, and then attempt to parse the sentence into a form that matches a grammar. Using various rules, the program can then detect various errors, such as agreement in tense, number, word order, and so on. It is also possible to detect some stylistic problems with the text. For example, some popular style guides such as The Elements of Style deprecate excessive use of the passive voice. Grammar checkers may attempt to identify passive sentences and suggest an active-voice alternative. The software elements required for grammar checking are closely related to some of the development issues that need to be addressed for speech recognition software. In voice recognition, parsing can be used to help predict which word is most likely intended, based on part of speech and position in the sentence. In grammar checking, the parsing is used to detect words that fail to follow accepted grammar usage. Recently, research has focused on developing algorithms which can recognize grammar errors based on the context of the surrounding words. == Criticism == Grammar checkers are considered a type of foreign language writing aid which non-native speakers can use to proofread their writings as such programs endeavor to identify syntactical errors. However, as with other computerized writing aids such as spell checkers, popular grammar checkers are often criticized when they fail to spot errors and incorrectly flag correct text as erroneous. The linguist Geoffrey K. Pullum argued in 2007 that they were generally so inaccurate as to do more harm than good: "for the most part, accepting the advice of a computer grammar checker on your prose will make it much worse, sometimes hilariously incoherent."
Stephanie Dinkins
Stephanie Dinkins (born 1964) is a transdisciplinary American artist based in Brooklyn, New York. She creates art about artificial intelligence (AI) as it intersects race, gender, and history. Her aim is to "create a unique culturally attuned AI entity in collaboration with coders, engineers and in close consultation with local communities of color that reflects and is empowered to work toward the goals of its community." Dinkins projects include Conversations with Bina48, a series of conversations between Dinkins and the first social, artificially intelligent humanoid robot BINA48 who looks like a black woman and Not the Only One, a multigenerational artificially intelligent memoir trained off of three generations of Dinkins's family. == Early life and education == Dinkins was born in Perth Amboy, New Jersey to Black American parents who raised her in Staten Island, New York. She credits her grandmother with teaching her how to think about art as a social practice, saying "my grandmother . . . was a gardener and the garden was her art . . . that was a community practice." Dinkins attended the International Center of Photography School in New York City in 1995, where she completed the general studies in photography certificate program. Dinkins received a MFA in photography from the Maryland Institute College of Art in 1997 She completed the Independent Study Program at the Whitney Museum of American Art in 1998. == Career == Dinkins is the Yayoi Kusama Professor of Art at Stony Brook University in New York. == Activism == Dinkins advocates for co-creation within a social practice art framework, so that vulnerable communities understand how to use technology to their advantage, instead of being subjected to their use. This is exemplified in her works such as Project al-Khwarzmi, a series of workshops entitled PAK POP-UP at the nonprofit community center Recess in Brooklyn, NY. The workshops involved collaborating with youth in the criminal justice system and uplifting the voices of vulnerable communities in determining how technologies are created and utilized. Dinkins warns of the dangers to members of minority groups that are absent from the creation of the computer algorithms that now affect their lives. == Art == Dinkins's practice employs technologies including, but not limited to, new media such as artificial intelligence and machine learning. Dinkins uses oral history techniques of interviewing to craft community-authored narratives and databases which inform the subjects of her work and serve as acts of social intervention or protest. === Conversations with Bina48 (2014–present) === Dinkins began working on Conversations with Bina48 in 2014. For the series, Dinkins recorded her conversations with BINA48, a social robot that resembles a middle-aged black woman. Dinkins mirrors Bina48 while they discuss identity and technological singularity. In 2010, Hanson Robotics, an engineering and robotics company known for its development of humanoid robots, developed and released BINA48. Bina48 is a robot modeled after the memories, beliefs, attitudes, commentary and mannerisms of Bina Aspen Rothblatt, the spousal partner of Martine Rothblatt. Both Bina and Martine Rothblatt own Bina48 under their organization, the Terasem Movement Foundation. Five years after Bina48 was released, Dinkins came across a YouTube video of Bina48. She asked, "how did a black woman become the most advanced of the technologies at the time?" Her questioning led her to travel to Lincoln, Vermont (the site of the Terasem Movement Foundation) where she conducted a series of interviews with Bina48 and engaged the robot in conversations pertaining to race, intimacy and the nature of being. The conversations suggest opportunities for complementing human existence with artificially intelligent agents that have an identity and history, but also show artificial intelligence's current limitations. Although it is based on a black woman, Dinkins found that Bina48 was shaped by the biases of its white, male creators. === Project al Kwarizmi (PAK) (2017–present) === Project al Kwarizmi (PAK) was a series of pop up workshops in Brooklyn, NY at Eyebeam and Recess; Manhattan, New York at Google; and Durham, North Carolina at Duke University. The workshops were centered for "communities of color that use art as a vehicle to help citizens understand how algorithms, the artificially intelligent systems they underpin, and big data impact their lives and empowers them to do something about it. Project al-Khwarizmi uses art and aesthetics as the common language to help citizens understand what algorithms and artificial intelligent systems are, and where these systems already impact our daily lives." === Not the Only One (N'TOO) (2018–present) === Not the only one (N’TOO) is a voice-interactive chatbot that was trained with data from members of her family to tell a multi-generational story. Dinkins described Not The Only One (NTOO or N'TOO) as an "experimental" multigenerational memoir of one Black American family told from the "mind" of an artificial intelligence of evolving intellect. N'TOO uses a recursive neural network, a deep learning algorithm. It is a voice-interactive AI robot designed, trained, and aligned with the needs and ideals of black and brown people who are drastically underrepresented in the tech sector. NTOO can also be described as a "physically embodied artificially intelligent agent that senses and acts on its world." == Exhibitions == Dinkins's work is exhibited internationally at various public, private, community, and institutional venues, including the Whitney Museum of American Art, the de Young Museum, the Philadelphia Museum of Art, the Studio Museum in Harlem;, Museum of Contemporary Photography, the Long Island Museum of American Art, History, and Carriages, the International Center of Photography in New York, Herning Kunstmuseum in Herning, Denmark, The Barbican in London, UK, Islip Art Museum, Wave Hill, Taller Boricua, the Queens Museum, and the corner of Putnam and Malcolm X Blvd in Bedford Stuyvesant, Brooklyn, New York. She has presented her work in symposia at the Museum of Modern Art, amongst other venues. == Future Histories Studio == Dinkins is the founder and director of Future Histories Studio, a research laboratory for arts-centered inquiry and production based at Stony Brook University. The studio was established with support from the Mellon Foundation as part of the Digital Inquiry, Speculation, Collaboration, and Optimism (DISCO) network. Future Histories Studio operates as an interdisciplinary hub exploring the intersections of art, technology, race, and storytelling through collaborative and practice-based research. Its activities include exhibitions, workshops, and public programs that examine the social and cultural implications of emerging technologies, particularly artificial intelligence and data systems. == Awards and recognition == Dinkins is the recipient of many awards, including: the 2023 LG Guggenheim Award, an international art prize established as part of a long-term global partnership between LG Group and the Solomon R. Guggenheim Museum to recognize groundbreaking artists in technology-based art; a Berggruen Institute artist fellowship; a Sundance New Frontiers Story Lab fellowship; a Soros Equality Fellowship; a Lucas Artists fellowship; a Creative Capital grant; a Bell Labs artist residency; a Blade of Grass fellowship; and a Data & Society fellowship. == Media coverage == Dinkins appeared in episode six of the HBO television series Random Acts of Flyness directed by Terence Nance, where she described her conversations with BINA48. == Other activities == Dinkins was part of the juries that selected Shu Lea Cheang for the LG Guggenheim Award in 2024.
Estimation of distribution algorithm
Estimation of distribution algorithms (EDAs), sometimes called probabilistic model-building genetic algorithms (PMBGAs), are stochastic optimization methods that guide the search for the optimum by building and sampling explicit probabilistic models of promising candidate solutions. Optimization is viewed as a series of incremental updates of a probabilistic model, starting with the model encoding an uninformative prior over admissible solutions and ending with the model that generates only the global optima. EDAs belong to the class of evolutionary algorithms. The main difference between EDAs and most conventional evolutionary algorithms is that evolutionary algorithms generate new candidate solutions using an implicit distribution defined by one or more variation operators, whereas EDAs use an explicit probability distribution encoded by a Bayesian network, a multivariate normal distribution, or another model class. Similarly as other evolutionary algorithms, EDAs can be used to solve optimization problems defined over a number of representations from vectors to LISP style S expressions, and the quality of candidate solutions is often evaluated using one or more objective functions. The general procedure of an EDA is outlined in the following: t := 0 initialize model M(0) to represent uniform distribution over admissible solutions while (termination criteria not met) do P := generate N>0 candidate solutions by sampling M(t) F := evaluate all candidate solutions in P M(t + 1) := adjust_model(P, F, M(t)) t := t + 1 Using explicit probabilistic models in optimization allowed EDAs to feasibly solve optimization problems that were notoriously difficult for most conventional evolutionary algorithms and traditional optimization techniques, such as problems with high levels of epistasis. Nonetheless, the advantage of EDAs is also that these algorithms provide an optimization practitioner with a series of probabilistic models that reveal a lot of information about the problem being solved. This information can in turn be used to design problem-specific neighborhood operators for local search, to bias future runs of EDAs on a similar problem, or to create an efficient computational model of the problem. For example, if the population is represented by bit strings of length 4, the EDA can represent the population of promising solution using a single vector of four probabilities (p1, p2, p3, p4) where each component of p defines the probability of that position being a 1. Using this probability vector it is possible to create an arbitrary number of candidate solutions. == Estimation of distribution algorithms (EDAs) == This section describes the models built by some well known EDAs of different levels of complexity. It is always assumed a population P ( t ) {\displaystyle P(t)} at the generation t {\displaystyle t} , a selection operator S {\displaystyle S} , a model-building operator α {\displaystyle \alpha } and a sampling operator β {\displaystyle \beta } . == Univariate factorizations == The most simple EDAs assume that decision variables are independent, i.e. p ( X 1 , X 2 ) = p ( X 1 ) ⋅ p ( X 2 ) {\displaystyle p(X_{1},X_{2})=p(X_{1})\cdot p(X_{2})} . Therefore, univariate EDAs rely only on univariate statistics and multivariate distributions must be factorized as the product of N {\displaystyle N} univariate probability distributions, D Univariate := p ( X 1 , … , X N ) = ∏ i = 1 N p ( X i ) . {\displaystyle D_{\text{Univariate}}:=p(X_{1},\dots ,X_{N})=\prod _{i=1}^{N}p(X_{i}).} Such factorizations are used in many different EDAs, next we describe some of them. === Univariate marginal distribution algorithm (UMDA) === The UMDA is a simple EDA that uses an operator α U M D A {\displaystyle \alpha _{UMDA}} to estimate marginal probabilities from a selected population S ( P ( t ) ) {\displaystyle S(P(t))} . By assuming S ( P ( t ) ) {\displaystyle S(P(t))} contain λ {\displaystyle \lambda } elements, α U M D A {\displaystyle \alpha _{UMDA}} produces probabilities: p t + 1 ( X i ) = 1 λ ∑ x ∈ S ( P ( t ) ) x i , ∀ i ∈ 1 , 2 , … , N . {\displaystyle p_{t+1}(X_{i})={\dfrac {1}{\lambda }}\sum _{x\in S(P(t))}x_{i},~\forall i\in 1,2,\dots ,N.} Every UMDA step can be described as follows D ( t + 1 ) = α UMDA ∘ S ∘ β λ ( D ( t ) ) . {\displaystyle D(t+1)=\alpha _{\text{UMDA}}\circ S\circ \beta _{\lambda }(D(t)).} === Population-based incremental learning (PBIL) === The PBIL, represents the population implicitly by its model, from which it samples new solutions and updates the model. At each generation, μ {\displaystyle \mu } individuals are sampled and λ ≤ μ {\displaystyle \lambda \leq \mu } are selected. Such individuals are then used to update the model as follows p t + 1 ( X i ) = ( 1 − γ ) p t ( X i ) + ( γ / λ ) ∑ x ∈ S ( P ( t ) ) x i , ∀ i ∈ 1 , 2 , … , N , {\displaystyle p_{t+1}(X_{i})=(1-\gamma )p_{t}(X_{i})+(\gamma /\lambda )\sum _{x\in S(P(t))}x_{i},~\forall i\in 1,2,\dots ,N,} where γ ∈ ( 0 , 1 ] {\displaystyle \gamma \in (0,1]} is a parameter defining the learning rate, a small value determines that the previous model p t ( X i ) {\displaystyle p_{t}(X_{i})} should be only slightly modified by the new solutions sampled. PBIL can be described as D ( t + 1 ) = α PIBIL ∘ S ∘ β μ ( D ( t ) ) {\displaystyle D(t+1)=\alpha _{\text{PIBIL}}\circ S\circ \beta _{\mu }(D(t))} === Compact genetic algorithm (cGA) === The CGA, also relies on the implicit populations defined by univariate distributions. At each generation t {\displaystyle t} , two individuals x , y {\displaystyle x,y} are sampled, P ( t ) = β 2 ( D ( t ) ) {\displaystyle P(t)=\beta _{2}(D(t))} . The population P ( t ) {\displaystyle P(t)} is then sorted in decreasing order of fitness, S Sort ( f ) ( P ( t ) ) {\displaystyle S_{{\text{Sort}}(f)}(P(t))} , with u {\displaystyle u} being the best and v {\displaystyle v} being the worst solution. The CGA estimates univariate probabilities as follows p t + 1 ( X i ) = p t ( X i ) + γ ( u i − v i ) , ∀ i ∈ 1 , 2 , … , N , {\displaystyle p_{t+1}(X_{i})=p_{t}(X_{i})+\gamma (u_{i}-v_{i}),\quad \forall i\in 1,2,\dots ,N,} where, γ ∈ ( 0 , 1 ] {\displaystyle \gamma \in (0,1]} is a constant defining the learning rate, usually set to γ = 1 / N {\displaystyle \gamma =1/N} . The CGA can be defined as D ( t + 1 ) = α CGA ∘ S Sort ( f ) ∘ β 2 ( D ( t ) ) {\displaystyle D(t+1)=\alpha _{\text{CGA}}\circ S_{{\text{Sort}}(f)}\circ \beta _{2}(D(t))} == Bivariate factorizations == Although univariate models can be computed efficiently, in many cases they are not representative enough to provide better performance than GAs. In order to overcome such a drawback, the use of bivariate factorizations was proposed in the EDA community, in which dependencies between pairs of variables could be modeled. A bivariate factorization can be defined as follows, where π i {\displaystyle \pi _{i}} contains a possible variable dependent to X i {\displaystyle X_{i}} , i.e. | π i | = 1 {\displaystyle |\pi _{i}|=1} . D Bivariate := p ( X 1 , … , X N ) = ∏ i = 1 N p ( X i | π i ) . {\displaystyle D_{\text{Bivariate}}:=p(X_{1},\dots ,X_{N})=\prod _{i=1}^{N}p(X_{i}|\pi _{i}).} Bivariate and multivariate distributions are usually represented as probabilistic graphical models (graphs), in which edges denote statistical dependencies (or conditional probabilities) and vertices denote variables. To learn the structure of a PGM from data linkage-learning is employed. === Mutual information maximizing input clustering (MIMIC) === The MIMIC factorizes the joint probability distribution in a chain-like model representing successive dependencies between variables. It finds a permutation of the decision variables, r : i ↦ j {\displaystyle r:i\mapsto j} , such that x r ( 1 ) x r ( 2 ) , … , x r ( N ) {\displaystyle x_{r(1)}x_{r(2)},\dots ,x_{r(N)}} minimizes the Kullback–Leibler divergence in relation to the true probability distribution, i.e. π r ( i + 1 ) = { X r ( i ) } {\displaystyle \pi _{r(i+1)}=\{X_{r(i)}\}} . MIMIC models a distribution p t + 1 ( X 1 , … , X N ) = p t ( X r ( N ) ) ∏ i = 1 N − 1 p t ( X r ( i ) | X r ( i + 1 ) ) . {\displaystyle p_{t+1}(X_{1},\dots ,X_{N})=p_{t}(X_{r(N)})\prod _{i=1}^{N-1}p_{t}(X_{r(i)}|X_{r(i+1)}).} New solutions are sampled from the leftmost to the rightmost variable, the first is generated independently and the others according to conditional probabilities. Since the estimated distribution must be recomputed each generation, MIMIC uses concrete populations in the following way P ( t + 1 ) = β μ ∘ α MIMIC ∘ S ( P ( t ) ) . {\displaystyle P(t+1)=\beta _{\mu }\circ \alpha _{\text{MIMIC}}\circ S(P(t)).} === Bivariate marginal distribution algorithm (BMDA) === The BMDA factorizes the joint probability distribution in bivariate distributions. First, a randomly chosen variable is added as a node in a graph, the most dependent variable to one of those in the graph is chosen among those not yet in the graph, this procedure is repeated until no remain
GITEX Vietnam
GITEX AI Vietnam is an upcoming technology exhibition and conference scheduled to take place in Hanoi, Vietnam, on 1–2 October 2026. The event is organised by KAOUN International in partnership with the Dubai World Trade Centre and the Vietnam National Innovation Center (NIC). It is part of the global GITEX network of technology exhibitions. The event supported by Vietnam's Ministry of Finance and Ministry of Science and Technology. == Activity == GITEX AI Vietnam was announced in 2025 as part of GITEX's expansion into Southeast Asia. Its launch coincides with Vietnam's National Innovation Week. Media reports linked to the announcement projected Vietnam's digital economy could reach around US$200 billion by 2030. The event includes exhibitions, conferences, and networking sessions. Co-located platforms include AI Everything Vietnam, Startups North Star Vietnam, GITEX Cyber Valley Vietnam, and FDX Vietnam. Expected participants include policymakers, technology companies, startups, investors, and researchers.
Shape context
Shape context is a feature descriptor used in object recognition. Serge Belongie and Jitendra Malik proposed the term in their paper "Matching with Shape Contexts" in 2000. == Theory == The shape context is intended to be a way of describing shapes that allows for measuring shape similarity and the recovering of point correspondences. The basic idea is to pick n points on the contours of a shape. For each point pi on the shape, consider the n − 1 vectors obtained by connecting pi to all other points. The set of all these vectors is a rich description of the shape localized at that point but is far too detailed. The key idea is that the distribution over relative positions is a robust, compact, and highly discriminative descriptor. So, for the point pi, the coarse histogram of the relative coordinates of the remaining n − 1 points, h i ( k ) = # { q ≠ p i : ( q − p i ) ∈ bin ( k ) } {\displaystyle h_{i}(k)=\#\{q\neq p_{i}:(q-p_{i})\in {\mbox{bin}}(k)\}} is defined to be the shape context of p i {\displaystyle p_{i}} . The bins are normally taken to be uniform in log-polar space. The fact that the shape context is a rich and discriminative descriptor can be seen in the figure below, in which the shape contexts of two different versions of the letter "A" are shown. (a) and (b) are the sampled edge points of the two shapes. (c) is the diagram of the log-polar bins used to compute the shape context. (d) is the shape context for the point marked with a circle in (a), (e) is that for the point marked as a diamond in (b), and (f) is that for the triangle. As can be seen, since (d) and (e) are the shape contexts for two closely related points, they are quite similar, while the shape context in (f) is very different. For a feature descriptor to be useful, it needs to have certain invariances. In particular it needs to be invariant to translation, scaling, small perturbations, and, depending on the application, rotation. Translational invariance comes naturally to shape context. Scale invariance is obtained by normalizing all radial distances by the mean distance α {\displaystyle \alpha } between all the point pairs in the shape although the median distance can also be used. Shape contexts are empirically demonstrated to be robust to deformations, noise, and outliers using synthetic point set matching experiments. One can provide complete rotational invariance in shape contexts. One way is to measure angles at each point relative to the direction of the tangent at that point (since the points are chosen on edges). This results in a completely rotationally invariant descriptor. But of course this is not always desired since some local features lose their discriminative power if not measured relative to the same frame. Many applications in fact forbid rotational invariance e.g. distinguishing a "6" from a "9". == Use in shape matching == A complete system that uses shape contexts for shape matching consists of the following steps (which will be covered in more detail in the Details of Implementation section): Randomly select a set of points that lie on the edges of a known shape and another set of points on an unknown shape. Compute the shape context of each point found in step 1. Match each point from the known shape to a point on an unknown shape. To minimize the cost of matching, first choose a transformation (e.g. affine, thin plate spline, etc.) that warps the edges of the known shape to the unknown (essentially aligning the two shapes). Then select the point on the unknown shape that most closely corresponds to each warped point on the known shape. Calculate the "shape distance" between each pair of points on the two shapes. Use a weighted sum of the shape context distance, the image appearance distance, and the bending energy (a measure of how much transformation is required to bring the two shapes into alignment). To identify the unknown shape, use a nearest-neighbor classifier to compare its shape distance to shape distances of known objects. == Details of implementation == === Step 1: Finding a list of points on shape edges === The approach assumes that the shape of an object is essentially captured by a finite subset of the points on the internal or external contours on the object. These can be simply obtained using the Canny edge detector and picking a random set of points from the edges. Note that these points need not and in general do not correspond to key-points such as maxima of curvature or inflection points. It is preferable to sample the shape with roughly uniform spacing, though it is not critical. === Step 2: Computing the shape context === This step is described in detail in the Theory section. === Step 3: Computing the cost matrix === Consider two points p and q that have normalized K-bin histograms (i.e. shape contexts) g(k) and h(k). As shape contexts are distributions represented as histograms, it is natural to use the χ2 test statistic as the "shape context cost" of matching the two points: C S = 1 2 ∑ k = 1 K [ g ( k ) − h ( k ) ] 2 g ( k ) + h ( k ) {\displaystyle C_{S}={\frac {1}{2}}\sum _{k=1}^{K}{\frac {[g(k)-h(k)]^{2}}{g(k)+h(k)}}} The values of this range from 0 to 1. In addition to the shape context cost, an extra cost based on the appearance can be added. For instance, it could be a measure of tangent angle dissimilarity (particularly useful in digit recognition): C A = 1 2 ‖ ( cos ( θ 1 ) sin ( θ 1 ) ) − ( cos ( θ 2 ) sin ( θ 2 ) ) ‖ {\displaystyle C_{A}={\frac {1}{2}}{\begin{Vmatrix}{\dbinom {\cos(\theta _{1})}{\sin(\theta _{1})}}-{\dbinom {\cos(\theta _{2})}{\sin(\theta _{2})}}\end{Vmatrix}}} This is half the length of the chord in unit circle between the unit vectors with angles θ 1 {\displaystyle \theta _{1}} and θ 2 {\displaystyle \theta _{2}} . Its values also range from 0 to 1. Now the total cost of matching the two points could be a weighted-sum of the two costs: C = ( 1 − β ) C S + β C A {\displaystyle C=(1-\beta )C_{S}+\beta C_{A}\!\,} Now for each point pi on the first shape and a point qj on the second shape, calculate the cost as described and call it Ci,j. This is the cost matrix. === Step 4: Finding the matching that minimizes total cost === Now, a one-to-one matching π ( i ) {\displaystyle \pi (i)} that matches each point pi on shape 1 and qj on shape 2 that minimizes the total cost of matching, H ( π ) = ∑ i C ( p i , q π ( i ) ) {\displaystyle H(\pi )=\sum _{i}C\left(p_{i},q_{\pi (i)}\right)} is needed. This can be done in O ( N 3 ) {\displaystyle O(N^{3})} time using the Hungarian method, although there are more efficient algorithms. To have robust handling of outliers, one can add "dummy" nodes that have a constant but reasonably large cost of matching to the cost matrix. This would cause the matching algorithm to match outliers to a "dummy" if there is no real match. === Step 5: Modeling transformation === Given the set of correspondences between a finite set of points on the two shapes, a transformation T : R 2 → R 2 {\displaystyle T:\mathbb {R} ^{2}\to \mathbb {R} ^{2}} can be estimated to map any point from one shape to the other. There are several choices for this transformation, described below. ==== Affine ==== The affine model is a standard choice: T ( p ) = A p + o {\displaystyle T(p)=Ap+o\!} . The least squares solution for the matrix A {\displaystyle A} and the translational offset vector o is obtained by: o = 1 n ∑ i = 1 n ( p i − q π ( i ) ) , A = ( Q + P ) t {\displaystyle o={\frac {1}{n}}\sum _{i=1}^{n}\left(p_{i}-q_{\pi (i)}\right),A=(Q^{+}P)^{t}} Where P = ( 1 p 11 p 12 ⋮ ⋮ ⋮ 1 p n 1 p n 2 ) {\displaystyle P={\begin{pmatrix}1&p_{11}&p_{12}\\\vdots &\vdots &\vdots \\1&p_{n1}&p_{n2}\end{pmatrix}}} with a similar expression for Q {\displaystyle Q\!} . Q + {\displaystyle Q^{+}\!} is the pseudoinverse of Q {\displaystyle Q\!} . ==== Thin plate spline ==== The thin plate spline (TPS) model is the most widely used model for transformations when working with shape contexts. A 2D transformation can be separated into two TPS function to model a coordinate transform: T ( x , y ) = ( f x ( x , y ) , f y ( x , y ) ) {\displaystyle T(x,y)=\left(f_{x}(x,y),f_{y}(x,y)\right)} where each of the ƒx and ƒy have the form: f ( x , y ) = a 1 + a x x + a y y + ∑ i = 1 n ω i U ( ‖ ( x i , y i ) − ( x , y ) ‖ ) , {\displaystyle f(x,y)=a_{1}+a_{x}x+a_{y}y+\sum _{i=1}^{n}\omega _{i}U\left({\begin{Vmatrix}(x_{i},y_{i})-(x,y)\end{Vmatrix}}\right),} and the kernel function U ( r ) {\displaystyle U(r)\!} is defined by U ( r ) = r 2 log r 2 {\displaystyle U(r)=r^{2}\log r^{2}\!} . The exact details of how to solve for the parameters can be found elsewhere but it essentially involves solving a linear system of equations. The bending energy (a measure of how much transformation is needed to align the points) will also be easily obtained. ==== Regularized TPS ==== The TPS formulation above has exact matching requirement for the pairs of points on the two shapes. For noisy data, it is best to
Blended artificial intelligence
Blended artificial intelligence (blended AI) refers to the blending of different artificial intelligence techniques or approaches to achieve more robust and practical solutions. It involves integrating multiple AI models, algorithms, and technologies to leverage their respective strengths and compensate for their weaknesses. == Background == In the context of machine learning, blended AI can involve using different types of models, such as generative AI, decision trees, neural networks, and support vector machines. By combining their results, predictions are more accurate and reliable. This blending of models can be done through techniques like ensemble learning, where multiple models are trained independently and their predictions are combined to make a final decision. Blended AI can also involve combining different AI techniques or technologies, such as natural language processing, computer vision, and expert systems, to tackle complex problems that require a multi-dimensional approach. For example, in a sales scenario AI could be used for lead generation and gathering information from social media such as LinkedIn posts, or understanding a prospect's hobbies and interests. Another blended AI could achieve customer profiling including past interactions and purchasing habits, by them, their industry and growth areas. Blended AI could be used to do predictive analytics to look at historical sales data, market trends, and external factors to generate accurate sales forecasts. This method is critical to gauge and increase "efficiency, revenue, and productivity". Lastly, another could integrate all the information into the CRM to build and maintain better prospect and customer profiles. Blended AI aims to leverage the strengths of different AI techniques and technologies, allowing them to complement each other and create more powerful and comprehensive AI solutions. By combining multiple approaches, blended AI aims to achieve better performance, higher accuracy, improved robustness, and enhanced capabilities in solving diverse and challenging problems.