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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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  Calibration (statistics)

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

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  Spatial Analysis of Principal Components

  Spatial Principal Component Analysis (sPCA) is a multivariate statistical technique that complements the traditional Principal Component Analysis (PCA) by incorporating spatial information into the analysis of genetic variation. While traditional PCA can be used to find spatial patterns, it focuses on reducing data dimensionality by identifying uncorrelated principal components that capture maximum variance, thus often lacking power to identify non-trivial spatial genetic patterns. By accounting for spatial autocorrelation, sPCA is able to uncover spatial patterns in the data and find the spatial structure of datasets where observations are either geographically or topologically linked. This statistical power improvement allows the investigation of cryptic spatial patterns of genetic variability otherwise overlooked. sPCA has been applied in various fields, including geography, ecology and genetics. == History == sPCA was introduced in 2008 by Thibaut Jombart, Sébastien Devillard, Anne-Béatrice Dufour, and D. Pontier as a spatially explicit method to investigate the spatial pattern of genetic variation among individuals or populations. In 2017, Valeria Montano and Thibaut Jombart published an alternative non-parametric test to evaluate the significance of global and local spatial genetic patterns with improved statistical power. == Details == sPCA modifies the PCA framework by integrating spatial weights, typically in the form of connectivity matrices or spatial adjacency graphs. It identifies principal components (PCs) that maximize both genentic variance and spatial autocorreation, as measured by Moran's I. These weights represent relationships between observations based on geographic distance or other spatial criteria. The method decomposes variance into two components: Global structures, correspond to positive autocorrelation, that is, reflect broad-scale spatial patterns where similar values cluster over large regions. Local structures, correspond to negative autocorrelation, that is, capture fine-scale spatial variations or localized patterns. The core of sPCA relies on the eigenanalysis of a spatially weighted covariance or correlation matrix. The spatial weight matrix can be constructed using techniques such as Delaunay triangulation, nearest-neighbor graphs, or distance-based criteria. Applications of sPCA should be used only as an explorative tool. == Applications == sPCA has been widely used in many fields, including: Ecology: To find spatial patterns in species distributions and environmental gradients. Genetics: Population structure and gene flow analysis while allowing for spatial autocorrelation considerations. Biogeography: To identify historical dispersal routes, and barriers to gene flow, providing insights into species distribution patterns and evolutionary history. == Software/Source Code == sPCA implementations are available in R in adegenet and ntbox . These tools facilitate the application of sPCA by providing functions for constructing spatial weight matrices, performing eigenanalysis, and obtaining spatial principal components in an easy-to-read form.

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  Relation network

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

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  Point distribution model

  The point distribution model is a model for representing the mean geometry of a shape and some statistical modes of geometric variation inferred from a training set of shapes. == Background == The point distribution model concept has been developed by Cootes, Taylor et al. and became a standard in computer vision for the statistical study of shape and for segmentation of medical images where shape priors really help interpretation of noisy and low-contrasted pixels/voxels. The latter point leads to active shape models (ASM) and active appearance models (AAM). Point distribution models rely on landmark points. A landmark is an annotating point posed by an anatomist onto a given locus for every shape instance across the training set population. For instance, the same landmark will designate the tip of the index finger in a training set of 2D hands outlines. Principal component analysis (PCA), for instance, is a relevant tool for studying correlations of movement between groups of landmarks among the training set population. Typically, it might detect that all the landmarks located along the same finger move exactly together across the training set examples showing different finger spacing for a flat-posed hands collection. == Details == First, a set of training images are manually landmarked with enough corresponding landmarks to sufficiently approximate the geometry of the original shapes. These landmarks are aligned using the generalized procrustes analysis, which minimizes the least squared error between the points. k {\displaystyle k} aligned landmarks in two dimensions are given as X = ( x 1 , y 1 , … , x k , y k ) {\displaystyle \mathbf {X} =(x_{1},y_{1},\ldots ,x_{k},y_{k})} . It's important to note that each landmark i ∈ { 1 , … k } {\displaystyle i\in \lbrace 1,\ldots k\rbrace } should represent the same anatomical location. For example, landmark #3, ( x 3 , y 3 ) {\displaystyle (x_{3},y_{3})} might represent the tip of the ring finger across all training images. Now the shape outlines are reduced to sequences of k {\displaystyle k} landmarks, so that a given training shape is defined as the vector X ∈ R 2 k {\displaystyle \mathbf {X} \in \mathbb {R} ^{2k}} . Assuming the scattering is gaussian in this space, PCA is used to compute normalized eigenvectors and eigenvalues of the covariance matrix across all training shapes. The matrix of the top d {\displaystyle d} eigenvectors is given as P ∈ R 2 k × d {\displaystyle \mathbf {P} \in \mathbb {R} ^{2k\times d}} , and each eigenvector describes a principal mode of variation along the set. Finally, a linear combination of the eigenvectors is used to define a new shape X ′ {\displaystyle \mathbf {X} '} , mathematically defined as: X ′ = X ¯ + P b {\displaystyle \mathbf {X} '={\overline {\mathbf {X} }}+\mathbf {P} \mathbf {b} } where X ¯ {\displaystyle {\overline {\mathbf {X} }}} is defined as the mean shape across all training images, and b {\displaystyle \mathbf {b} } is a vector of scaling values for each principal component. Therefore, by modifying the variable b {\displaystyle \mathbf {b} } an infinite number of shapes can be defined. To ensure that the new shapes are all within the variation seen in the training set, it is common to only allow each element of b {\displaystyle \mathbf {b} } to be within ± {\displaystyle \pm } 3 standard deviations, where the standard deviation of a given principal component is defined as the square root of its corresponding eigenvalue. PDM's can be extended to any arbitrary number of dimensions, but are typically used in 2D image and 3D volume applications (where each landmark point is R 2 {\displaystyle \mathbb {R} ^{2}} or R 3 {\displaystyle \mathbb {R} ^{3}} ). == Discussion == An eigenvector, interpreted in euclidean space, can be seen as a sequence of k {\displaystyle k} euclidean vectors associated to corresponding landmark and designating a compound move for the whole shape. Global nonlinear variation is usually well handled provided nonlinear variation is kept to a reasonable level. Typically, a twisting nematode worm is used as an example in the teaching of kernel PCA-based methods. Due to the PCA properties: eigenvectors are mutually orthogonal, form a basis of the training set cloud in the shape space, and cross at the 0 in this space, which represents the mean shape. Also, PCA is a traditional way of fitting a closed ellipsoid to a Gaussian cloud of points (whatever their dimension): this suggests the concept of bounded variation. The idea behind PDMs is that eigenvectors can be linearly combined to create an infinity of new shape instances that will 'look like' the one in the training set. The coefficients are bounded alike the values of the corresponding eigenvalues, so as to ensure the generated 2n/3n-dimensional dot will remain into the hyper-ellipsoidal allowed domain—allowable shape domain (ASD).

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  Harrison White

  Harrison Colyar White (March 21, 1930 – May 18, 2024) was an American sociologist who was the Giddings Professor of Sociology at Columbia University. White played an influential role in the “Harvard Revolution” in social networks and the New York School of relational sociology. He is credited with the development of a number of mathematical models of social structure including vacancy chains and blockmodels. He has been a leader of a revolution in sociology that is still in process, using models of social structure that are based on patterns of relations instead of the attributes and attitudes of individuals. Among social network researchers, White is widely respected. For instance, at the 1997 International Network of Social Network Analysis conference, the organizer held a special “White Tie” event, dedicated to White. Social network researcher Emmanuel Lazega refers to him as both “Copernicus and Galileo” because he invented both the vision and the tools. The most comprehensive documentation of his theories can be found in the book Identity and Control, first published in 1992. A major rewrite of the book appeared in June 2008. In 2011, White received the W.E.B. DuBois Career of Distinguished Scholarship Award from the American Sociological Association, which honors "scholars who have shown outstanding commitment to the profession of sociology and whose cumulative work has contributed in important ways to the advancement of the discipline." Before his retirement to live in Tucson, Arizona, White was interested in sociolinguistics and business strategy as well as sociology. == Life and career == === Early years === White was born on March 21, 1930, in Washington, D.C. He had three siblings and his father was a doctor in the US Navy. Although moving around to different Naval bases throughout his adolescence, he considered himself Southern, and Nashville, TN to be his home. At the age of 15, he entered the Massachusetts Institute of Technology (MIT), receiving his undergraduate degree at 20 years of age; five years later, in 1955, he received a doctorate in theoretical physics, also from MIT with John C. Slater as his advisor. His dissertation was titled A quantum-mechanical calculation of inter-atomic force constants in copper. This was published in the Physical Review as "Atomic Force Constants of Copper from Feynman's Theorem" (1958). While at MIT he also took a course with the political scientist Karl Deutsch, who White credits with encouraging him to move toward the social sciences. === Princeton University === After receiving his PhD in theoretical physics, he received a Fellowship from the Ford Foundation to begin his second doctorate in sociology at Princeton University. His dissertation advisor was Marion J. Levy. White also worked with Wilbert Moore, Fred Stephan, and Frank W. Notestein while at Princeton. His cohort was very small, with only four or five other graduate students including David Matza, and Stanley Udy. At the same time, he took up a position as an operations analyst at the Operations Research Office, Johns Hopkins University from 1955 to 1956. During this period, he worked with Lee S. Christie on Queuing with Preemptive Priorities or with Breakdown, which was published in 1958. Christie previously worked alongside mathematical psychologist R. Duncan Luce in the Small Group Laboratory at MIT while White was completing his first PhD in physics also at MIT. While continuing his studies at Princeton, White also spent a year as a fellow at the Center for Advanced Study in the Behavioral Sciences, Stanford University, California where he met Harold Guetzkow. Guetzkow was a faculty member at the Carnegie Institute of Technology, known for his application of simulations to social behavior and long-time collaborator with many other pioneers in organization studies, including Herbert A. Simon, James March, and Richard Cyert. Upon meeting Simon through his mutual acquaintance with Guetzkow, White received an invitation to move from California to Pittsburgh to work as an assistant professor of Industrial Administration and Sociology at the Graduate School of Industrial Administration, Carnegie Institute of Technology (later Carnegie-Mellon University), where he stayed for a couple of years, between 1957 and 1959. In an interview, he claimed to have fought with the dean, Leyland Bock, to have the word "sociology" included in his title. It was also during his time at the Stanford Center for Advanced Study that White met his first wife, Cynthia A. Johnson, who was a graduate of Radcliffe College, where she had majored in art history. The couple's joint work on the French Impressionists, Canvases and Careers (1965) and “Institutional Changes in the French Painting World” (1964), originally grew out of a seminar on art in 1957 at the Center for Advanced Study led by Robert Wilson. White originally hoped to use sociometry to map the social structure of French art to predict shifts, but he had an epiphany that it was not social structure but institutional structure which explained the shift. It was also during these years that White, still a graduate student in sociology, wrote and published his first social scientific work, "Sleep: A Sociological Interpretation" in Acta Sociologica in 1960, together with Vilhelm Aubert, a Norwegian sociologist. This work was a phenomenological examination of sleep which attempted to "demonstrate that sleep was more than a straightforward biological activity... [but rather also] a social event". For his dissertation, White carried out empirical research on a research and development department in a manufacturing firm, consisting of interviews and a 110-item questionnaire with managers. He specifically used sociometric questions, which he used to model the "social structure" of relationships between various departments and teams in the organization. In May 1960 he submitted as his doctoral dissertation, titled Research and Development as a Pattern in Industrial Management: A Case Study in Institutionalisation and Uncertainty, earning a PhD in sociology from Princeton University. His first publication based on his dissertation was ''Management conflict and sociometric structure'' in the American Journal of Sociology. === University of Chicago === In 1959 James Coleman left the University of Chicago to found a new department of social relations at Johns Hopkins University, this left a vacancy open for a mathematical sociologist like White. He moved to Chicago to start working as an associate professor at the Department of Sociology. At that time, highly influential sociologists, such as Peter Blau, Mayer Zald, Elihu Katz, Everett Hughes, Erving Goffman were there. As Princeton only required one year in residence, and White took the opportunity to take positions at Johns Hopkins, Stanford, and Carnegie while still working on his dissertation, it was at Chicago that White credits as being his "real socialization in a way, into sociology." It was here that White advised his first two graduate students Joel H. Levine and Morris Friedell, both who went on to make contributions to social network analysis in sociology. While at the Center for Advanced Study, White began learning anthropology and became fascinated with kinship. During his stay at the University of Chicago White was able to finish An Anatomy of Kinship, published in 1963 within the Prentice-Hall series in Mathematical Analysis of Social Behavior, with James Coleman and James March as chief editors. The book received significant attention from many mathematical sociologists of the time, and contributed greatly to establish White as a model builder. === The Harvard Revolution === In 1963, White left Chicago to be an associate professor of sociology at the Harvard Department of Social Relations—the same department founded by Talcott Parsons and still heavily influenced by the structural-functionalist paradigm of Parsons. As White previously only taught graduate courses at Carnegie and Chicago, his first undergraduate course was An Introduction to Social Relations (see Influence) at Harvard, which became infamous among network analysts. As he "thought existing textbooks were grotesquely unscientific," the syllabus of the class was noted for including few readings by sociologists, and comparatively more readings by anthropologists, social psychologists, and historians. White was also a vocal critic of what he called the "attributes and attitudes" approach of Parsonsian sociology, and came to be the leader of what has been variously known as the “Harvard Revolution," the "Harvard breakthrough," or the "Harvard renaissance" in social networks. He worked closely with small group researchers George C. Homans and Robert F. Bales, which was largely compatible with his prior work in organizational research and his efforts to formalize network analysis. Overlapping White's early years, Charles Tilly, a graduate of the Harvard Department of Social

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  Clustering illusion

  The clustering illusion is the tendency to erroneously consider the inevitable "streaks" or "clusters" arising in small samples from random distributions to be non-random. The illusion is caused by a human tendency to underpredict the amount of variability likely to appear in a small sample of random or pseudorandom data. Thomas Gilovich, an early author on the subject, argued that the effect occurs for different types of random dispersions. Some might perceive patterns in stock market price fluctuations over time, or clusters in two-dimensional data such as the locations of impact of World War II V-1 flying bombs on maps of London. Although Londoners developed specific theories about the pattern of impacts within London, a statistical analysis by R. D. Clarke originally published in 1946 showed that the impacts of V-2 rockets on London were a close fit to a random distribution. == Similar biases == Using this cognitive bias in causal reasoning may result in the Texas sharpshooter fallacy, in which differences in data are ignored and similarities are overemphasized. More general forms of erroneous pattern recognition are pareidolia and apophenia. Related biases are the illusion of control which the clustering illusion could contribute to, and insensitivity to sample size in which people don't expect greater variation in smaller samples. A different cognitive bias involving misunderstanding of chance streams is the gambler's fallacy. == Possible causes == Daniel Kahneman and Amos Tversky explained this kind of misprediction as being caused by the representativeness heuristic (which itself they also first proposed).

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  Bayesian network

  A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks are special cases of Bayesian networks. Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms can perform inference and learning in Bayesian networks. Bayesian networks that model sequences of variables (e.g. speech signals or protein sequences) are called dynamic Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called influence diagrams. == Graphical model == Formally, Bayesian networks are directed acyclic graphs (DAGs) whose nodes represent variables in the Bayesian sense: they may be observable quantities, latent variables, unknown parameters or hypotheses. Each edge represents a direct conditional dependency. Any pair of nodes that are not connected (i.e. no path connects one node to the other) represent variables that are conditionally independent of each other. Each node is associated with a probability function that takes, as input, a particular set of values for the node's parent variables, and gives (as output) the probability (or probability distribution, if applicable) of the variable represented by the node. For example, if m {\displaystyle m} parent nodes represent m {\displaystyle m} Boolean variables, then the probability function could be represented by a table of 2 m {\displaystyle 2^{m}} entries, one entry for each of the 2 m {\displaystyle 2^{m}} possible parent combinations. Similar ideas may be applied to undirected, and possibly cyclic, graphs such as Markov networks. == Example == Suppose we want to model the dependencies between three variables: the sprinkler (or more appropriately, its state - whether it is on or not), the presence or absence of rain and whether the grass is wet or not. Observe that two events can cause the grass to become wet: an active sprinkler or rain. Rain has a direct effect on the use of the sprinkler (namely that when it rains, the sprinkler usually is not active). This situation can be modeled with a Bayesian network (shown to the right). Each variable has two possible values, T (for true) and F (for false). The joint probability function is, by the chain rule of probability, Pr ( G , S , R ) = Pr ( G ∣ S , R ) Pr ( S ∣ R ) Pr ( R ) {\displaystyle \Pr(G,S,R)=\Pr(G\mid S,R)\Pr(S\mid R)\Pr(R)} where G = "Grass wet (true/false)", S = "Sprinkler turned on (true/false)", and R = "Raining (true/false)". The model can answer questions about the presence of a cause given the presence of an effect (so-called inverse probability) like "What is the probability that it is raining, given the grass is wet?" by using the conditional probability formula and summing over all nuisance variables: Pr ( R = T ∣ G = T ) = Pr ( G = T , R = T ) Pr ( G = T ) = ∑ x ∈ { T , F } Pr ( G = T , S = x , R = T ) ∑ x , y ∈ { T , F } Pr ( G = T , S = x , R = y ) {\displaystyle \Pr(R=T\mid G=T)={\frac {\Pr(G=T,R=T)}{\Pr(G=T)}}={\frac {\sum _{x\in \{T,F\}}\Pr(G=T,S=x,R=T)}{\sum _{x,y\in \{T,F\}}\Pr(G=T,S=x,R=y)}}} Using the expansion for the joint probability function Pr ( G , S , R ) {\displaystyle \Pr(G,S,R)} and the conditional probabilities from the conditional probability tables (CPTs) stated in the diagram, one can evaluate each term in the sums in the numerator and denominator. For example, Pr ( G = T , S = T , R = T ) = Pr ( G = T ∣ S = T , R = T ) Pr ( S = T ∣ R = T ) Pr ( R = T ) = 0.99 × 0.01 × 0.2 = 0.00198. {\displaystyle {\begin{aligned}\Pr(G=T,S=T,R=T)&=\Pr(G=T\mid S=T,R=T)\Pr(S=T\mid R=T)\Pr(R=T)\\&=0.99\times 0.01\times 0.2\\&=0.00198.\end{aligned}}} Then the numerical results (subscripted by the associated variable values) are Pr ( R = T ∣ G = T ) = 0.00198 T T T + 0.1584 T F T 0.00198 T T T + 0.288 T T F + 0.1584 T F T + 0.0 T F F = 891 2491 ≈ 35.77 % . {\displaystyle \Pr(R=T\mid G=T)={\frac {0.00198_{TTT}+0.1584_{TFT}}{0.00198_{TTT}+0.288_{TTF}+0.1584_{TFT}+0.0_{TFF}}}={\frac {891}{2491}}\approx 35.77\%.} To answer an interventional question, such as "What is the probability that it would rain, given that we wet the grass?" the answer is governed by the post-intervention joint distribution function Pr ( S , R ∣ do ( G = T ) ) = Pr ( S ∣ R ) Pr ( R ) {\displaystyle \Pr(S,R\mid {\text{do}}(G=T))=\Pr(S\mid R)\Pr(R)} obtained by removing the factor Pr ( G ∣ S , R ) {\displaystyle \Pr(G\mid S,R)} from the pre-intervention distribution. The do operator forces the value of G to be true. The probability of rain is unaffected by the action: Pr ( R ∣ do ( G = T ) ) = Pr ( R ) . {\displaystyle \Pr(R\mid {\text{do}}(G=T))=\Pr(R).} To predict the impact of turning the sprinkler on: Pr ( R , G ∣ do ( S = T ) ) = Pr ( R ) Pr ( G ∣ R , S = T ) {\displaystyle \Pr(R,G\mid {\text{do}}(S=T))=\Pr(R)\Pr(G\mid R,S=T)} with the term Pr ( S = T ∣ R ) {\displaystyle \Pr(S=T\mid R)} removed, showing that the action affects the grass but not the rain. These predictions may not be feasible given unobserved variables, as in most policy evaluation problems. The effect of the action do ( x ) {\displaystyle {\text{do}}(x)} can still be predicted, however, whenever the back-door criterion is satisfied. It states that, if a set Z of nodes can be observed that d-separates (or blocks) all back-door paths from X to Y then Pr ( Y , Z ∣ do ( x ) ) = Pr ( Y , Z , X = x ) Pr ( X = x ∣ Z ) . {\displaystyle \Pr(Y,Z\mid {\text{do}}(x))={\frac {\Pr(Y,Z,X=x)}{\Pr(X=x\mid Z)}}.} A back-door path is one that ends with an arrow into X. Sets that satisfy the back-door criterion are called "sufficient" or "admissible." For example, the set Z = R is admissible for predicting the effect of S = T on G, because R d-separates the (only) back-door path S ← R → G. However, if S is not observed, no other set d-separates this path and the effect of turning the sprinkler on (S = T) on the grass (G) cannot be predicted from passive observations. In that case P(G | do(S = T)) is not "identified". This reflects the fact that, lacking interventional data, the observed dependence between S and G is due to a causal connection or is spurious (apparent dependence arising from a common cause, R). (see Simpson's paradox) To determine whether a causal relation is identified from an arbitrary Bayesian network with unobserved variables, one can use the three rules of "do-calculus" and test whether all do terms can be removed from the expression of that relation, thus confirming that the desired quantity is estimable from frequency data. Using a Bayesian network can save considerable amounts of memory over exhaustive probability tables, if the dependencies in the joint distribution are sparse. For example, a naive way of storing the conditional probabilities of 10 two-valued variables as a table requires storage space for 2 10 = 1024 {\displaystyle 2^{10}=1024} values. If no variable's local distribution depends on more than three parent variables, the Bayesian network representation stores at most 10 ⋅ 2 3 = 80 {\displaystyle 10\cdot 2^{3}=80} values. One advantage of Bayesian networks is that it is intuitively easier for a human to understand (a sparse set of) direct dependencies and local distributions than complete joint distributions. == Inference and learning == Bayesian networks perform three main inference tasks: Inferring unobserved variables Parameter learning for the probability distributions of each node in the network Structure learning of the graphical network === Inferring unobserved variables === Because a Bayesian network is a complete model for its variables and their relationships, it can be used to answer probabilistic queries about them. For example, the network can be used to update knowledge of the state of a subset of variables when other variables (the evidence variables) are observed. This process of computing the posterior distribution of variables given evidence is called probabilistic inference. The posterior gives a universal sufficient statistic for detection applications, when choosing values for the variable subset that minimize some expected loss function, for instance the probability of decision error. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to complex problems. The most common exact inference methods are: variable elimination, which eliminates (by integration or summation) the non-observed non-query variables one by one by distributing the sum over the prod

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  T-vertices

  T-vertices is a term used in computer graphics to describe a problem that can occur during mesh refinement or mesh simplification. The most common case occurs in naive implementations of continuous level of detail, where a finer-level mesh is "sewn" together with a coarser-level mesh by simply aligning the finer vertices on the edges of the coarse polygons. The result is a continuous mesh, however due to the nature of the z-buffer and certain lighting algorithms such as Gouraud shading, visual artifacts can often be detected. Some modeling algorithms such as subdivision surfaces will fail when a model contains T-vertices.

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  Curriculum learning

  Curriculum learning is a technique in machine learning in which a model is trained on examples of increasing difficulty, where the definition of "difficulty" may be provided externally or discovered as part of the training process. This is intended to attain good performance more quickly, or to converge to a better local optimum if the global optimum is not found. == Approach == Most generally, curriculum learning is the technique of successively increasing the difficulty of examples in the training set that is presented to a model over multiple training iterations. This can produce better results than exposing the model to the full training set immediately under some circumstances; most typically, when the model is able to learn general principles from easier examples, and then gradually incorporate more complex and nuanced information as harder examples are introduced, such as edge cases. This has been shown to work in many domains, most likely as a form of regularization. There are several major variations in how the technique is applied: A concept of "difficulty" must be defined. This may come from human annotation or an external heuristic; for example in language modeling, shorter sentences might be classified as easier than longer ones. Another approach is to use the performance of another model, with examples accurately predicted by that model being classified as easier (providing a connection to boosting). Difficulty can be increased steadily or in distinct epochs, and in a deterministic schedule or according to a probability distribution. This may also be moderated by a requirement for diversity at each stage, in cases where easier examples are likely to be disproportionately similar to each other. Applications must also decide the schedule for increasing the difficulty. Simple approaches may use a fixed schedule, such as training on easy examples for half of the available iterations and then all examples for the second half. Other approaches use self-paced learning to increase the difficulty in proportion to the performance of the model on the current set. Since curriculum learning only concerns the selection and ordering of training data, it can be combined with many other techniques in machine learning. The success of the method assumes that a model trained for an easier version of the problem can generalize to harder versions, so it can be seen as a form of transfer learning. Some authors also consider curriculum learning to include other forms of progressively increasing complexity, such as increasing the number of model parameters. It is frequently combined with reinforcement learning, such as learning a simplified version of a game first. Some domains have shown success with anti-curriculum learning: training on the most difficult examples first. One example is the ACCAN method for speech recognition, which trains on the examples with the lowest signal-to-noise ratio first. == History == The term "curriculum learning" was introduced by Yoshua Bengio et al in 2009, with reference to the psychological technique of shaping in animals and structured education for humans: beginning with the simplest concepts and then building on them. The authors also note that the application of this technique in machine learning has its roots in the early study of neural networks such as Jeffrey Elman's 1993 paper Learning and development in neural networks: the importance of starting small. Bengio et al showed good results for problems in image classification, such as identifying geometric shapes with progressively more complex forms, and language modeling, such as training with a gradually expanding vocabulary. They conclude that, for curriculum strategies, "their beneficial effect is most pronounced on the test set", suggesting good generalization. The technique has since been applied to many other domains: Natural language processing: Part-of-speech tagging Intent detection Sentiment analysis Machine translation Speech recognition Language model pre-training Image recognition: Facial recognition Object detection Reinforcement learning: Game-playing Graph learning Matrix factorization

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  Medoid

  Medoids are representative objects of a data set or a cluster within a data set whose sum of dissimilarities to all the objects in the cluster is minimal. Medoids are similar in concept to means or centroids, but medoids are always restricted to be members of the data set. Medoids are most commonly used on data when a mean or centroid cannot be defined, such as graphs. They are also used in contexts where the centroid is not representative of the dataset like in images, 3-D trajectories and gene expression (where while the data is sparse the medoid need not be). These are also of interest while wanting to find a representative using some distance other than squared euclidean distance (for instance in movie-ratings). For some data sets there may be more than one medoid, as with medians. A common application of the medoid is the k-medoids clustering algorithm, which is similar to the k-means algorithm but works when a mean or centroid is not definable. This algorithm basically works as follows. First, a set of medoids is chosen at random. Second, the distances to the other points are computed. Third, data are clustered according to the medoid they are most similar to. Fourth, the medoid set is optimized via an iterative process. Note that a medoid is not equivalent to a median, a geometric median, or centroid. A median is only defined on 1-dimensional data, and it only minimizes dissimilarity to other points for metrics induced by a norm (such as the Manhattan distance or Euclidean distance). A geometric median is defined in any dimension, but unlike a medoid, it is not necessarily a point from within the original dataset. == Definition == Let X := { x 1 , x 2 , … , x n } {\textstyle {\mathcal {X}}:=\{x_{1},x_{2},\dots ,x_{n}\}} be a set of n {\textstyle n} points in a space with a distance function d. Medoid is defined as x medoid = arg ⁡ min y ∈ X ∑ i = 1 n d ( y , x i ) . {\displaystyle x_{\text{medoid}}=\arg \min _{y\in {\mathcal {X}}}\sum _{i=1}^{n}d(y,x_{i}).} == Clustering with medoids == Medoids are a popular replacement for the cluster mean when the distance function is not (squared) Euclidean distance, or not even a metric (as the medoid does not require the triangle inequality). When partitioning the data set into clusters, the medoid of each cluster can be used as a representative of each cluster. Clustering algorithms based on the idea of medoids include: Partitioning Around Medoids (PAM), the standard k-medoids algorithm Hierarchical Clustering Around Medoids (HACAM), which uses medoids in hierarchical clustering == Algorithms to compute the medoid of a set == From the definition above, it is clear that the medoid of a set X {\displaystyle {\mathcal {X}}} can be computed after computing all pairwise distances between points in the ensemble. This would take O ( n 2 ) {\textstyle O(n^{2})} distance evaluations (with n = | X | {\displaystyle n=|{\mathcal {X}}|} ). In the worst case, one can not compute the medoid with fewer distance evaluations. However, there are many approaches that allow us to compute medoids either exactly or approximately in sub-quadratic time under different statistical models. If the points lie on the real line, computing the medoid reduces to computing the median which can be done in O ( n ) {\textstyle O(n)} by Quick-select algorithm of Hoare. However, in higher dimensional real spaces, no linear-time algorithm is known. RAND is an algorithm that estimates the average distance of each point to all the other points by sampling a random subset of other points. It takes a total of O ( n log ⁡ n ϵ 2 ) {\textstyle O\left({\frac {n\log n}{\epsilon ^{2}}}\right)} distance computations to approximate the medoid within a factor of ( 1 + ϵ Δ ) {\textstyle (1+\epsilon \Delta )} with high probability, where Δ {\textstyle \Delta } is the maximum distance between two points in the ensemble. Note that RAND is an approximation algorithm, and moreover Δ {\textstyle \Delta } may not be known apriori. RAND was leveraged by TOPRANK which uses the estimates obtained by RAND to focus on a small subset of candidate points, evaluates the average distance of these points exactly, and picks the minimum of those. TOPRANK needs O ( n 5 3 log 4 3 ⁡ n ) {\textstyle O(n^{\frac {5}{3}}\log ^{\frac {4}{3}}n)} distance computations to find the exact medoid with high probability under a distributional assumption on the average distances. trimed presents an algorithm to find the medoid with O ( n 3 2 2 Θ ( d ) ) {\textstyle O(n^{\frac {3}{2}}2^{\Theta (d)})} distance evaluations under a distributional assumption on the points. The algorithm uses the triangle inequality to cut down the search space. Meddit leverages a connection of the medoid computation with multi-armed bandits and uses an upper-Confidence-bound type of algorithm to get an algorithm which takes O ( n log ⁡ n ) {\textstyle O(n\log n)} distance evaluations under statistical assumptions on the points. Correlated Sequential Halving also leverages multi-armed bandit techniques, improving upon Meddit. By exploiting the correlation structure in the problem, the algorithm is able to provably yield drastic improvement (usually around 1-2 orders of magnitude) in both number of distance computations needed and wall clock time. == Implementations == An implementation of RAND, TOPRANK, and trimed can be found here. An implementation of Meddit can be found here and here. An implementation of Correlated Sequential Halving can be found here. == Medoids in text and natural language processing (NLP) == Medoids can be applied to various text and NLP tasks to improve the efficiency and accuracy of analyses. By clustering text data based on similarity, medoids can help identify representative examples within the dataset, leading to better understanding and interpretation of the data. === Text clustering === Text clustering is the process of grouping similar text or documents together based on their content. Medoid-based clustering algorithms can be employed to partition large amounts of text into clusters, with each cluster represented by a medoid document. This technique helps in organizing, summarizing, and retrieving information from large collections of documents, such as in search engines, social media analytics and recommendation systems. === Text summarization === Text summarization aims to produce a concise and coherent summary of a larger text by extracting the most important and relevant information. Medoid-based clustering can be used to identify the most representative sentences in a document or a group of documents, which can then be combined to create a summary. This approach is especially useful for extractive summarization tasks, where the goal is to generate a summary by selecting the most relevant sentences from the original text. === Sentiment analysis === Sentiment analysis involves determining the sentiment or emotion expressed in a piece of text, such as positive, negative, or neutral. Medoid-based clustering can be applied to group text data based on similar sentiment patterns. By analyzing the medoid of each cluster, researchers can gain insights into the predominant sentiment of the cluster, helping in tasks such as opinion mining, customer feedback analysis, and social media monitoring. === Topic modeling === Topic modeling is a technique used to discover abstract topics that occur in a collection of documents. Medoid-based clustering can be applied to group documents with similar themes or topics. By analyzing the medoids of these clusters, researchers can gain an understanding of the underlying topics in the text corpus, facilitating tasks such as document categorization, trend analysis, and content recommendation. === Techniques for measuring text similarity in medoid-based clustering === When applying medoid-based clustering to text data, it is essential to choose an appropriate similarity measure to compare documents effectively. Each technique has its advantages and limitations, and the choice of the similarity measure should be based on the specific requirements and characteristics of the text data being analyzed. The following are common techniques for measuring text similarity in medoid-based clustering: ==== Cosine similarity ==== Cosine similarity is a widely used measure to compare the similarity between two pieces of text. It calculates the cosine of the angle between two document vectors in a high-dimensional space. Cosine similarity ranges between -1 and 1, where a value closer to 1 indicates higher similarity, and a value closer to -1 indicates lower similarity. By visualizing two lines originating from the origin and extending to the respective points of interest, and then measuring the angle between these lines, one can determine the similarity between the associated points. Cosine similarity is less affected by document length, so it may be better at producing medoids that are representative of the content of a cluster instead of the lengt

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  Amazon Rekognition

  Amazon Rekognition is a cloud-based software as a service (SaaS) computer vision platform that was launched in 2016. It has been sold to, and used by, a number of United States government agencies, including U.S. Immigration and Customs Enforcement (ICE) and Orlando, Florida police, as well as private entities. == Capabilities == Rekognition provides a number of computer vision capabilities, which can be divided into two categories: Algorithms that are pre-trained on data collected by Amazon or its partners, and algorithms that a user can train on a custom dataset. As of July 2019, Rekognition provides the following computer vision capabilities. === Pre-trained algorithms === Celebrity recognition in images Facial attribute detection in images, including gender, age range, emotions (e.g. happy, calm, disgusted), whether the face has a beard or mustache, whether the face has eyeglasses or sunglasses, whether the eyes are open, whether the mouth is open, whether the person is smiling, and the location of several markers such as the pupils and jaw line. People Pathing enables tracking of people through a video. An advertised use-case of this capability is to track sports players for post-game analysis. Text detection and classification in images Unsafe visual content detection === Algorithms that a user can train on a custom dataset === SearchFaces enables users to import a database of images with pre-labeled faces, to train a machine learning model on this database, and to expose the model as a cloud service with an API. Then, the user can post new images to the API and receive information about the faces in the image. The API can be used to expose a number of capabilities, including identifying faces of known people, comparing faces, and finding similar faces in a database. Face-based user verification == History and use == === 2017 === In late 2017, the Washington County, Oregon Sheriff's Office began using Rekognition to identify suspects' faces. Rekognition was marketed as a general-purpose computer vision tool, and an engineer working for Washington County decided to use the tool for facial analysis of suspects. Rekognition was offered to the department for free, and Washington County became the first US law enforcement agency known to use Rekognition. In 2018, the agency logged over 1,000 facial searches. The county, according to the Washington Post, by 2019 was paying about $7 a month for all of its searches. The relationship was unknown to the public until May 2018. In 2018, Rekognition was also used to help identify celebrities during a royal wedding telecast. === 2018 === In April 2018, it was reported that FamilySearch was using Rekognition to enable their users to "see which of their ancestors they most resemble based on family photographs". In early 2018, the FBI also began using it as a pilot program for analyzing video surveillance. In May 2018, it was reported by the ACLU that Orlando, Florida was running a pilot using Rekognition for facial analysis in law enforcement, with that pilot ending in July 2019. After the report, on June 22, 2018, Gizmodo reported that Amazon workers had written a letter to CEO Jeff Bezos requesting he cease selling Rekognition to US law enforcement, particularly ICE and Homeland Security. A letter was also sent to Bezos by the ACLU. On June 26, 2018, it was reported that the Orlando police force had ceased using Rekognition after their trial contract expired, reserving the right to use it in the future. The Orlando Police Department said that they had "never gotten to the point to test images" due to old infrastructure and low bandwidth. In July 2018, the ACLU released a test showing that Rekognition had falsely matched 28 members of Congress with mugshot photos, particularly Congresspeople of color. 25 House members afterwards sent a letter to Bezos, expressing concern about Rekognition. Amazon responded saying the Rekognition test had generated 80 percent confidence, while it recommended law enforcement only use matches rated at 99 percent confidence. The Washington Post states that Oregon instead has officers pick a "best of five" result, instead of adhering to the recommendation. In September 2018, it was reported that Mapillary was using Rekognition to read the text on parking signs (e.g. no stopping, no parking, or specific parking hours) in cities. In October 2018, it was reported that Amazon had earlier that year pitched Rekognition to U.S. Immigration and Customs Enforcement agency. Amazon defended government use of Rekognition. On December 1, 2018, it was reported that 8 Democratic lawmakers had said in a letter that Amazon had "failed to provide sufficient answers" about Rekognition, writing that they had "serious concerns that this type of product has significant accuracy issues, places disproportionate burdens on communities of color, and could stifle Americans' willingness to exercise their First Amendment rights in public." === 2019 === In January 2019, MIT researchers published a peer-reviewed study asserting that Rekognition had more difficulty in identifying dark-skinned females than competitors such as IBM and Microsoft. In the study, Rekognition misidentified darker-skinned women as men 31% of the time, but made no mistakes for light-skinned men. Amazon called the report "misinterpreted results" of the research with an improper "default confidence threshold." In January 2019, Amazon's shareholders "urged Amazon to stop selling Rekognition software to law enforcement agencies." Amazon in response defended its use of Rekognition, but supported new federal oversight and guidelines to "make sure facial recognition technology cannot be used to discriminate." In February 2019, it was reported that Amazon was collaborating with the National Institute of Standards and Technology (NIST) on developing standardized tests to improve accuracy and remove bias with facial recognition. In March 2019, an open letter regarding Rekognition was sent by a group of prominent AI researchers to Amazon, criticizing its sale to law enforcement with around 50 signatures. In April 2019, Amazon was told by the Securities and Exchange Commission that they had to vote on two shareholder proposals seeking to limit Rekognition. Amazon argued that the proposals were an "insignificant public policy issue for the Company" not related to Amazon's ordinary business, but their appeal was denied. The vote was set for May. The first proposal was tabled by shareholders. On May 24, 2019, 2.4% of shareholders voted to stop selling Rekognition to government agencies, while a second proposal calling for a study into Rekognition and civil rights had 27.5% support. In August 2019, the ACLU again used Rekognition on members of government, with 26 of 120 lawmakers in California flagged as matches to mugshots. Amazon stated the ACLU was "misusing" the software in the tests, by not dismissing results that did not meet Amazon's recommended accuracy threshold of 99%. By August 2019, there had been protests against ICE's use of Rekognition to surveil immigrants. In March 2019, Amazon announced a Rekognition update that would improve emotional detection, and in August 2019, "fear" was added to emotions that Rekognition could detect. === 2020 === In June 2020, Amazon announced it was implementing a one-year moratorium on police use of Rekognition, in response to the George Floyd protests. === 2024 === The Department of Justice disclosed that the FBI is initiating the use of Amazon Rekognition. The DOJ's AI inventory revealed the FBI's "Project Tyr" aims to customize Rekognition to identify nudity, weapons, explosives, and other information from lawfully acquired media. === 2025 === In late 2025, the New York Times reported that scientist, Dr. Jürgen Matthäus, retired from as the head of research at the U.S. Holocaust Memorial Museum in Washington, D.C., used Amazon Rekognition to identify the shooter in the Holocaust photograph known as The Last Jew in Vinnitsa "with more than 99 percent certainty" — as Jakobus Onnen (1906–1943), a teacher from Tichelwarf near Weener in East Frisia who had been a member of the SS since 1934 and was later killed in action near Zhitomir in 1943. The photographer and victim remain unidentified. == Controversy regarding facial analysis == === Racial and gender bias === In 2018, MIT researchers Joy Buolamwini and Timnit Gebru published a study called Gender Shades. In this study, a set of images was collected, and faces in the images were labeled with face position, gender, and skin tone information. The images were run through SaaS facial recognition platforms from Face++, IBM, and Microsoft. In all three of these platforms, the classifiers performed best on male faces (with error rates on female faces being 8.1% to 20.6% higher than error rates on male faces), and they performed worst on dark female faces (with error rates ranging from 20.8% to 30.4%). The authors hypothesized that this discr

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  Kounta (software company)

  Kounta is an Australian software company founded in 2012. The company's flagship product, Kounta, comprises a cloud based point of sale mobile app. == History == Kounta was founded in 2012 by entrepreneur Nick Cloete. The company is headquartered in Sydney, Australia. In 2012, the company launched its flagship product, Kounta, a hospitality-focused point of sale (POS) mobile app for iPad, Android, Mac, and Windows. The app was initially a web-based application, and later developed into an online cash register and inventory management system that allows businesses to take payments from customers via mobile devices. The app has been made available for iPad, iPhone, and Android devices; as well as iOS, Windows, and other peripherals. In 2012, Kounta partnered with Epson, providing a cloud-based POS platform for Epson printers. In 2013, the company formed a partnership with PayPal, integrating cashless and cardless transaction options via PayPal's mobile app. In 2014, MYOB (company) made an undisclosed investment towards Kounta. This partnership led to the development of MYOB Kounta, a co-branded application merging Kounta's POS with MYOB's application software. MYOB Kounta launched in October of the same year. In 2016, Kounta announced a partnership with the Commonwealth Bank of Australia to include the Kounta app onto "Albert", the bank's EFTPOS tablet, which allowed the Commonwealth Bank of Australia to become the first bank to manage all customers operations from a single device and mobile application. == Technology == The Kounta POS is a software-as-a-service (SaaS) that runs as an application in web browsers as well as natively on iOS and Android operating systems. Kounta also incorporates an Open API, making it possible for other software providers to integrate complementary apps, further extending the software's use. Traditional IT tasks, such as data backup and encryption, hardware maintenance, and server upgrades are handled by Kounta's data center. Kounta is made accessible via paid monthly subscription licenses. == Acquisition by Lightspeed == In October 2019, Kounta was acquired by Lightspeed, an advanced commerce platform for retail, hospitality, and golf businesses based in Montreal, Canada. Lightspeed acquired Kounta for $35.3 million USD.

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  Weighted majority algorithm (machine learning)

  In machine learning, weighted majority algorithm (WMA) is a meta learning algorithm used to construct a compound algorithm from a pool of prediction algorithms, which could be any type of learning algorithms, classifiers, or even real human experts. The algorithm assumes that we have no prior knowledge about the accuracy of the algorithms in the pool, but there are sufficient reasons to believe that one or more will perform well. Assume that the problem is a binary decision problem. To construct the compound algorithm, a positive weight is given to each of the algorithms in the pool. The compound algorithm then collects weighted votes from all the algorithms in the pool, and gives the prediction that has a higher vote. If the compound algorithm makes a mistake, the algorithms in the pool that contributed to the wrong predicting will be discounted by a certain ratio β where 0<β<1. It can be shown that the upper bounds on the number of mistakes made in a given sequence of predictions from a pool of algorithms A {\displaystyle \mathbf {A} } is O ( l o g | A | + m ) {\displaystyle \mathbf {O(log|A|+m)} } if one algorithm in x i {\displaystyle \mathbf {x} _{i}} makes at most m {\displaystyle \mathbf {m} } mistakes. There are many variations of the weighted majority algorithm to handle different situations, like shifting targets, infinite pools, or randomized predictions. The core mechanism remains similar, with the final performances of the compound algorithm bounded by a function of the performance of the specialist (best performing algorithm) in the pool.

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  Weighted majority algorithm (machine learning)

  In machine learning, weighted majority algorithm (WMA) is a meta learning algorithm used to construct a compound algorithm from a pool of prediction algorithms, which could be any type of learning algorithms, classifiers, or even real human experts. The algorithm assumes that we have no prior knowledge about the accuracy of the algorithms in the pool, but there are sufficient reasons to believe that one or more will perform well. Assume that the problem is a binary decision problem. To construct the compound algorithm, a positive weight is given to each of the algorithms in the pool. The compound algorithm then collects weighted votes from all the algorithms in the pool, and gives the prediction that has a higher vote. If the compound algorithm makes a mistake, the algorithms in the pool that contributed to the wrong predicting will be discounted by a certain ratio β where 0<β<1. It can be shown that the upper bounds on the number of mistakes made in a given sequence of predictions from a pool of algorithms A {\displaystyle \mathbf {A} } is O ( l o g | A | + m ) {\displaystyle \mathbf {O(log|A|+m)} } if one algorithm in x i {\displaystyle \mathbf {x} _{i}} makes at most m {\displaystyle \mathbf {m} } mistakes. There are many variations of the weighted majority algorithm to handle different situations, like shifting targets, infinite pools, or randomized predictions. The core mechanism remains similar, with the final performances of the compound algorithm bounded by a function of the performance of the specialist (best performing algorithm) in the pool.

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