AI Writing Tools

Explore the best AI Writing Tools — independent reviews, comparisons, pricing and step-by-step how-to guides, curated by Aizhi.

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  1DayLater

  1DayLater was a free, web-based software that was focused on professional invoicing. The company was formed in 2009 and closed in October 2013. The main function of 1DayLater was to help users create invoices for clients. It could also be used to track time and other expenses, work to budgets, and to track projects. Multiple users could simultaneously work on the same projects together. PC Magazine (PCMag) voted 1DayLater as one of the 'Best Free Software of 2010'. == History == The software was developed by two brothers, Paul and David King; after they experienced similar frustrations while working freelance, the brothers wanted to create a product that would let them track time, expenses and business miles in a single online location. == Media coverage == 1DayLater had the following press coverage: BBC Webscape (July 2010) - Kate Russell gives her latest selection of the best sites on the World Wide Web PCMag (March 2010) - The best free software of 2010 Lifehacker (February 2010) - "A worthy addition to our 'Top Ten Tips and Tools for Freelancers'" Gigaom (February 2010) - Taking a closer look with 1DayLater The Journal (May 2009) - "Top Ten Brands of the North East" (UK) Techcrunch (January 2009) - "A 'feisty time tracking solution from the North East of England'"

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  Evolutionary algorithm

  Evolutionary algorithms (EA) reproduce essential elements of biological evolution in a computer algorithm in order to solve "difficult" problems, at least approximately, for which no exact or satisfactory solution methods are known. They are metaheuristics and population-based bio-inspired algorithms and evolutionary computation, which itself are part of the field of computational intelligence. The mechanisms of biological evolution that an EA mainly imitates are reproduction, mutation, recombination and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions (see also loss function). Evolution of the population then takes place after the repeated application of the above operators. Evolutionary algorithms often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying fitness landscape. Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of microevolution (microevolutionary processes) and planning models based upon cellular processes. In most real applications of EAs, computational complexity is a prohibiting factor. In fact, this computational complexity is due to fitness function evaluation. Fitness approximation is one of the solutions to overcome this difficulty. However, seemingly simple EA can solve often complex problems; therefore, there may be no direct link between algorithm complexity and problem complexity. == Generic definition == The following is an example of a generic evolutionary algorithm: Randomly generate the initial population of individuals, the first generation. Evaluate the fitness of each individual in the population. Check, if the goal is reached and the algorithm can be terminated. Select individuals as parents, preferably of higher fitness. Produce offspring with optional crossover (mimicking reproduction). Apply mutation operations on the offspring. Select individuals preferably of lower fitness for replacement with new individuals (mimicking natural selection). Return to 2 == Types == Similar techniques differ in genetic representation and other implementation details, and the nature of the particular applied problem. Genetic algorithm – This is the most popular type of EA. One seeks the solution of a problem in the form of strings of numbers (traditionally binary, although the best representations are usually those that reflect something about the problem being solved), by applying operators such as recombination and mutation (sometimes one, sometimes both). This type of EA is often used in optimization problems. Genetic programming – Here the solutions are in the form of computer programs, and their fitness is determined by their ability to solve a computational problem. There are many variants of Genetic Programming: Cartesian genetic programming Gene expression programming Grammatical evolution Linear genetic programming Multi expression programming Evolutionary programming – Similar to evolution strategy, but with a deterministic selection of all parents. Evolution strategy (ES) – Works with vectors of real numbers as representations of solutions, and typically uses self-adaptive mutation rates. The method is mainly used for numerical optimization, although there are also variants for combinatorial tasks. CMA-ES Natural evolution strategy Differential evolution – Based on vector differences and is therefore primarily suited for numerical optimization problems. Coevolutionary algorithm – Similar to genetic algorithms and evolution strategies, but the created solutions are compared on the basis of their outcomes from interactions with other solutions. Solutions can either compete or cooperate during the search process. Coevolutionary algorithms are often used in scenarios where the fitness landscape is dynamic, complex, or involves competitive interactions. Neuroevolution – Similar to genetic programming but the genomes represent artificial neural networks by describing structure and connection weights. The genome encoding can be direct or indirect. Learning classifier system – Here the solution is a set of classifiers (rules or conditions). A Michigan-LCS evolves at the level of individual classifiers whereas a Pittsburgh-LCS uses populations of classifier-sets. Initially, classifiers were only binary, but now include real, neural net, or S-expression types. Fitness is typically determined with either a strength or accuracy based reinforcement learning or supervised learning approach. Quality–Diversity algorithms – QD algorithms simultaneously aim for high-quality and diverse solutions. Unlike traditional optimization algorithms that solely focus on finding the best solution to a problem, QD algorithms explore a wide variety of solutions across a problem space and keep those that are not just high performing, but also diverse and unique. == Theoretical background == The following theoretical principles apply to all or almost all EAs. === No free lunch theorem === The no free lunch theorem of optimization states that all optimization strategies are equally effective when the set of all optimization problems is considered. Under the same condition, no evolutionary algorithm is fundamentally better than another. This can only be the case if the set of all problems is restricted. This is exactly what is inevitably done in practice. Therefore, to improve an EA, it must exploit problem knowledge in some form (e.g. by choosing a certain mutation strength or a problem-adapted coding). Thus, if two EAs are compared, this constraint is implied. In addition, an EA can use problem specific knowledge by, for example, not randomly generating the entire start population, but creating some individuals through heuristics or other procedures. Another possibility to tailor an EA to a given problem domain is to involve suitable heuristics, local search procedures or other problem-related procedures in the process of generating the offspring. This form of extension of an EA is also known as a memetic algorithm. Both extensions play a major role in practical applications, as they can speed up the search process and make it more robust. === Convergence === For EAs in which, in addition to the offspring, at least the best individual of the parent generation is used to form the subsequent generation (so-called elitist EAs), there is a general proof of convergence under the condition that an optimum exists. Without loss of generality, a maximum search is assumed for the proof: From the property of elitist offspring acceptance and the existence of the optimum it follows that per generation k {\displaystyle k} an improvement of the fitness F {\displaystyle F} of the respective best individual x ′ {\displaystyle x'} will occur with a probability P > 0 {\displaystyle P>0} . Thus: F ( x 1 ′ ) ≤ F ( x 2 ′ ) ≤ F ( x 3 ′ ) ≤ ⋯ ≤ F ( x k ′ ) ≤ ⋯ {\displaystyle F(x'_{1})\leq F(x'_{2})\leq F(x'_{3})\leq \cdots \leq F(x'_{k})\leq \cdots } I.e., the fitness values represent a monotonically non-decreasing sequence, which is bounded due to the existence of the optimum. From this follows the convergence of the sequence against the optimum. Since the proof makes no statement about the speed of convergence, it is of little help in practical applications of EAs. But it does justify the recommendation to use elitist EAs. However, when using the usual panmictic population model, elitist EAs tend to converge prematurely more than non-elitist ones. In a panmictic population model, mate selection (see step 4 of the generic definition) is such that every individual in the entire population is eligible as a mate. In non-panmictic populations, selection is suitably restricted, so that the dispersal speed of better individuals is reduced compared to panmictic ones. Thus, the general risk of premature convergence of elitist EAs can be significantly reduced by suitable population models that restrict mate selection. === Virtual alphabets === With the theory of virtual alphabets, David E. Goldberg showed in 1990 that by using a representation with real numbers, an EA that uses classical recombination operators (e.g. uniform or n-point crossover) cannot reach certain areas of the search space, in contrast to a coding with binary numbers. This results in the recommendation for EAs with real representation to use arithmetic operators for recombination (e.g. arithmetic mean or intermediate recombination). With suitable operators, real-valued representations are more effective than binary ones, contrary to earlier opinion. == Comparison to other concepts == === Biological processes === A possible limitation of many evolutionary algorithms is their lack of a clear genotype–phenotype distinction. In nature, the fertilized egg cell undergoes a complex process known as embryogenesis to become a mature p

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  Probably approximately correct learning

  In computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed in 1984 by Leslie Valiant. In this framework, the learner receives samples and must select a generalization function (called the hypothesis) from a certain class of possible functions. The goal is that, with high probability (the "probably" part), the selected function will have low generalization error (the "approximately correct" part). The learner must be able to learn the concept given any arbitrary approximation ratio, probability of success, or distribution of the samples. The model was later extended to treat noise (misclassified samples). An important innovation of the PAC framework is the introduction of computational complexity theory concepts to machine learning. In particular, the learner is expected to find efficient functions (time and space requirements bounded to a polynomial of the example size), and the learner itself must implement an efficient procedure (requiring an example count bounded to a polynomial of the concept size, modified by the approximation and likelihood bounds). == Definitions and terminology == In order to give the definition for something that is PAC-learnable, we first have to introduce some terminology. For the following definitions, two examples will be used. The first is the problem of character recognition given an array of n {\displaystyle n} bits encoding a binary-valued image. The other example is the problem of finding an interval that will correctly classify points within the interval as positive and the points outside of the range as negative. Let X {\displaystyle X} be a set called the instance space or the encoding of all the samples. In the character recognition problem, the instance space is X = { 0 , 1 } n {\displaystyle X=\{0,1\}^{n}} . In the interval problem the instance space, X {\displaystyle X} , is the set of all bounded intervals in R {\displaystyle \mathbb {R} } , where R {\displaystyle \mathbb {R} } denotes the set of all real numbers. A concept is a subset c ⊂ X {\displaystyle c\subset X} . One concept is the set of all patterns of bits in X = { 0 , 1 } n {\displaystyle X=\{0,1\}^{n}} that encode a picture of the letter "P". An example concept from the second example is the set of open intervals, { ( a , b ) ∣ 0 ≤ a ≤ π / 2 , π ≤ b ≤ 13 } {\displaystyle \{(a,b)\mid 0\leq a\leq \pi /2,\pi \leq b\leq {\sqrt {13}}\}} , each of which contains only the positive points. A concept class C {\displaystyle C} is a collection of concepts over X {\displaystyle X} . This could be the set of all subsets of the array of bits that are skeletonized 4-connected (width of the font is 1). Let EX ⁡ ( c , D ) {\displaystyle \operatorname {EX} (c,D)} be a procedure that draws an example, x {\displaystyle x} , using a probability distribution D {\displaystyle D} and gives the correct label c ( x ) {\displaystyle c(x)} , that is 1 if x ∈ c {\displaystyle x\in c} and 0 otherwise. Now, given 0 < ϵ , δ < 1 {\displaystyle 0<\epsilon ,\delta <1} , assume there is an algorithm A {\displaystyle A} and a polynomial p {\displaystyle p} in 1 / ϵ , 1 / δ {\displaystyle 1/\epsilon ,1/\delta } (and other relevant parameters of the class C {\displaystyle C} ) such that, given a sample of size p {\displaystyle p} drawn according to EX ⁡ ( c , D ) {\displaystyle \operatorname {EX} (c,D)} , then, with probability of at least 1 − δ {\displaystyle 1-\delta } , A {\displaystyle A} outputs a hypothesis h ∈ C {\displaystyle h\in C} that has an average error less than or equal to ϵ {\displaystyle \epsilon } on X {\displaystyle X} with the same distribution D {\displaystyle D} . Further if the above statement for algorithm A {\displaystyle A} is true for every concept c ∈ C {\displaystyle c\in C} and for every distribution D {\displaystyle D} over X {\displaystyle X} , and for all 0 < ϵ , δ < 1 {\displaystyle 0<\epsilon ,\delta <1} then C {\displaystyle C} is (efficiently) PAC learnable (or distribution-free PAC learnable). We can also say that A {\displaystyle A} is a PAC learning algorithm for C {\displaystyle C} . == Equivalence == Under some regularity conditions these conditions are equivalent: The concept class C is PAC learnable. The VC dimension of C is finite. C is a uniformly Glivenko-Cantelli class. C is compressible in the sense of Littlestone and Warmuth

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  Ni1000

  The Ni1000 is an artificial neural network chip developed by Nestor Corporation and Intel, developed in the 1990s. It is Intel's second-generation neural network chip, but the first all-digital chip. The chip is aimed at image analysis applications– containing more than 3 million transistors – and can analyze 40,000 patterns per second. Prototypes running Nestor's OCR software in 1994 were capable of recognizing around 100 handwritten characters per second. The development was funded with money from DARPA and Office of Naval Research.

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  StatMuse

  StatMuse Inc. is an American artificial intelligence company founded in 2014. It operates an eponymous website that hosts a database of sports statistics covering the four major North American sports leagues, the Women's National Basketball Association (WNBA), NCAA Division I men's basketball, NCAA Division I Football Bowl Subdivision, the Big Five association football leagues in Europe, and various professional golf tours. == History == The company was founded by friends Adam Elmore and Eli Dawson in 2014. In email correspondence to the Springfield News-Leader, Elmore detailed that he and Dawson, fans of the National Basketball Association (NBA), were compelled to create StatMuse after they realized there was no online platform where they could search "Lebron James most points" [sic] and quickly get a result "showing his highest scoring games." As a startup, the company's goal was to utilize a type of artificial intelligence called natural language processing (NLP) for sports. In 2015, the company was part of the second group of startups accepted into the Disney Accelerator program. The company secured support from several investors, including The Walt Disney Company, Techstars, Allen & Company, the NFL Players Association, Greycroft and NBA Commissioner David Stern. As part of their partnership with Disney, StatMuse signed a content deal with ESPN (owned by Disney) to provide stats content on social media and television during the 2015–16 NBA season. Initially, the company only had stats available for the NBA, but eventually expanded to provide stats for the other major North American sports leagues. The company's initial demographic was players of fantasy sports, but it eventually expanded to target general sports fans as well. StatMuse offers responses to user queries in the voices of sports-related public figures. Dawson shared with VentureBeat that StatMuse brings people in and records them saying different words and phrases. These celebrity voices were made accessible through Google's Google Assistant service, Microsoft's Cortana virtual assistant, and Amazon's Echo devices. The company launched its phone app in September 2017. The app allows users to access StatMuse's sports statistics database by submitting queries in their natural language. Upon the launch of the phone app, Fitz Tepper of TechCrunch wrote that: "The technology isn't perfect – some of the pauses between words are a bit awkward, making it clear that some phrases are being stitched together on the fly. But this is the exception, and on the whole, most responses sound pretty good." StatMuse plug-ins for Slack and Facebook Messenger were also made, providing text-based sports stats. In 2019, StatMuse received investment from the Google Assistant Investment program. The service launched a premium option dubbed StatMuse+ in May 2023, offering options that had previously been included for free, such as unlimited searches and full results in data tables. The premium version also included early access to new features and a personalized search history, as well as not having ads. The app received a variety of feedback. In January 2024, the service launched a Premier League version of the website dubbed StatMuse FC. It is planned to introduce more leagues on the website.

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  Elastic net regularization

  In statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2 penalties of the lasso and ridge methods. Nevertheless, elastic net regularization is typically more accurate than both methods with regard to reconstruction. == Specification == The elastic net method overcomes the limitations of the LASSO (least absolute shrinkage and selection operator) method which uses a penalty function based on ‖ β ‖ 1 = ∑ j = 1 p | β j | . {\displaystyle \|\beta \|_{1}=\textstyle \sum _{j=1}^{p}|\beta _{j}|.} Use of this penalty function has several limitations. For example, in the "large p, small n" case (high-dimensional data with few examples), the LASSO selects at most n variables before it saturates. Also if there is a group of highly correlated variables, then the LASSO tends to select one variable from a group and ignore the others. To overcome these limitations, the elastic net adds a quadratic part ( ‖ β ‖ 2 {\displaystyle \|\beta \|^{2}} ) to the penalty, which when used alone is ridge regression (known also as Tikhonov regularization). The estimates from the elastic net method are defined by β ^ ≡ argmin β ( ‖ y − X β ‖ 2 + λ 2 ‖ β ‖ 2 + λ 1 ‖ β ‖ 1 ) . {\displaystyle {\hat {\beta }}\equiv {\underset {\beta }{\operatorname {argmin} }}(\|y-X\beta \|^{2}+\lambda _{2}\|\beta \|^{2}+\lambda _{1}\|\beta \|_{1}).} The quadratic penalty term makes the loss function strongly convex, and it therefore has a unique minimum. The elastic net method includes the LASSO and ridge regression: in other words, each of them is a special case where λ 1 = λ , λ 2 = 0 {\displaystyle \lambda _{1}=\lambda ,\lambda _{2}=0} or λ 1 = 0 , λ 2 = λ {\displaystyle \lambda _{1}=0,\lambda _{2}=\lambda } . Meanwhile, the naive version of elastic net method finds an estimator in a two-stage procedure : first for each fixed λ 2 {\displaystyle \lambda _{2}} it finds the ridge regression coefficients, and then does a LASSO type shrinkage. This kind of estimation incurs a double amount of shrinkage, which leads to increased bias and poor predictions. To improve the prediction performance, sometimes the coefficients of the naive version of elastic net is rescaled by multiplying the estimated coefficients by ( 1 + λ 2 ) {\displaystyle (1+\lambda _{2})} . Examples of where the elastic net method has been applied are: Support vector machine Metric learning Portfolio optimization Cancer prognosis == Reduction to support vector machine == It was proven in 2014 that the elastic net can be reduced to the linear support vector machine. A similar reduction was previously proven for the LASSO in 2014. The authors showed that for every instance of the elastic net, an artificial binary classification problem can be constructed such that the hyper-plane solution of a linear support vector machine (SVM) is identical to the solution β {\displaystyle \beta } (after re-scaling). The reduction immediately enables the use of highly optimized SVM solvers for elastic net problems. It also enables the use of GPU acceleration, which is often already used for large-scale SVM solvers. The reduction is a simple transformation of the original data and regularization constants X ∈ R n × p , y ∈ R n , λ 1 ≥ 0 , λ 2 ≥ 0 {\displaystyle X\in {\mathbb {R} }^{n\times p},y\in {\mathbb {R} }^{n},\lambda _{1}\geq 0,\lambda _{2}\geq 0} into new artificial data instances and a regularization constant that specify a binary classification problem and the SVM regularization constant X 2 ∈ R 2 p × n , y 2 ∈ { − 1 , 1 } 2 p , C ≥ 0. {\displaystyle X_{2}\in {\mathbb {R} }^{2p\times n},y_{2}\in \{-1,1\}^{2p},C\geq 0.} Here, y 2 {\displaystyle y_{2}} consists of binary labels − 1 , 1 {\displaystyle {-1,1}} . When 2 p > n {\displaystyle 2p>n} it is typically faster to solve the linear SVM in the primal, whereas otherwise the dual formulation is faster. Some authors have referred to the transformation as Support Vector Elastic Net (SVEN), and provided the following MATLAB pseudo-code: == Software == "Glmnet: Lasso and elastic-net regularized generalized linear models" is a software which is implemented as an R source package and as a MATLAB toolbox. This includes fast algorithms for estimation of generalized linear models with ℓ1 (the lasso), ℓ2 (ridge regression) and mixtures of the two penalties (the elastic net) using cyclical coordinate descent, computed along a regularization path. JMP Pro 11 includes elastic net regularization, using the Generalized Regression personality with Fit Model. "pensim: Simulation of high-dimensional data and parallelized repeated penalized regression" implements an alternate, parallelised "2D" tuning method of the ℓ parameters, a method claimed to result in improved prediction accuracy. scikit-learn includes linear regression and logistic regression with elastic net regularization. SVEN, a Matlab implementation of Support Vector Elastic Net. This solver reduces the Elastic Net problem to an instance of SVM binary classification and uses a Matlab SVM solver to find the solution. Because SVM is easily parallelizable, the code can be faster than Glmnet on modern hardware. SpaSM, a Matlab implementation of sparse regression, classification and principal component analysis, including elastic net regularized regression. Apache Spark provides support for Elastic Net Regression in its MLlib machine learning library. The method is available as a parameter of the more general LinearRegression class. SAS (software) The SAS procedure Glmselect and SAS Viya procedure Regselect support the use of elastic net regularization for model selection.

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  Promoter based genetic algorithm

  The promoter based genetic algorithm (PBGA) is a genetic algorithm for neuroevolution developed by F. Bellas and R.J. Duro in the Integrated Group for Engineering Research (GII) at the University of Coruña, in Spain. It evolves variable size feedforward artificial neural networks (ANN) that are encoded into sequences of genes for constructing a basic ANN unit. Each of these blocks is preceded by a gene promoter acting as an on/off switch that determines if that particular unit will be expressed or not. == PBGA basics == The basic unit in the PBGA is a neuron with all of its inbound connections as represented in the following figure: The genotype of a basic unit is a set of real valued weights followed by the parameters of the neuron and proceeded by an integer valued field that determines the promoter gene value and, consequently, the expression of the unit. By concatenating units of this type we can construct the whole network. With this encoding it is imposed that the information that is not expressed is still carried by the genotype in evolution but it is shielded from direct selective pressure, maintaining this way the diversity in the population, which has been a design premise for this algorithm. Therefore, a clear difference is established between the search space and the solution space, permitting information learned and encoded into the genotypic representation to be preserved by disabling promoter genes. == Results == The PBGA was originally presented within the field of autonomous robotics, in particular in the real time learning of environment models of the robot. It has been used inside the Multilevel Darwinist Brain (MDB) cognitive mechanism developed in the GII for real robots on-line learning. In another paper it is shown how the application of the PBGA together with an external memory that stores the successful obtained world models, is an optimal strategy for adaptation in dynamic environments. Recently, the PBGA has provided results that outperform other neuroevolutionary algorithms in non-stationary problems, where the fitness function varies in time.

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  Neocognitron

  The neocognitron is a hierarchical, multilayered artificial neural network proposed by Kunihiko Fukushima in 1979. It has been used for Japanese handwritten character recognition and other pattern recognition tasks, and served as the inspiration for convolutional neural networks. Previously in 1969, he published a similar architecture, but with hand-designed kernels inspired by convolutions in mammalian vision. In 1975 he improved it to the Cognitron, and in 1979 he improved it to the neocognitron, which learns all convolutional kernels by unsupervised learning (in his terminology, "self-organized by 'learning without a teacher'"). The neocognitron was inspired by the model proposed by Hubel & Wiesel in 1959. They found two types of cells in the visual primary cortex called simple cell and complex cell, and also proposed a cascading model of these two types of cells for use in pattern recognition tasks. The neocognitron is a natural extension of these cascading models. The neocognitron consists of multiple types of cells, the most important of which are called S-cells and C-cells. The local features are extracted by S-cells, and these features' deformation, such as local shifts, are tolerated by C-cells. Local features in the input are integrated gradually and classified in the higher layers. The idea of local feature integration is found in several other models, such as the Convolutional Neural Network model, the SIFT method, and the HoG method. There are various kinds of neocognitron. For example, some types of neocognitron can detect multiple patterns in the same input by using backward signals to achieve selective attention.

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  Language Computer Corporation

  Language Computer Corporation (LCC) is a natural language processing research company based in Richardson, Texas. The company develops a variety of natural language processing products, including software for question answering, information extraction, and automatic summarization. Since its founding in 1995, the low-profile company has landed significant United States Government contracts, with $8,353,476 in contracts in 2006-2008. While the company has focused primarily on the government software market, LCC has also used its technology to spin off three start-up companies. The first spin-off, known as Lymba Corporation, markets the PowerAnswer question answering product originally developed at LCC. In 2010, LCC's CEO, Andrew Hickl, co-founded two start-ups which made use of the company's technology. These included Swingly, an automatic question answering start-up, and Extractiv, an information extraction service that was founded in partnership with Houston, Texas-based 80legs.

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  Facial recognition system

  A facial recognition system is a technology potentially capable of matching a human face from a digital image or a video frame against a database of faces. Such a system is typically employed to authenticate users through ID verification services, and works by pinpointing and measuring facial features from a given image. Development on similar systems began in the 1960s as a form of computer application. Since their inception, facial recognition systems have seen wider uses in recent times on smartphones and in other forms of technology, such as robotics. Because computerized facial recognition involves the measurement of a human's physiological characteristics, facial recognition systems are categorized as biometrics. Although the accuracy of facial recognition systems as a biometric technology is lower than iris recognition, fingerprint image acquisition, palm recognition or voice recognition, it is widely adopted due to its contactless process. Facial recognition systems have been deployed in advanced human–computer interaction, video surveillance, law enforcement, passenger screening, decisions on employment and housing, and automatic indexing of images. Facial recognition systems are employed throughout the world today by governments and private companies. Their effectiveness varies, and some systems have previously been scrapped because of their ineffectiveness. The use of facial recognition systems has also raised controversy, with claims that the systems violate citizens' privacy, commonly make incorrect identifications, encourage gender norms and racial profiling, and do not protect important biometric data. The appearance of synthetic media such as deepfakes has also raised concerns about its security. These claims have led to the ban of facial recognition systems in several cities in the United States. Growing societal concerns led social networking company Meta Platforms to shut down its Facebook facial recognition system in 2021, deleting the face-scan data of more than one billion users. The change represented one of the largest shifts in facial recognition usage in the technology's history. IBM also stopped offering facial recognition technology due to similar concerns. == History of facial recognition technology == Automated facial recognition was pioneered in the 1960s by Woody Bledsoe, Helen Chan Wolf, and Charles Bisson, whose work focused on teaching computers to recognize human faces. Their early facial recognition project was dubbed "man-machine" because a human first needed to establish the coordinates of facial features in a photograph before they could be used by a computer for recognition. Using a graphics tablet, a human would pinpoint facial features coordinates, such as the pupil centers, the inside and outside corners of eyes, and the widows peak in the hairline. The coordinates were used to calculate 20 individual distances, including the width of the mouth and of the eyes. A human could process about 40 pictures an hour, building a database of these computed distances. A computer would then automatically compare the distances for each photograph, calculate the difference between the distances, and return the closed records as a possible match. In 1970, Takeo Kanade publicly demonstrated a face-matching system that located anatomical features such as the chin and calculated the distance ratio between facial features without human intervention. Later tests revealed that the system could not always reliably identify facial features. Nonetheless, interest in the subject grew and in 1977 Kanade published the first detailed book on facial recognition technology. In 1993, the Defense Advanced Research Project Agency (DARPA) and the Army Research Laboratory (ARL) established the face recognition technology program FERET to develop "automatic face recognition capabilities" that could be employed in a productive real life environment "to assist security, intelligence, and law enforcement personnel in the performance of their duties." Face recognition systems that had been trialled in research labs were evaluated. The FERET tests found that while the performance of existing automated facial recognition systems varied, a handful of existing methods could viably be used to recognize faces in still images taken in a controlled environment. The FERET tests spawned three US companies that sold automated facial recognition systems. Vision Corporation and Miros Inc were founded in 1994, by researchers who used the results of the FERET tests as a selling point. Viisage Technology was established by an identification card defense contractor in 1996 to commercially exploit the rights to the facial recognition algorithm developed by Alex Pentland at MIT. Following the 1993 FERET face-recognition vendor test, the Department of Motor Vehicles (DMV) offices in West Virginia and New Mexico became the first DMV offices to use automated facial recognition systems to prevent people from obtaining multiple driving licenses using different names. Driver's licenses in the United States were at that point a commonly accepted form of photo identification. DMV offices across the United States were undergoing a technological upgrade and were in the process of establishing databases of digital ID photographs. This enabled DMV offices to deploy the facial recognition systems on the market to search photographs for new driving licenses against the existing DMV database. DMV offices became one of the first major markets for automated facial recognition technology and introduced US citizens to facial recognition as a standard method of identification. The increase of the US prison population in the 1990s prompted U.S. states to established connected and automated identification systems that incorporated digital biometric databases, in some instances this included facial recognition. In 1999, Minnesota incorporated the facial recognition system FaceIT by Visionics into a mug shot booking system that allowed police, judges and court officers to track criminals across the state. Until the 1990s, facial recognition systems were developed primarily by using photographic portraits of human faces. Research on face recognition to reliably locate a face in an image that contains other objects gained traction in the early 1990s with the principal component analysis (PCA). The PCA method of face detection is also known as Eigenface and was developed by Matthew Turk and Alex Pentland. Turk and Pentland combined the conceptual approach of the Karhunen–Loève theorem and factor analysis, to develop a linear model. Eigenfaces are determined based on global and orthogonal features in human faces. A human face is calculated as a weighted combination of a number of Eigenfaces. Because few Eigenfaces were used to encode human faces of a given population, Turk and Pentland's PCA face detection method greatly reduced the amount of data that had to be processed to detect a face. Pentland in 1994 defined Eigenface features, including eigen eyes, eigen mouths and eigen noses, to advance the use of PCA in facial recognition. In 1997, the PCA Eigenface method of face recognition was improved upon using linear discriminant analysis (LDA) to produce Fisherfaces. LDA Fisherfaces became dominantly used in PCA feature based face recognition. While Eigenfaces were also used for face reconstruction. In these approaches no global structure of the face is calculated which links the facial features or parts. Purely feature based approaches to facial recognition were overtaken in the late 1990s by the Bochum system, which used Gabor filter to record the face features and computed a grid of the face structure to link the features. Christoph von der Malsburg and his research team at the University of Bochum developed Elastic Bunch Graph Matching in the mid-1990s to extract a face out of an image using skin segmentation. By 1997, the face detection method developed by Malsburg outperformed most other facial detection systems on the market. The so-called "Bochum system" of face detection was sold commercially on the market as ZN-Face to operators of airports and other busy locations. The software was "robust enough to make identifications from less-than-perfect face views. It can also often see through such impediments to identification as mustaches, beards, changed hairstyles and glasses—even sunglasses". Real-time face detection in video footage became possible in 2001 with the Viola–Jones object detection framework for faces. Paul Viola and Michael Jones combined their face detection method with the Haar-like feature approach to object recognition in digital images to launch AdaBoost, the first real-time frontal-view face detector. By 2015, the Viola–Jones algorithm had been implemented using small low power detectors on handheld devices and embedded systems. Therefore, the Viola–Jones algorithm has not only broadened the practical application of face recognition systems but

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  Word2vec

  Word2vec is a technique in natural language processing for obtaining vector representations of words. These vectors capture information about the meaning of the word based on the surrounding words. The word2vec algorithm estimates these representations by modeling text in a large corpus. Once trained, such a model can detect synonymous words or suggest additional words for a partial sentence. Word2vec was developed by Tomáš Mikolov, Kai Chen, Greg Corrado, Ilya Sutskever and Jeff Dean at Google, and published in 2013. Word2vec represents a word as a high-dimension vector of numbers which capture relationships between words. In particular, words which appear in similar contexts are mapped to vectors which are nearby as measured by cosine similarity. This indicates the level of semantic similarity between the words, so for example the vectors for walk and ran are nearby, as are those for "but" and "however", and "Berlin" and "Germany". == Approach == Word2vec is a group of related models that are used to produce word embeddings. These models are shallow, two-layer neural networks that are trained to reconstruct linguistic contexts of words. Word2vec takes as its input a large corpus of text and produces a mapping of the set of words to a vector space, typically of several hundred dimensions, with each unique word in the corpus being assigned a vector in the space. Word2vec can use either of two model architectures to produce these distributed representations of words: continuous bag of words (CBOW) or continuously sliding skip-gram. In both architectures, word2vec considers both individual words and a sliding context window as it iterates over the corpus. The CBOW can be viewed as a 'fill in the blank' task, where the word embedding represents the way the word influences the relative probabilities of other words in the context window. Words which are semantically similar should influence these probabilities in similar ways, because semantically similar words should be used in similar contexts. The order of context words does not influence prediction (bag of words assumption). In the continuous skip-gram architecture, the model uses the current word to predict the surrounding window of context words. The skip-gram architecture weighs nearby context words more heavily than more distant context words. According to the authors' note, CBOW is faster while skip-gram does a better job for infrequent words. After the model is trained, the learned word embeddings are positioned in the vector space such that words that share common contexts in the corpus — that is, words that are semantically and syntactically similar — are located close to one another in the space. More dissimilar words are located farther from one another in the space. == Mathematical details == This section is based on expositions. A corpus is a sequence of words. Both CBOW and skip-gram are methods to learn one vector per word appearing in the corpus. Let V {\displaystyle V} ("vocabulary") be the set of all words appearing in the corpus C {\displaystyle C} . Our goal is to learn one vector v w ∈ R d {\displaystyle v_{w}\in \mathbb {R} ^{d}} for each word w ∈ V {\displaystyle w\in V} . The idea of skip-gram is that the vector of a word should be close to the vector of each of its neighbors. The idea of CBOW is that the vector-sum of a word's neighbors should be close to the vector of the word. === Continuous bag-of-words (CBOW) === The idea of CBOW is to represent each word with a vector, such that it is possible to predict a word using the sum of the vectors of its neighbors. Specifically, for each word w i {\displaystyle w_{i}} in the corpus, the one-hot encoding of the word is used as the input to the neural network. The output of the neural network is a probability distribution over the dictionary, representing a prediction of individual words in the neighborhood of w i {\displaystyle w_{i}} . The objective of training is to maximize ∑ i ln ⁡ Pr ( w i ∣ w i + j : j ∈ N ) {\displaystyle \sum _{i}\ln \Pr(w_{i}\mid w_{i+j}\colon j\in N)} where N {\displaystyle N} is a set of (non-zero) indices representing the relative locations of nearby words considered to be in w i {\displaystyle w_{i}} 's neighborhood. For example, if we want each word in the corpus to be predicted by every other word in a small span of 4 words. The set of relative indexes of neighbor words will be: N = { − 2 , − 1 , + 1 , + 2 } {\displaystyle N=\{-2,-1,+1,+2\}} , and the objective is to maximize ∑ i ln ⁡ Pr ( w i ∣ w i − 2 , w i − 1 , w i + 1 , w i + 2 ) {\displaystyle \sum _{i}\ln \Pr(w_{i}\mid w_{i-2},w_{i-1},w_{i+1},w_{i+2})} . In standard bag-of-words, a word's context is represented by a word-count (aka a word histogram) of its neighboring words. For example, the "sat" in "the cat sat on the mat" is represented as {"the": 2, "cat": 1, "on": 1}. Note that the last word "mat" is not used to represent "sat", because it is outside the neighborhood N = { − 2 , − 1 , + 1 , + 2 } {\displaystyle N=\{-2,-1,+1,+2\}} . In continuous bag-of-words, the histogram is multiplied by a matrix V {\displaystyle V} to obtain a continuous representation of the word's context. The matrix V {\displaystyle V} is also called a dictionary. Its columns are the word vectors. It has D {\displaystyle D} columns, where D {\displaystyle D} is the size of the dictionary. Let d {\displaystyle d} be the length of each word vector. We have V ∈ R d × D {\displaystyle V\in \mathbb {R} ^{d\times D}} . For example, multiplying the word histogram {"the": 2, "cat": 1, "on": 1} with V {\displaystyle V} , we obtain 2 v the + v cat + v on {\displaystyle 2v_{\text{the}}+v_{\text{cat}}+v_{\text{on}}} . This is then multiplied with another matrix V ′ {\displaystyle V'} of shape R D × d {\displaystyle \mathbb {R} ^{D\times d}} . Each row of it is a word vector v ′ {\displaystyle v'} . This results in a vector of length D {\displaystyle D} , one entry per dictionary entry. Then, apply the softmax to obtain a probability distribution over the dictionary. This system can be visualized as a neural network, similar in spirit to an autoencoder, of architecture linear-linear-softmax, as depicted in the diagram. The system is trained by gradient descent to minimize the cross-entropy loss. In full formula, the cross-entropy loss is: − ∑ i ln ⁡ e v w i ′ ⋅ ( ∑ j ∈ N v w j + i ) ∑ w ′ e v w ′ ′ ⋅ ( ∑ j ∈ N v w j + i ) {\displaystyle -\sum _{i}\ln {\frac {e^{v_{w_{i}}'\cdot (\sum _{j\in N}v_{w_{j+i}})}}{\sum _{w'}e^{v_{w'}'\cdot (\sum _{j\in N}v_{w_{j+i}})}}}} where the outer summation ∑ i {\displaystyle \sum _{i}} is over the words in a corpus, the quantity ∑ j ∈ N v w j + i {\displaystyle \sum _{j\in N}v_{w_{j+i}}} is the sum of a word's neighbors' vectors, etc. Once such a system is trained, we have two trained matrices V , V ′ {\displaystyle V,V'} . Either the column vectors of V {\displaystyle V} or the row vectors of V ′ {\displaystyle V'} can serve as the dictionary. For example, the word "sat" can be represented as either the "sat"-th column of V {\displaystyle V} or the "sat"-th row of V ′ {\displaystyle V'} . It is also possible to simply define V ′ = V ⊤ {\displaystyle V'=V^{\top }} , in which case there would no longer be a choice. === Skip-gram === The idea of skip-gram is to represent each word with a vector, such that it is possible to predict the vectors of its neighbors using the vector of a word. The architecture is still linear-linear-softmax, the same as CBOW, but the input and the output are switched. Specifically, for each word w i {\displaystyle w_{i}} in the corpus, the one-hot encoding of the word is used as the input to the neural network. The output of the neural network is a probability distribution over the dictionary, representing a prediction of individual words in the neighborhood of w i {\displaystyle w_{i}} . The objective of training is to maximize ∑ i ∑ j ∈ N ln ⁡ Pr ( w j + i ∣ w i ) {\displaystyle \sum _{i}\sum _{j\in N}\ln \Pr(w_{j+i}\mid w_{i})} . In full formula, the loss function is − ∑ i ∑ j ∈ N ln ⁡ e v w j + i ′ ⋅ v w i ∑ w ′ e v w ′ ′ ⋅ v w i {\displaystyle -\sum _{i}\sum _{j\in N}\ln {\frac {e^{v_{w_{j+i}}'\cdot v_{w_{i}}}}{\sum _{w'}e^{v_{w'}'\cdot v_{w_{i}}}}}} Same as CBOW, once such a system is trained, we have two trained matrices V , V ′ {\displaystyle V,V'} . Either the column vectors of V {\displaystyle V} or the row vectors of V ′ {\displaystyle V'} can serve as the dictionary. It is also possible to simply define V ′ = V ⊤ {\displaystyle V'=V^{\top }} , in which case there would no longer be a choice. Essentially, skip-gram and CBOW are exactly the same in architecture. They only differ in the objective function during training. == History == During the 1980s, there were some early attempts at using neural networks to represent words and concepts as vectors. In 2010, Tomáš Mikolov (then at Brno University of Technology) with co-authors applied a simple recurrent neural network with a single hidden

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  Multinomial logistic regression

  In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.). Multinomial logistic regression is known by a variety of other names, including polytomous LR, multiclass LR, softmax regression, multinomial logit (mlogit), the maximum entropy (MaxEnt) classifier, and the conditional maximum entropy model. == Background == Multinomial logistic regression is used when the dependent variable in question is nominal (equivalently categorical, meaning that it falls into any one of a set of categories that cannot be ordered in any meaningful way) and for which there are more than two categories. Some examples would be: Which major will a college student choose, given their grades, stated likes and dislikes, etc.? Which blood type does a person have, given the results of various diagnostic tests? In a hands-free mobile phone dialing application, which person's name was spoken, given various properties of the speech signal? Which candidate will a person vote for, given particular demographic characteristics? Which country will a firm locate an office in, given the characteristics of the firm and of the various candidate countries? These are all statistical classification problems. They all have in common a dependent variable to be predicted that comes from one of a limited set of items that cannot be meaningfully ordered, as well as a set of independent variables (also known as features, explanators, etc.), which are used to predict the dependent variable. Multinomial logistic regression is a particular solution to classification problems that use a linear combination of the observed features and some problem-specific parameters to estimate the probability of each particular value of the dependent variable. The best values of the parameters for a given problem are usually determined from some training data (e.g. some people for whom both the diagnostic test results and blood types are known, or some examples of known words being spoken). == Assumptions == The multinomial logistic model assumes that data are case-specific; that is, each independent variable has a single value for each case. As with other types of regression, there is no need for the independent variables to be statistically independent from each other (unlike, for example, in a naive Bayes classifier); however, collinearity is assumed to be relatively low, as it becomes difficult to differentiate between the impact of several variables if this is not the case. If the multinomial logit is used to model choices, it relies on the assumption of independence of irrelevant alternatives (IIA), which is not always desirable. This assumption states that the odds of preferring one class over another do not depend on the presence or absence of other "irrelevant" alternatives. For example, the relative probabilities of taking a car or bus to work do not change if a bicycle is added as an additional possibility. This allows the choice of K alternatives to be modeled as a set of K − 1 independent binary choices, in which one alternative is chosen as a "pivot" and the other K − 1 compared against it, one at a time. The IIA hypothesis is a core hypothesis in rational choice theory; however numerous studies in psychology show that individuals often violate this assumption when making choices. An example of a problem case arises if choices include a car and a blue bus. Suppose the odds ratio between the two is 1 : 1. Now if the option of a red bus is introduced, a person may be indifferent between a red and a blue bus, and hence may exhibit a car : blue bus : red bus odds ratio of 1 : 0.5 : 0.5, thus maintaining a 1 : 1 ratio of car : any bus while adopting a changed car : blue bus ratio of 1 : 0.5. Here the red bus option was not in fact irrelevant, because a red bus was a perfect substitute for a blue bus. If the multinomial logit is used to model choices, it may in some situations impose too much constraint on the relative preferences between the different alternatives. It is especially important to take into account if the analysis aims to predict how choices would change if one alternative were to disappear (for instance if one political candidate withdraws from a three candidate race). Other models like the nested logit or the multinomial probit may be used in such cases as they allow for violation of the IIA. == Model == === Introduction === There are multiple equivalent ways to describe the mathematical model underlying multinomial logistic regression. This can make it difficult to compare different treatments of the subject in different texts. The article on logistic regression presents a number of equivalent formulations of simple logistic regression, and many of these have analogues in the multinomial logit model. The idea behind all of them, as in many other statistical classification techniques, is to construct a linear predictor function that constructs a score from a set of weights that are linearly combined with the explanatory variables (features) of a given observation using a dot product: score ⁡ ( X i , k ) = β k ⋅ X i , {\displaystyle \operatorname {score} (\mathbf {X} _{i},k)={\boldsymbol {\beta }}_{k}\cdot \mathbf {X} _{i},} where Xi is the vector of explanatory variables describing observation i, βk is a vector of weights (or regression coefficients) corresponding to outcome k, and score(Xi, k) is the score associated with assigning observation i to category k. In discrete choice theory, where observations represent people and outcomes represent choices, the score is considered the utility associated with person i choosing outcome k. The predicted outcome is the one with the highest score. The difference between the multinomial logit model and numerous other methods, models, algorithms, etc. with the same basic setup (the perceptron algorithm, support vector machines, linear discriminant analysis, etc.) is the procedure for determining (training) the optimal weights/coefficients and the way that the score is interpreted. In particular, in the multinomial logit model, the score can directly be converted to a probability value, indicating the probability of observation i choosing outcome k given the measured characteristics of the observation. This provides a principled way of incorporating the prediction of a particular multinomial logit model into a larger procedure that may involve multiple such predictions, each with a possibility of error. Without such means of combining predictions, errors tend to multiply. For example, imagine a large predictive model that is broken down into a series of submodels where the prediction of a given submodel is used as the input of another submodel, and that prediction is in turn used as the input into a third submodel, etc. If each submodel has 90% accuracy in its predictions, and there are five submodels in series, then the overall model has only 0.95 = 59% accuracy. If each submodel has 80% accuracy, then overall accuracy drops to 0.85 = 33% accuracy. This issue is known as error propagation and is a serious problem in real-world predictive models, which are usually composed of numerous parts. Predicting probabilities of each possible outcome, rather than simply making a single optimal prediction, is one means of alleviating this issue. === Setup === The basic setup is the same as in logistic regression, the only difference being that the dependent variables are categorical rather than binary, i.e. there are K possible outcomes rather than just two. The following description is somewhat shortened; for more details, consult the logistic regression article. ==== Data points ==== Specifically, it is assumed that we have a series of N observed data points. Each data point i (ranging from 1 to N) consists of a set of M explanatory variables x1,i ... xM,i (also known as independent variables, predictor variables, features, etc.), and an associated categorical outcome Yi (also known as dependent variable, response variable), which can take on one of K possible values. These possible values represent logically separate categories (e.g. different political parties, blood types, etc.), and are often described mathematically by arbitrarily assigning each a number from 1 to K. The explanatory variables and outcome represent observed properties of the data points, and are often thought of as originating in the observations of N "experiments" — although an "experiment" may consist of nothing more than gathering data. The goal of multinomial logistic regression is to construct a model that explains the relationship between the explanatory variables and the outcome, so tha

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  Event condition action

  Event condition action (ECA) is a short-cut for referring to the structure of active rules in event-driven architecture and active database systems. Such a rule traditionally consisted of three parts: The event part specifies the signal that triggers the invocation of the rule The condition part is a logical test that, if satisfied or evaluates to true, causes the action to be carried out The action part consists of updates or invocations on the local data This structure was used by the early research in active databases which started to use the term ECA. Current state of the art ECA rule engines use many variations on rule structure. Also other features not considered by the early research is introduced, such as strategies for event selection into the event part. In a memory-based rule engine, the condition could be some tests on local data and actions could be updates to object attributes. In a database system, the condition could simply be a query to the database, with the result set (if not null) being passed to the action part for changes to the database. In either case, actions could also be calls to external programs or remote procedures. Note that for database usage, updates to the database are regarded as internal events. As a consequence, the execution of the action part of an active rule can match the event part of the same or another active rule, thus triggering it. The equivalent in a memory-based rule engine would be to invoke an external method that caused an external event to trigger another ECA rule. ECA rules can also be used in rule engines that use variants of the Rete algorithm for rule processing. == ECA rule engines == Rulecore Concurrent Rules Apart Database Detect Invocation Rules ConceptBase ECArules

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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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  Mean squared error

  In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the true value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate. In machine learning, specifically empirical risk minimization, MSE may refer to the empirical risk (the average loss on an observed data set), as an estimate of the true MSE (the true risk: the average loss on the actual population distribution). The MSE is a measure of the quality of an estimator. As it is derived from the square of Euclidean distance, it is always a positive value that decreases as the error approaches zero. The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator (how widely spread the estimates are from one data sample to another) and its bias (how far off the average estimated value is from the true value). For an unbiased estimator, the MSE is the variance of the estimator. Like the variance, MSE has the same units of measurement as the square of the quantity being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root-mean-square error or root-mean-square deviation (RMSE or RMSD), which has the same units as the quantity being estimated; for an unbiased estimator, the RMSE is the square root of the variance, known as the standard error. == Definition and basic properties == The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled). In the context of prediction, understanding the prediction interval can also be useful as it provides a range within which a future observation will fall, with a certain probability. The definition of an MSE differs according to whether one is describing a predictor or an estimator. === Predictor === If a vector of n {\displaystyle n} predictions is generated from a sample of n {\displaystyle n} data points on all variables, and Y {\displaystyle Y} is the vector of observed values of the variable being predicted, with Y ^ {\displaystyle {\hat {Y}}} being the predicted values (e.g. as from a least-squares fit), then the within-sample MSE of the predictor is computed as MSE = 1 n ∑ i = 1 n ( Y i − Y i ^ ) 2 {\displaystyle \operatorname {MSE} ={\frac {1}{n}}\sum _{i=1}^{n}\left(Y_{i}-{\hat {Y_{i}}}\right)^{2}} In other words, the MSE is the mean ( 1 n ∑ i = 1 n ) {\textstyle \left({\frac {1}{n}}\sum _{i=1}^{n}\right)} of the squares of the errors ( Y i − Y i ^ ) 2 {\textstyle \left(Y_{i}-{\hat {Y_{i}}}\right)^{2}} . This is an easily computable quantity for a particular sample (and hence is sample-dependent). In matrix notation, MSE = 1 n ∑ i = 1 n ( e i ) 2 = 1 n e T e {\displaystyle \operatorname {MSE} ={\frac {1}{n}}\sum _{i=1}^{n}(e_{i})^{2}={\frac {1}{n}}\mathbf {e} ^{\mathsf {T}}\mathbf {e} } where e i {\displaystyle e_{i}} is Y i − Y i ^ {\displaystyle Y_{i}-{\hat {Y_{i}}}} and e {\displaystyle \mathbf {e} } is a n × 1 {\displaystyle n\times 1} column vector. The MSE can also be computed on q data points that were not used in estimating the model, either because they were held back for this purpose, or because these data have been newly obtained. Within this process, known as cross-validation, the MSE is often called the test MSE, and is computed as MSE = 1 q ∑ i = n + 1 n + q ( Y i − Y i ^ ) 2 {\displaystyle \operatorname {MSE} ={\frac {1}{q}}\sum _{i=n+1}^{n+q}\left(Y_{i}-{\hat {Y_{i}}}\right)^{2}} === Estimator === The MSE of an estimator θ ^ {\displaystyle {\hat {\theta }}} with respect to an unknown parameter θ {\displaystyle \theta } is defined as MSE ⁡ ( θ ^ ) = E θ ⁡ [ ( θ ^ − θ ) 2 ] . {\displaystyle \operatorname {MSE} ({\hat {\theta }})=\operatorname {E} _{\theta }\left[({\hat {\theta }}-\theta )^{2}\right].} This definition depends on the unknown parameter, therefore the MSE is a priori property of an estimator. The MSE could be a function of unknown parameters, in which case any estimator of the MSE based on estimates of these parameters would be a function of the data (and thus a random variable). If the estimator θ ^ {\displaystyle {\hat {\theta }}} is derived as a sample statistic and is used to estimate some population parameter, then the expectation is with respect to the sampling distribution of the sample statistic. The MSE can be written as the sum of the variance of the estimator and the squared bias of the estimator, providing a useful way to calculate the MSE and implying that in the case of unbiased estimators, the MSE and variance are equivalent. MSE ⁡ ( θ ^ ) = Var θ ⁡ ( θ ^ ) + Bias ⁡ ( θ ^ , θ ) 2 . {\displaystyle \operatorname {MSE} ({\hat {\theta }})=\operatorname {Var} _{\theta }({\hat {\theta }})+\operatorname {Bias} ({\hat {\theta }},\theta )^{2}.} ==== Proof of variance and bias relationship ==== MSE ⁡ ( θ ^ ) = E θ ⁡ [ ( θ ^ − θ ) 2 ] = E θ ⁡ [ ( θ ^ − E θ ⁡ [ θ ^ ] + E θ ⁡ [ θ ^ ] − θ ) 2 ] = E θ ⁡ [ ( θ ^ − E θ ⁡ [ θ ^ ] ) 2 + 2 ( θ ^ − E θ ⁡ [ θ ^ ] ) ( E θ ⁡ [ θ ^ ] − θ ) + ( E θ ⁡ [ θ ^ ] − θ ) 2 ] = E θ ⁡ [ ( θ ^ − E θ ⁡ [ θ ^ ] ) 2 ] + E θ ⁡ [ 2 ( θ ^ − E θ ⁡ [ θ ^ ] ) ( E θ ⁡ [ θ ^ ] − θ ) ] + E θ ⁡ [ ( E θ ⁡ [ θ ^ ] − θ ) 2 ] = E θ ⁡ [ ( θ ^ − E θ ⁡ [ θ ^ ] ) 2 ] + 2 ( E θ ⁡ [ θ ^ ] − θ ) E θ ⁡ [ θ ^ − E θ ⁡ [ θ ^ ] ] + ( E θ ⁡ [ θ ^ ] − θ ) 2 E θ ⁡ [ θ ^ ] − θ = constant = E θ ⁡ [ ( θ ^ − E θ ⁡ [ θ ^ ] ) 2 ] + 2 ( E θ ⁡ [ θ ^ ] − θ ) ( E θ ⁡ [ θ ^ ] − E θ ⁡ [ θ ^ ] ) + ( E θ ⁡ [ θ ^ ] − θ ) 2 E θ ⁡ [ θ ^ ] = constant = E θ ⁡ [ ( θ ^ − E θ ⁡ [ θ ^ ] ) 2 ] + ( E θ ⁡ [ θ ^ ] − θ ) 2 = Var θ ⁡ ( θ ^ ) + Bias θ ⁡ ( θ ^ , θ ) 2 {\displaystyle {\begin{aligned}\operatorname {MSE} ({\hat {\theta }})&=\operatorname {E} _{\theta }\left[({\hat {\theta }}-\theta )^{2}\right]\\&=\operatorname {E} _{\theta }\left[\left({\hat {\theta }}-\operatorname {E} _{\theta }[{\hat {\theta }}]+\operatorname {E} _{\theta }[{\hat {\theta }}]-\theta \right)^{2}\right]\\&=\operatorname {E} _{\theta }\left[\left({\hat {\theta }}-\operatorname {E} _{\theta }[{\hat {\theta }}]\right)^{2}+2\left({\hat {\theta }}-\operatorname {E} _{\theta }[{\hat {\theta }}]\right)\left(\operatorname {E} _{\theta }[{\hat {\theta }}]-\theta \right)+\left(\operatorname {E} _{\theta }[{\hat {\theta }}]-\theta \right)^{2}\right]\\&=\operatorname {E} _{\theta }\left[\left({\hat {\theta }}-\operatorname {E} _{\theta }[{\hat {\theta }}]\right)^{2}\right]+\operatorname {E} _{\theta }\left[2\left({\hat {\theta }}-\operatorname {E} _{\theta }[{\hat {\theta }}]\right)\left(\operatorname {E} _{\theta }[{\hat {\theta }}]-\theta \right)\right]+\operatorname {E} _{\theta }\left[\left(\operatorname {E} _{\theta }[{\hat {\theta }}]-\theta \right)^{2}\right]\\&=\operatorname {E} _{\theta }\left[\left({\hat {\theta }}-\operatorname {E} _{\theta }[{\hat {\theta }}]\right)^{2}\right]+2\left(\operatorname {E} _{\theta }[{\hat {\theta }}]-\theta \right)\operatorname {E} _{\theta }\left[{\hat {\theta }}-\operatorname {E} _{\theta }[{\hat {\theta }}]\right]+\left(\operatorname {E} _{\theta }[{\hat {\theta }}]-\theta \right)^{2}&&\operatorname {E} _{\theta }[{\hat {\theta }}]-\theta ={\text{constant}}\\&=\operatorname {E} _{\theta }\left[\left({\hat {\theta }}-\operatorname {E} _{\theta }[{\hat {\theta }}]\right)^{2}\right]+2\left(\operatorname {E} _{\theta }[{\hat {\theta }}]-\theta \right)\left(\operatorname {E} _{\theta }[{\hat {\theta }}]-\operatorname {E} _{\theta }[{\hat {\theta }}]\right)+\left(\operatorname {E} _{\theta }[{\hat {\theta }}]-\theta \right)^{2}&&\operatorname {E} _{\theta }[{\hat {\theta }}]={\text{constant}}\\&=\operatorname {E} _{\theta }\left[\left({\hat {\theta }}-\operatorname {E} _{\theta }[{\hat {\theta }}]\right)^{2}\right]+\left(\operatorname {E} _{\theta }[{\hat {\theta }}]-\theta \right)^{2}\\&=\operatorname {Var} _{\theta }({\hat {\theta }})+\operatorname {Bias} _{\theta }({\hat {\theta }},\theta )^{2}\end{aligned}}} An even shorter proof can be achieved using the well-known formula that for a random variable X {\textstyle X} , E ( X 2 ) = Var ⁡ ( X ) + ( E ( X ) ) 2 {\textstyle \mathbb {E} (X^{2})=\operatorname {Var} (X)+(\mathbb {E} (X))^{2}} . By substituting X {\textstyle X} with, θ ^ − θ {\textstyle {\hat {\theta }}-\theta } , we have MSE ⁡ ( θ ^ ) = E [ ( θ ^ − θ ) 2 ] = Var ⁡ ( θ ^ − θ ) + ( E [ θ ^ − θ ] ) 2 = Var ⁡ ( θ ^ ) + Bias 2 ⁡ ( θ ^ , θ ) {\displaystyle {\begin{aligned}\operatorname {MSE} ({\hat {\theta }})&=\mathbb {E} [({\hat {\theta }}-\theta )^{2}]\\&=\operator

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