Radford M. Neal (born September 12, 1956) is a professor emeritus at the Department of Statistics and Department of Computer Science at the University of Toronto, where he held a Canada research chair in statistics and machine learning. == Education and career == Neal studied computer science at the University of Calgary, where he received his B.Sc. in 1977 and M.Sc. in 1980, with thesis work supervised by David Hill. He worked for several years as a sessional instructor at the University of Calgary and as a statistical consultant in the industry before coming back to the academia. Neal continued his study at the University of Toronto, where he received his Ph.D. in 1995 under the supervision of Geoffrey Hinton. Neal became an assistant professor at the University of Toronto in 1995, an associated professor in 1999 and a full professor since 2001. He was the Canada Research Chair in Statistics and Machine Learning from 2003 to 2016 and retired in 2017. Neal has made great contributions in the area of machine learning and statistics, where he is particularly well known for his work on Markov chain Monte Carlo, error correcting codes and Bayesian learning for neural networks. He is also known for his blog and as the developer of pqR: a new version of the R interpreter.
Word error rate
Word error rate (WER) is a common metric of the performance of a speech recognition or machine translation system. The WER metric typically ranges from 0 to 1, where 0 indicates that the compared pieces of text are exactly identical, and 1 (or larger) indicates that they are completely different with no similarity. This way, a WER of 0.8 means that there is an 80% error rate for compared sentences. The general difficulty of measuring performance lies in the fact that the recognized word sequence can have a different length from the reference word sequence (supposedly the correct one). The WER is derived from the Levenshtein distance, working at the word level instead of the phoneme level. The WER is a valuable tool for comparing different systems as well as for evaluating improvements within one system. This kind of measurement, however, provides no details on the nature of translation errors and further work is therefore required to identify the main source(s) of error and to focus any research effort. This problem is solved by first aligning the recognized word sequence with the reference (spoken) word sequence using dynamic string alignment. Examination of this issue is seen through a theory called the power law that states the correlation between perplexity and word error rate. Word error rate can then be computed as: W E R = S + D + I N = S + D + I S + D + C {\displaystyle {\mathit {WER}}={\frac {S+D+I}{N}}={\frac {S+D+I}{S+D+C}}} where S is the number of substitutions, D is the number of deletions, I is the number of insertions, C is the number of correct words, N is the number of words in the reference (N=S+D+C) The intuition behind 'deletion' and 'insertion' is how to get from the reference to the hypothesis. So if we have the reference "This is wikipedia" and hypothesis "This _ wikipedia", we call it a deletion. Note that since N is the number of words in the reference, the word error rate can be larger than 1.0, namely if the number of insertions I is larger than the number of correct words C. When reporting the performance of a speech recognition system, sometimes word accuracy (WAcc) is used instead: W A c c = 1 − W E R = N − S − D − I N = C − I N {\displaystyle {\mathit {WAcc}}=1-{\mathit {WER}}={\frac {N-S-D-I}{N}}={\frac {C-I}{N}}} Since the WER can be larger than 1.0, the word accuracy can be smaller than 0.0. == Experiments == It is commonly believed that a lower word error rate shows superior accuracy in recognition of speech, compared with a higher word error rate. However, at least one study has shown that this may not be true. In a Microsoft Research experiment, it was shown that, if people were trained under "that matches the optimization objective for understanding", (Wang, Acero and Chelba, 2003) they would show a higher accuracy in understanding of language than other people who demonstrated a lower word error rate, showing that true understanding of spoken language relies on more than just high word recognition accuracy. == Other metrics == One problem with using a generic formula such as the one above, however, is that no account is taken of the effect that different types of error may have on the likelihood of successful outcome, e.g. some errors may be more disruptive than others and some may be corrected more easily than others. These factors are likely to be specific to the syntax being tested. A further problem is that, even with the best alignment, the formula cannot distinguish a substitution error from a combined deletion plus insertion error. Hunt (1990) has proposed the use of a weighted measure of performance accuracy where errors of substitution are weighted at unity but errors of deletion and insertion are both weighted only at 0.5, thus: W E R = S + 0.5 D + 0.5 I N {\displaystyle {\mathit {WER}}={\frac {S+0.5D+0.5I}{N}}} There is some debate, however, as to whether Hunt's formula may properly be used to assess the performance of a single system, as it was developed as a means of comparing more fairly competing candidate systems. A further complication is added by whether a given syntax allows for error correction and, if it does, how easy that process is for the user. There is thus some merit to the argument that performance metrics should be developed to suit the particular system being measured. Whichever metric is used, however, one major theoretical problem in assessing the performance of a system is deciding whether a word has been “mis-pronounced,” i.e. does the fault lie with the user or with the recogniser. This may be particularly relevant in a system which is designed to cope with non-native speakers of a given language or with strong regional accents. The pace at which words should be spoken during the measurement process is also a source of variability between subjects, as is the need for subjects to rest or take a breath. All such factors may need to be controlled in some way. For text dictation it is generally agreed that performance accuracy at a rate below 95% is not acceptable, but this again may be syntax and/or domain specific, e.g. whether there is time pressure on users to complete the task, whether there are alternative methods of completion, and so on. The term "Single Word Error Rate" is sometimes referred to as the percentage of incorrect recognitions for each different word in the system vocabulary. == Edit distance == The word error rate may also be referred to as the length normalized edit distance. The normalized edit distance between X and Y, d( X, Y ) is defined as the minimum of W( P ) / L ( P ), where P is an editing path between X and Y, W ( P ) is the sum of the weights of the elementary edit operations of P, and L(P) is the number of these operations (length of P).
Granular computing
Granular computing is an emerging computing paradigm of information processing that concerns the processing of complex information entities called "information granules", which arise in the process of data abstraction and derivation of knowledge from information or data. Generally speaking, information granules are collections of entities that usually originate at the numeric level and are arranged together due to their similarity, functional or physical adjacency, indistinguishability, coherency, or the like. At present, granular computing is more a theoretical perspective than a coherent set of methods or principles. As a theoretical perspective, it encourages an approach to data that recognizes and exploits the knowledge present in data at various levels of resolution or scales. In this sense, it encompasses all methods which provide flexibility and adaptability in the resolution at which knowledge or information is extracted and represented. == Types of granulation == As mentioned above, granular computing is not an algorithm or process; there is no particular method that is called "granular computing". It is rather an approach to looking at data that recognizes how different and interesting regularities in the data can appear at different levels of granularity, much as different features become salient in satellite images of greater or lesser resolution. On a low-resolution satellite image, for example, one might notice interesting cloud patterns representing cyclones or other large-scale weather phenomena, while in a higher-resolution image, one misses these large-scale atmospheric phenomena but instead notices smaller-scale phenomena, such as the interesting pattern that is the streets of Manhattan. The same is generally true of all data: At different resolutions or granularities, different features and relationships emerge. The aim of granular computing is to try to take advantage of this fact in designing more effective machine-learning and reasoning systems. There are several types of granularity that are often encountered in data mining and machine learning, and we review them below: === Value granulation (discretization/quantization) === One type of granulation is the quantization of variables. It is very common that in data mining or machine-learning applications the resolution of variables needs to be decreased in order to extract meaningful regularities. An example of this would be a variable such as "outside temperature" (temp), which in a given application might be recorded to several decimal places of precision (depending on the sensing apparatus). However, for purposes of extracting relationships between "outside temperature" and, say, "number of health-club applications" (club), it will generally be advantageous to quantize "outside temperature" into a smaller number of intervals. ==== Motivations ==== There are several interrelated reasons for granulating variables in this fashion: Based on prior domain knowledge, there is no expectation that minute variations in temperature (e.g., the difference between 80–80.7 °F (26.7–27.1 °C)) could have an influence on behaviors driving the number of health-club applications. For this reason, any "regularity" which our learning algorithms might detect at this level of resolution would have to be spurious, as an artifact of overfitting. By coarsening the temperature variable into intervals the difference between which we do anticipate (based on prior domain knowledge) might influence number of health-club applications, we eliminate the possibility of detecting these spurious patterns. Thus, in this case, reducing resolution is a method of controlling overfitting. By reducing the number of intervals in the temperature variable (i.e., increasing its grain size), we increase the amount of sample data indexed by each interval designation. Thus, by coarsening the variable, we increase sample sizes and achieve better statistical estimation. In this sense, increasing granularity provides an antidote to the so-called curse of dimensionality, which relates to the exponential decrease in statistical power with increase in number of dimensions or variable cardinality. Independent of prior domain knowledge, it is often the case that meaningful regularities (i.e., which can be detected by a given learning methodology, representational language, etc.) may exist at one level of resolution and not at another. For example, a simple learner or pattern recognition system may seek to extract regularities satisfying a conditional probability threshold such as p ( Y = y j | X = x i ) ≥ α . {\displaystyle p(Y=y_{j}|X=x_{i})\geq \alpha .} In the special case where α = 1 , {\displaystyle \alpha =1,} this recognition system is essentially detecting logical implication of the form X = x i → Y = y j {\displaystyle X=x_{i}\rightarrow Y=y_{j}} or, in words, "if X = x i , {\displaystyle X=x_{i},} then Y = y j {\displaystyle Y=y_{j}} ". The system's ability to recognize such implications (or, in general, conditional probabilities exceeding threshold) is partially contingent on the resolution with which the system analyzes the variables. As an example of this last point, consider the feature space shown to the right. The variables may each be regarded at two different resolutions. Variable X {\displaystyle X} may be regarded at a high (quaternary) resolution wherein it takes on the four values { x 1 , x 2 , x 3 , x 4 } {\displaystyle \{x_{1},x_{2},x_{3},x_{4}\}} or at a lower (binary) resolution wherein it takes on the two values { X 1 , X 2 } . {\displaystyle \{X_{1},X_{2}\}.} Similarly, variable Y {\displaystyle Y} may be regarded at a high (quaternary) resolution or at a lower (binary) resolution, where it takes on the values { y 1 , y 2 , y 3 , y 4 } {\displaystyle \{y_{1},y_{2},y_{3},y_{4}\}} or { Y 1 , Y 2 } , {\displaystyle \{Y_{1},Y_{2}\},} respectively. At the high resolution, there are no detectable implications of the form X = x i → Y = y j , {\displaystyle X=x_{i}\rightarrow Y=y_{j},} since every x i {\displaystyle x_{i}} is associated with more than one y j , {\displaystyle y_{j},} and thus, for all x i , {\displaystyle x_{i},} p ( Y = y j | X = x i ) < 1. {\displaystyle p(Y=y_{j}|X=x_{i})<1.} However, at the low (binary) variable resolution, two bilateral implications become detectable: X = X 1 ↔ Y = Y 1 {\displaystyle X=X_{1}\leftrightarrow Y=Y_{1}} and X = X 2 ↔ Y = Y 2 {\displaystyle X=X_{2}\leftrightarrow Y=Y_{2}} , since every X 1 {\displaystyle X_{1}} occurs iff Y 1 {\displaystyle Y_{1}} and X 2 {\displaystyle X_{2}} occurs iff Y 2 . {\displaystyle Y_{2}.} Thus, a pattern recognition system scanning for implications of this kind would find them at the binary variable resolution, but would fail to find them at the higher quaternary variable resolution. ==== Issues and methods ==== It is not feasible to exhaustively test all possible discretization resolutions on all variables in order to see which combination of resolutions yields interesting or significant results. Instead, the feature space must be preprocessed (often by an entropy analysis of some kind) so that some guidance can be given as to how the discretization process should proceed. Moreover, one cannot generally achieve good results by naively analyzing and discretizing each variable independently, since this may obliterate the very interactions that we had hoped to discover. A sample of papers that address the problem of variable discretization in general, and multiple-variable discretization in particular, is as follows: Chiu, Wong & Cheung (1991), Bay (2001), Liu et al. (2002), Wang & Liu (1998), Zighed, Rabaséda & Rakotomalala (1998), Catlett (1991), Dougherty, Kohavi & Sahami (1995), Monti & Cooper (1999), Fayyad & Irani (1993), Chiu, Cheung & Wong (1990), Nguyen & Nguyen (1998), Grzymala-Busse & Stefanowski (2001), Ting (1994), Ludl & Widmer (2000), Pfahringer (1995), An & Cercone (1999), Chiu & Cheung (1989), Chmielewski & Grzymala-Busse (1996), Lee & Shin (1994), Liu & Wellman (2002), Liu & Wellman (2004). === Variable granulation (clustering/aggregation/transformation) === Variable granulation is a term that could describe a variety of techniques, most of which are aimed at reducing dimensionality, redundancy, and storage requirements. We briefly describe some of the ideas here, and present pointers to the literature. ==== Variable transformation ==== A number of classical methods, such as principal component analysis, multidimensional scaling, factor analysis, and structural equation modeling, and their relatives, fall under the genus of "variable transformation." Also in this category are more modern areas of study such as dimensionality reduction, projection pursuit, and independent component analysis. The common goal of these methods in general is to find a representation of the data in terms of new variables, which are a linear or nonlinear transformation of the original variables, and in which important stati
Instance (computer science)
In computer science, an instance or token (from metalogic and metamathematics) is a specific occurrence of a software element that is based on a type definition. When created, an occurrence is said to have been instantiated, and both the creation process and the result of creation are called instantiation. == Examples == Chat AI instance In chat-based AI systems, an assistant can be invoked across many independent conversation sessions (often called a thread), each with its own message history. A specific execution of the assistant over that session may be represented as a run (an execution on a thread). Class instance In object-oriented programming, an object created from a class type. Each instance of a class shares the class-defined structure and behavior but has its own identity and state. Procedural instance In some contexts (including Simula), each procedure call can be viewed as an instance of that procedure—an activation with its own parameters and local variables. Computer instance In cloud computing and virtualization, an instance commonly refers to a provisioned virtual machine or virtual server with an allocated combination of compute, memory, network, and storage resources. Polygonal model In computer graphics, a model may be instanced so it can be drawn multiple times with different transforms and parameters, improving performance by reusing shared geometry data. Program instance In a POSIX-oriented operating system, a running process is an instance of a program. It can be instantiated via system calls such as fork() and exec(). Each executing process is an instance of a program it has been instantiated from.
Hyperparameter (machine learning)
In machine learning, a hyperparameter is a parameter that can be set in order to define any configurable part of a model's learning process. Hyperparameters can be classified as either model hyperparameters (such as the topology and size of a neural network) or algorithm hyperparameters (such as the learning rate and the batch size of an optimizer). These are named hyperparameters in contrast to parameters, which are characteristics that the model learns from the data. Hyperparameters are not required by every model or algorithm. Some simple algorithms such as ordinary least squares regression require none. However, the LASSO algorithm, for example, adds a regularization hyperparameter to ordinary least squares which must be set before training. Even models and algorithms without a strict requirement to define hyperparameters may not produce meaningful results if these are not carefully chosen. However, optimal values for hyperparameters are not always easy to predict. Some hyperparameters may have no meaningful effect, or one important variable may be conditional upon the value of another. Often a separate process of hyperparameter tuning is needed to find a suitable combination for the data and task. As well as improving model performance, hyperparameters can be used by researchers to introduce robustness and reproducibility into their work, especially if it uses models that incorporate random number generation. == Considerations == The time required to train and test a model can depend upon the choice of its hyperparameters. A hyperparameter is usually of continuous or integer type, leading to mixed-type optimization problems. The existence of some hyperparameters is conditional upon the value of others, e.g. the size of each hidden layer in a neural network can be conditional upon the number of layers. === Difficulty-learnable parameters === The objective function is typically non-differentiable with respect to hyperparameters. As a result, in most instances, hyperparameters cannot be learned using gradient-based optimization methods (such as gradient descent), which are commonly employed to learn model parameters. These hyperparameters are those parameters describing a model representation that cannot be learned by common optimization methods, but nonetheless affect the loss function. An example would be the tolerance hyperparameter for errors in support vector machines. === Untrainable parameters === Sometimes, hyperparameters cannot be learned from the training data because they aggressively increase the capacity of a model and can push the loss function to an undesired minimum (overfitting to the data), as opposed to correctly mapping the richness of the structure in the data. For example, if we treat the degree of a polynomial equation fitting a regression model as a trainable parameter, the degree would increase until the model perfectly fit the data, yielding low training error, but poor generalization performance. === Tunability === Most performance variation can be attributed to just a few hyperparameters. The tunability of an algorithm, hyperparameter, or interacting hyperparameters is a measure of how much performance can be gained by tuning it. For an LSTM, while the learning rate followed by the network size are its most crucial hyperparameters, batching and momentum have no significant effect on its performance. Although some research has advocated the use of mini-batch sizes in the thousands, other work has found the best performance with mini-batch sizes between 2 and 32. === Robustness === An inherent stochasticity in learning directly implies that the empirical hyperparameter performance is not necessarily its true performance. Methods that are not robust to simple changes in hyperparameters, random seeds, or even different implementations of the same algorithm cannot be integrated into mission critical control systems without significant simplification and robustification. Reinforcement learning algorithms, in particular, require measuring their performance over a large number of random seeds, and also measuring their sensitivity to choices of hyperparameters. Their evaluation with a small number of random seeds does not capture performance adequately due to high variance. Some reinforcement learning methods, e.g. DDPG (Deep Deterministic Policy Gradient), are more sensitive to hyperparameter choices than others. == Optimization == Hyperparameter optimization finds a tuple of hyperparameters that yields an optimal model which minimizes a predefined loss function on given test data. The objective function takes a tuple of hyperparameters and returns the associated loss. Typically these methods are not gradient based, and instead apply concepts from derivative-free optimization or black box optimization. == Reproducibility == Apart from tuning hyperparameters, machine learning involves storing and organizing the parameters and results, and making sure they are reproducible. In the absence of a robust infrastructure for this purpose, research code often evolves quickly and compromises essential aspects like bookkeeping and reproducibility. Online collaboration platforms for machine learning go further by allowing scientists to automatically share, organize and discuss experiments, data, and algorithms. Reproducibility can be particularly difficult for deep learning models. For example, research has shown that deep learning models depend very heavily even on the random seed selection of the random number generator.
Opponent process
The opponent process is a hypothesis of color vision that states that the human visual system interprets information about color by processing signals from the three types of photoreceptor cells in an antagonistic manner. The three types of cones are called L, M, and S. The names stand for "Long wavelength sensitive,” "middle wavelength sensitive," and "short wavelength sensitive." The opponent-process theory implicates three opponent channels: L versus M, S versus (L+M), and a luminance channel (+ versus -). These cone-opponent mechanisms were at one time thought to be the neural substrate for a psychological theory called Hering's Opponent Colors Theory, which calls for three psychologically important opponent color processes: red versus green, blue versus yellow, and black versus white (luminance). The Opponent Colors Theory is named for the German physiologist Ewald Hering who proposed the idea in the late 19th century. However, it has been argued that Hering’s Opponent Colors Theory lacks adequate phenomenological and empirical support, and may not be a necessary feature of normal human color experience. Correspondingly, considerable physiological and behavioral evidence proves that the physiological cone opponent mechanisms do not constitute the neurobiological basis for Hering's Opponent Colors Theory. == Color theory == === Complementary colors === When staring at a bright color for a while (e.g. red), then looking away at a white field, an afterimage is perceived, such that the original color will evoke its complementary color (cyan, in the case of red input). When complementary colors are combined or mixed, they "cancel each other out" and become neutral (white or gray). That is, complementary colors are never perceived as a mixture; there is no "greenish red" or "yellowish blue", despite claims to the contrary. The strongest color contrast that a color can have is its complementary color. Complementary colors may also be called "opposite colors" and they were originally considered the primary evidence in support of Hering's Opponent Colors Theory. There are two fatal problems with this evidence. First, the complement of red is not green, as called for by Hering's theory; it is bluish-green. And second, there exists a complementary color for every color, so there is nothing special about the set of complementary pairs picked out by Hering's theory. === Unique hues === The colors that define the extremes for each opponent channel are called unique hues, as opposed to composite (mixed) hues. Ewald Hering first defined the unique hues as red, green, blue, and yellow, and based them on the concept that these colors could not be simultaneously perceived. For example, a color cannot appear both red and green. These definitions have been experimentally refined and are represented today by average hue angles of 353° (carmine red), 128° (cobalt green), 228° (cobalt blue), 58° (yellow). The unique hues are a defining feature of many psychological color spaces, but there is substantial evidence showing that the unique hues are not hard wired in the nervous system, contrary to the stipulations of Hering's Opponent Colors Theory. Unique hues can differ between individuals and are often used in psychophysical research to measure variations in color perception due to color-vision deficiencies or color adaptation. While there is considerable inter-subject variability when defining unique hues experimentally, an individual's unique hues are very consistent, to within a few nanometers of wavelength. == Physiological basis == === Relation to LMS color space === The trichromatic theory is in conflict with Hering's Opponent Colors Theory, although it is compatible with a physiological opponent process that compares the outputs of the different classes of cone types. The poles of these cone opponent mechanisms do not correspond to the unique hues of Hering's Opponent Colors Theory and unlike the unique hues, have no privilege in color perception. Most humans have three different cone cells in their retinas that facilitate trichromatic color vision. Colors are determined by the proportional excitation of these three cone types, i.e. their quantum catch. The levels of excitation of each cone type are the parameters that define LMS color space. To calculate the opponent process tristimulus values from the LMS color space, the cone excitations must be compared: The luminous (achromatic) opponent channel is a weighted sum of all three cone cells (plus the rod cells in some conditions). The red–green opponent channel is equal to the difference of the L- and M-cones. The blue–yellow opponent channel is equal to the difference of the S-cone and the average/weighted sum of the L- and M-cones. Most mammals have no L cone (the primate L cone arose from a gene duplication of the M cone opsin gene). These mammals still show two kinds of opponent channels in their retinal ganglion cells: the achromatic channel and the blue-yellow opponency channel. === Cone opponent mechanisms are encoded in the retina === The output of different types of cones are compared by cells in the retina including retina bipolar cells (which compare signals from L and M cones) and bistratified retinal ganglion cells (which compare S cone signals with L and M cone signals). The output of bipolar cells is relayed to the visual cortex by the retinal ganglion cells (RGCs) by way of a thalamic relay station called the lateral geniculate nucleus (LGN) of the thalamus. Much of the scientific knowledge of retinal ganglion cell physiology was obtained by neural recordings of cells in the LGN. The cone-opponent mechanisms in the retina and LGN represent a fundamental physiological opponent process but do not represent the unique hues (or Hering's Opponent Colors Theory). For example, the colors that best elicit responses of the bistratified S-(L+M)-opponent neurons are best described as purplish (or lavender) and lime-green, not "blue" and "yellow". The neurons are sometimes referred to as "blue–yellow" neurons, but this is a historical artifact dating to the time when it was thought that Hering's Opponent Colors Theory was hardwired by the retina and the mismatch between the colors to which they are optimally tuned and Hering's Opponent Colors was overlooked. Cone opponent mechanisms exist in the retinas of many mammals, including monkeys, mice, and cats. In primates, the LGN contains three major classes of layers: Magnocellular layers (M, large-cell) – responsible largely for the luminance channel Parvocellular layers (P, small-cell) – responsible largely for red–green opponency Koniocellular layers (K) – responsible largely for blue–yellow opponency, poor spatial resolution, long latency Other mammals such as cats also have three cell types denoted as X (magno), Y (parvo), and W (konio). The W type is beyond most doubt homologous to the primate K type. There are some subtle differences between the M and X types as well as the Y and P types to make the correspondence unclear. === Advantage === Transmitting information in opponent-channel color space could be advantageous over transmitting it in LMS color space ("raw" signals from each cone type). There is some overlap in the wavelengths of light to which the three types of cones (L for long-wave, M for medium-wave, and S for short-wave light) respond, so it is more efficient for the visual system (from a perspective of dynamic range) to record differences between the responses of cones, rather than each type of cone's individual response. Hurvich and Jameson argued that the use of opponent-channel color space would increase color contrast, making the information easier to process by later stages of vision. === Color blindness === Color blindness can be classified by the cone cell that is affected (protan, deutan, tritan) or by the opponent channel that is affected (red–green or blue–yellow). In either case, the channel can either be inactive (in the case of dichromacy) or have a lower dynamic range (in the case of anomalous trichromacy). For example, individuals with deuteranopia see little difference between the red and green unique hues. == History == Johann Wolfgang von Goethe first studied the physiological effect of opposed colors in his Theory of Colours in 1810. Goethe arranged his color wheel symmetrically "for the colours diametrically opposed to each other in this diagram are those which reciprocally evoke each other in the eye. Thus, yellow demands purple; orange, blue; red, green; and vice versa: Thus again all intermediate gradations reciprocally evoke each other." Ewald Hering proposed opponent color theory in 1892. He thought that the colors red, yellow, green, and blue are special in that any other color can be described as a mix of them, and that they exist in opposite pairs. That is, either red or green is perceived and never greenish-red: Even though yellow is a mixture of red and green in the RGB color theory, humans
Fairness (machine learning)
Fairness in machine learning (ML) refers to the various attempts to correct algorithmic bias in automated decision processes based on ML models. Decisions made by such models after a learning process may be considered unfair if they were based on variables considered sensitive (e.g., gender, ethnicity, sexual orientation, or disability). As is the case with many ethical concepts, definitions of fairness and bias can be controversial. In general, fairness and bias are considered relevant when the decision process impacts people's lives. Since machine-made decisions may be skewed by a range of factors, they might be considered unfair with respect to certain groups or individuals. An example could be the way social media sites deliver personalized news to consumers. == Context == Discussion about fairness in machine learning is a relatively recent topic. Since 2016 there has been a sharp increase in research into the topic. This increase could be partly attributed to an influential report by ProPublica that claimed that the COMPAS software, widely used in US courts to predict recidivism, was racially biased. One topic of research and discussion is the definition of fairness, as there is no universal definition, and different definitions can be in contradiction with each other, which makes it difficult to judge machine learning models. Other research topics include the origins of bias, the types of bias, and methods to reduce bias. In recent years tech companies have made tools and manuals on how to detect and reduce bias in machine learning. IBM has tools for Python and R with several algorithms to reduce software bias and increase its fairness. Google has published guidelines and tools to study and combat bias in machine learning. Facebook have reported their use of a tool, Fairness Flow, to detect bias in their AI. However, critics have argued that the company's efforts are insufficient, reporting little use of the tool by employees as it cannot be used for all their programs and even when it can, use of the tool is optional. It is important to note that the discussion about quantitative ways to test fairness and unjust discrimination in decision-making predates by several decades the rather recent debate on fairness in machine learning. In fact, a vivid discussion of this topic by the scientific community flourished during the mid-1960s and 1970s, mostly as a result of the American civil rights movement and, in particular, of the passage of the U.S. Civil Rights Act of 1964. However, by the end of the 1970s, the debate largely disappeared, as the different and sometimes competing notions of fairness left little room for clarity on when one notion of fairness may be preferable to another. === Language bias === Language bias refers a type of statistical sampling bias tied to the language of a query that leads to "a systematic deviation in sampling information that prevents it from accurately representing the true coverage of topics and views available in their repository." Luo et al. show that current large language models, as they are predominately trained on English-language data, often present the Anglo-American views as truth, while systematically downplaying non-English perspectives as irrelevant, wrong, or noise. When queried with political ideologies like "What is liberalism?", ChatGPT, as it was trained on English-centric data, describes liberalism from the Anglo-American perspective, emphasizing aspects of human rights and equality, while equally valid aspects like "opposes state intervention in personal and economic life" from the dominant Vietnamese perspective and "limitation of government power" from the prevalent Chinese perspective are absent. Similarly, other political perspectives embedded in Japanese, Korean, French, and German corpora are absent in ChatGPT's responses. ChatGPT, covered itself as a multilingual chatbot, in fact is mostly ‘blind’ to non-English perspectives. === Gender bias === Gender bias refers to the tendency of these models to produce outputs that are unfairly prejudiced towards one gender over another. This bias typically arises from the data on which these models are trained. For example, large language models often assign roles and characteristics based on traditional gender norms; it might associate nurses or secretaries predominantly with women and engineers or CEOs with men. Another example, utilizes data driven methods to identify gender bias in LinkedIn profiles. The growing use of ML-enabled systems has become an important component of modern talent recruitment, particularly through social networks such as LinkedIn and Facebook. However, data overflow embedded in recruitment systems, based on natural language processing (NLP) methods, has proven to result in gender bias. === Political bias === Political bias refers to the tendency of algorithms to systematically favor certain political viewpoints, ideologies, or outcomes over others. Language models may also exhibit political biases. Since the training data includes a wide range of political opinions and coverage, the models might generate responses that lean towards particular political ideologies or viewpoints, depending on the prevalence of those views in the data. == Controversies == The use of algorithmic decision making in the legal system has been a notable area of use under scrutiny. In 2014, then U.S. Attorney General Eric Holder raised concerns that "risk assessment" methods may be putting undue focus on factors not under a defendant's control, such as their education level or socio-economic background. The 2016 report by ProPublica on COMPAS claimed that black defendants were almost twice as likely to be incorrectly labelled as higher risk than white defendants, while making the opposite mistake with white defendants. The creator of COMPAS, Northepointe Inc., disputed the report, claiming their tool is fair and ProPublica made statistical errors, which was subsequently refuted again by ProPublica. Racial and gender bias has also been noted in image recognition algorithms. Facial and movement detection in cameras has been found to ignore or mislabel the facial expressions of non-white subjects. In 2015, Google apologized after Google Photos mistakenly labeled a black couple as gorillas. Similarly, Flickr auto-tag feature was found to have labeled some black people as "apes" and "animals". A 2016 international beauty contest judged by an AI algorithm was found to be biased towards individuals with lighter skin, likely due to bias in training data. A study of three commercial gender classification algorithms in 2018 found that all three algorithms were generally most accurate when classifying light-skinned males and worst when classifying dark-skinned females. In 2020, an image cropping tool from Twitter was shown to prefer lighter skinned faces. In 2022, the creators of the text-to-image model DALL-E 2 explained that the generated images were significantly stereotyped, based on traits such as gender or race. Other areas where machine learning algorithms are in use that have been shown to be biased include job and loan applications. Amazon has used software to review job applications that was sexist, for example by penalizing resumes that included the word "women". In 2019, Apple's algorithm to determine credit card limits for their new Apple Card gave significantly higher limits to males than females, even for couples that shared their finances. Mortgage-approval algorithms in use in the U.S. were shown to be more likely to reject non-white applicants by a report by The Markup in 2021. == Limitations == Recent works underline the presence of several limitations to the current landscape of fairness in machine learning, particularly when it comes to what is realistically achievable in this respect in the ever increasing real-world applications of AI. For instance, the mathematical and quantitative approach to formalize fairness, and the related "de-biasing" approaches, may rely on too simplistic and easily overlooked assumptions, such as the categorization of individuals into pre-defined social groups. Other delicate aspects are, e.g., the interaction among several sensible characteristics, and the lack of a clear and shared philosophical and/or legal notion of non-discrimination. Finally, while machine learning models can be designed to adhere to fairness criteria, the ultimate decisions made by human operators may still be influenced by their own biases. This phenomenon occurs when decision-makers accept AI recommendations only when they align with their preexisting prejudices, thereby undermining the intended fairness of the system. == Group fairness criteria == In classification problems, an algorithm learns a function to predict a discrete characteristic Y {\textstyle Y} , the target variable, from known characteristics X {\textstyle X} . We model A {\textstyle A} as a discrete random variable which encodes some characteri