AI Analytics For Retail

AI Analytics For Retail — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Example-based machine translation

  Example-based machine translation (EBMT) is a method of machine translation often characterized by its use of a bilingual corpus with parallel texts as its main knowledge base at run-time. It is essentially a translation by analogy and can be viewed as an implementation of a case-based reasoning approach to machine learning. == Translation by analogy == At the foundation of example-based machine translation is the idea of translation by analogy. When applied to the process of human translation, the idea that translation takes place by analogy is a rejection of the idea that people translate sentences by doing deep linguistic analysis. Instead, it is founded on the belief that people translate by first decomposing a sentence into certain phrases, then by translating these phrases, and finally by properly composing these fragments into one long sentence. Phrasal translations are translated by analogy to previous translations. The principle of translation by analogy is encoded to example-based machine translation through the example translations that are used to train such a system. Other approaches to machine translation, including statistical machine translation, also use bilingual corpora to learn the process of translation. == History == Example-based machine translation was first suggested by Makoto Nagao in 1984. He pointed out that it is especially adapted to translation between two totally different languages, such as English and Japanese. In this case, one sentence can be translated into several well-structured sentences in another language, therefore, it is no use to do the deep linguistic analysis characteristic of rule-based machine translation. == Example == Example-based machine translation systems are trained from bilingual parallel corpora containing sentence pairs like the example shown in the table above. Sentence pairs contain sentences in one language with their translations into another. The particular example shows an example of a minimal pair, meaning that the sentences vary by just one element. These sentences make it simple to learn translations of portions of a sentence. For example, an example-based machine translation system would learn three units of translation from the above example: How much is that X ? corresponds to Ano X wa ikura desu ka. red umbrella corresponds to akai kasa small camera corresponds to chiisai kamera Composing these units can be used to produce novel translations in the future. For example, if we have been trained using some text containing the sentences: President Kennedy was shot dead during the parade. and The convict escaped on July 15th., then we could translate the sentence The convict was shot dead during the parade. by substituting the appropriate parts of the sentences. == Phrasal verbs == Example-based machine translation is best suited for sub-language phenomena like phrasal verbs. Phrasal verbs have highly context-dependent meanings. They are common in English, where they comprise a verb followed by an adverb and/or a preposition, which are called the particle to the verb. Phrasal verbs produce specialized context-specific meanings that may not be derived from the meaning of the constituents. There is almost always an ambiguity during word-to-word translation from source to the target language. As an example, consider the phrasal verb "put on" and its Hindustani translation. It may be used in any of the following ways: Ram put on the lights. (Switched on) (Hindustani translation: Jalana) Ram put on a cap. (Wear) (Hindustani translation: Pahenna)

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  Distributional Soft Actor Critic

  Distributional Soft Actor Critic (DSAC) is a suite of model-free off-policy reinforcement learning algorithms, tailored for learning decision-making or control policies in complex systems with continuous action spaces. Distinct from traditional methods that focus solely on expected returns, DSAC algorithms are designed to learn a Gaussian distribution over stochastic returns, called value distribution. This focus on Gaussian value distribution learning notably diminishes value overestimations, which in turn boosts policy performance. Additionally, the value distribution learned by DSAC can also be used for risk-aware policy learning. From a technical standpoint, DSAC is essentially a distributional adaptation of the well-established soft actor-critic (SAC) method. To date, the DSAC family comprises two iterations: the original DSAC-v1 and its successor, DSAC-T (also known as DSAC-v2), with the latter demonstrating superior capabilities over the Soft Actor-Critic (SAC) in Mujoco benchmark tasks. The source code for DSAC-T can be found at the following URL: Jingliang-Duan/DSAC-T. Both iterations have been integrated into an advanced, Pytorch-powered reinforcement learning toolkit named GOPS: GOPS (General Optimal control Problem Solver).

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  Ensemble learning

  In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone. Unlike a statistical ensemble in statistical mechanics, which is usually infinite, a machine learning ensemble consists of only a concrete finite set of alternative models, but typically allows for much more flexible structure to exist among those alternatives. == Overview == Supervised learning algorithms search through a hypothesis space to find a suitable hypothesis that will make good predictions with a particular problem. Even if this space contains hypotheses that are very well-suited for a particular problem, it may be very difficult to find a good one. Ensembles combine multiple hypotheses to form one which should be theoretically better. Ensemble learning trains two or more machine learning algorithms on a specific classification or regression task. The algorithms within the ensemble model are generally referred as "base models", "base learners", or "weak learners" in literature. These base models can be constructed using a single modelling algorithm, or several different algorithms. The idea is to train a diverse set of weak models on the same modelling task, such that the outputs of each weak learner have poor predictive ability (i.e., high bias), and among all weak learners, the outcome and error values exhibit high variance. Fundamentally, an ensemble learning model trains at least two high-bias (weak) and high-variance (diverse) models to be combined into a better-performing model. The set of weak models — which would not produce satisfactory predictive results individually — are combined or averaged to produce a single, high performing, accurate, and low-variance model to fit the task as required. Ensemble learning typically refers to bagging (bootstrap aggregating), boosting or stacking/blending techniques to induce high variance among the base models. Bagging creates diversity by generating random samples from the training observations and fitting the same model to each different sample — also known as homogeneous parallel ensembles. Boosting follows an iterative process by sequentially training each base model on the up-weighted errors of the previous base model, producing an additive model to reduce the final model errors — also known as sequential ensemble learning. Stacking or blending consists of different base models, each trained independently (i.e. diverse/high variance) to be combined into the ensemble model — producing a heterogeneous parallel ensemble. Common applications of ensemble learning include random forests (an extension of bagging), Boosted Tree models, and Gradient Boosted Tree Models. Models in applications of stacking are generally more task-specific — such as combining clustering techniques with other parametric and/or non-parametric techniques. Evaluating the prediction of an ensemble typically requires more computation than evaluating the prediction of a single model. In one sense, ensemble learning may be thought of as a way to compensate for poor learning algorithms by performing a lot of extra computation. On the other hand, the alternative is to do a lot more learning with one non-ensemble model. An ensemble may be more efficient at improving overall accuracy for the same increase in compute, storage, or communication resources by using that increase on two or more methods, than would have been improved by increasing resource use for a single method. Fast algorithms such as decision trees are commonly used in ensemble methods (e.g., random forests), although slower algorithms can benefit from ensemble techniques as well. By analogy, ensemble techniques have been used also in unsupervised learning scenarios, for example in consensus clustering or in anomaly detection. == Ensemble theory == Empirically, ensembles tend to yield better results when there is a significant diversity among the models. Many ensemble methods, therefore, seek to promote diversity among the models they combine. Although perhaps non-intuitive, more random algorithms (like random decision trees) can be used to produce a stronger ensemble than very deliberate algorithms (like entropy-reducing decision trees). Using a variety of strong learning algorithms, however, has been shown to be more effective than using techniques that attempt to dumb-down the models in order to promote diversity. It is possible to increase diversity in the training stage of the model using correlation for regression tasks or using information measures such as cross entropy for classification tasks. Theoretically, one can justify the diversity concept because the lower bound of the error rate of an ensemble system can be decomposed into accuracy, diversity, and the other term. === The geometric framework === Ensemble learning, including both regression and classification tasks, can be explained using a geometric framework. Within this framework, the output of each individual classifier or regressor for the entire dataset can be viewed as a point in a multi-dimensional space. Additionally, the target result is also represented as a point in this space, referred to as the "ideal point." The Euclidean distance is used as the metric to measure both the performance of a single classifier or regressor (the distance between its point and the ideal point) and the dissimilarity between two classifiers or regressors (the distance between their respective points). This perspective transforms ensemble learning into a deterministic problem. For example, within this geometric framework, it can be proved that the averaging of the outputs (scores) of all base classifiers or regressors can lead to equal or better results than the average of all the individual models. It can also be proved that if the optimal weighting scheme is used, then a weighted averaging approach can outperform any of the individual classifiers or regressors that make up the ensemble or as good as the best performer at least. == Ensemble size == While the number of component classifiers of an ensemble has a great impact on the accuracy of prediction, there is a limited number of studies addressing this problem. A priori determining of ensemble size and the volume and velocity of big data streams make this even more crucial for online ensemble classifiers. Mostly statistical tests were used for determining the proper number of components. More recently, a theoretical framework suggested that there is an ideal number of component classifiers for an ensemble such that having more or less than this number of classifiers would deteriorate the accuracy. It is called "the law of diminishing returns in ensemble construction." Their theoretical framework shows that using the same number of independent component classifiers as class labels gives the highest accuracy. == Common types of ensembles == === Bayes optimal classifier === The Bayes optimal classifier is a classification technique. It is an ensemble of all the hypotheses in the hypothesis space. On average, no other ensemble can outperform it. The Naive Bayes classifier is a version of this that assumes that the data is conditionally independent on the class and makes the computation more feasible. Each hypothesis is given a vote proportional to the likelihood that the training dataset would be sampled from a system if that hypothesis were true. To facilitate training data of finite size, the vote of each hypothesis is also multiplied by the prior probability of that hypothesis. The Bayes optimal classifier can be expressed with the following equation: y = a r g m a x c j ∈ C ∑ h i ∈ H P ( c j | h i ) P ( T | h i ) P ( h i ) {\displaystyle y={\underset {c_{j}\in C}{\mathrm {argmax} }}\sum _{h_{i}\in H}{P(c_{j}|h_{i})P(T|h_{i})P(h_{i})}} where y {\displaystyle y} is the predicted class, C {\displaystyle C} is the set of all possible classes, H {\displaystyle H} is the hypothesis space, P {\displaystyle P} refers to a probability, and T {\displaystyle T} is the training data. As an ensemble, the Bayes optimal classifier represents a hypothesis that is not necessarily in H {\displaystyle H} . The hypothesis represented by the Bayes optimal classifier, however, is the optimal hypothesis in ensemble space (the space of all possible ensembles consisting only of hypotheses in H {\displaystyle H} ). This formula can be restated using Bayes' theorem, which says that the posterior is proportional to the likelihood times the prior: P ( h i | T ) ∝ P ( T | h i ) P ( h i ) {\displaystyle P(h_{i}|T)\propto P(T|h_{i})P(h_{i})} hence, y = a r g m a x c j ∈ C ∑ h i ∈ H P ( c j | h i ) P ( h i | T ) {\displaystyle y={\underset {c_{j}\in C}{\mathrm {argmax} }}\sum _{h_{i}\in H}{P(c_{j}|h_{i})P(h_{i}|T)}} === Bootstrap aggregating (bagging) === Bootstrap aggregation (bagging) involves training an ensemble on bootstrapped data sets. A bootstrapped set is cr

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  Concept class

  In computational learning theory in mathematics, a concept over a domain X is a total Boolean function over X. A concept class is a class of concepts. Concept classes are a subject of computational learning theory. Concept class terminology frequently appears in model theory associated with probably approximately correct (PAC) learning. In this setting, if one takes a set Y as a set of (classifier output) labels, and X is a set of examples, the map c : X → Y {\displaystyle c:X\to Y} , i.e. from examples to classifier labels (where Y = { 0 , 1 } {\displaystyle Y=\{0,1\}} and where c is a subset of X), c is then said to be a concept. A concept class C {\displaystyle C} is then a collection of such concepts. Given a class of concepts C, a subclass D is reachable if there exists a sample s such that D contains exactly those concepts in C that are extensions to s. Not every subclass is reachable. == Background == A sample s {\displaystyle s} is a partial function from X {\displaystyle X} to { 0 , 1 } {\displaystyle \{0,1\}} . Identifying a concept with its characteristic function mapping X {\displaystyle X} to { 0 , 1 } {\displaystyle \{0,1\}} , it is a special case of a sample. Two samples are consistent if they agree on the intersection of their domains. A sample s ′ {\displaystyle s'} extends another sample s {\displaystyle s} if the two are consistent and the domain of s {\displaystyle s} is contained in the domain of s ′ {\displaystyle s'} . == Examples == Suppose that C = S + ( X ) {\displaystyle C=S^{+}(X)} . Then: the subclass { { x } } {\displaystyle \{\{x\}\}} is reachable with the sample s = { ( x , 1 ) } {\displaystyle s=\{(x,1)\}} ; the subclass S + ( Y ) {\displaystyle S^{+}(Y)} for Y ⊆ X {\displaystyle Y\subseteq X} are reachable with a sample that maps the elements of X − Y {\displaystyle X-Y} to zero; the subclass S ( X ) {\displaystyle S(X)} , which consists of the singleton sets, is not reachable. == Applications == Let C {\displaystyle C} be some concept class. For any concept c ∈ C {\displaystyle c\in C} , we call this concept 1 / d {\displaystyle 1/d} -good for a positive integer d {\displaystyle d} if, for all x ∈ X {\displaystyle x\in X} , at least 1 / d {\displaystyle 1/d} of the concepts in C {\displaystyle C} agree with c {\displaystyle c} on the classification of x {\displaystyle x} . The fingerprint dimension F D ( C ) {\displaystyle FD(C)} of the entire concept class C {\displaystyle C} is the least positive integer d {\displaystyle d} such that every reachable subclass C ′ ⊆ C {\displaystyle C'\subseteq C} contains a concept that is 1 / d {\displaystyle 1/d} -good for it. This quantity can be used to bound the minimum number of equivalence queries needed to learn a class of concepts according to the following inequality: F D ( C ) − 1 ≤ # E Q ( C ) ≤ ⌈ F D ( C ) ln ⁡ ( | C | ) ⌉ {\textstyle FD(C)-1\leq \#EQ(C)\leq \lceil FD(C)\ln(|C|)\rceil } .

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  Variable data publishing

  Variable-data publishing (VDP) (also known as database publishing) is a term referring to the output of a variable composition system. While these systems can produce both electronically viewable and hard-copy (print) output, the "variable-data publishing" term today often distinguishes output destined for electronic viewing, rather than that which is destined for hard-copy print (e.g. variable data printing). Essentially the same techniques are employed to perform variable-data publishing, as those utilized with variable data printing. The difference is in the interpretation for output. While variable-data printing may be interpreted to produce various print streams or page-description files (e.g. AFP/IPDS, PostScript, PCL), variable-data publishing produces electronically viewable files, most commonly seen in the forms of PDF, HTML, or XML. Variable-data composition involves the use of data to conditionally: exhibit text (static blocks and/or variable content) exhibit images select fonts select colors format page layouts & flows Variable-data may be as simple as an address block or salutation. However, it can be any or all of the document's textual content—including words, sentences, paragraphs, pages, or the entire document. In other words, it can make up as little or as much of the document as the composer desires. Variable data may also be used to exhibit various images, such as logos, products, or membership photos. Further, variable-data can be used to build rule-based design schemes, including fonts, colors, and page formats. The possibilities are vast. The variable-data tools available today, make it possible to perform variable-data composition at nearly every stage of document production. However, the level of control that can be achieved varies, based upon how far into the document production process a variable-data tool is deployed. For example, if variable-data insertion occurs just prior to output...it's not likely that the text flow or layout can be altered with nearly as much control as would be available at the time of initial document composition. Many organizations will produce multiple forms of output (aka: multi-channel output), for the same document. This ensures that the published content is available to recipients via any form of access method they might require. When multi-channel output is utilized, integrity between those output channels often becomes important. Variable-data publishing may be performed on everything from a personal computer to a mainframe system. However, the speed and practical output volumes which can be achieved are directly affected by the computer power utilized. == Origin of the concept == The term variable-data publishing was likely an offshoot of the term "variable-data printing", first introduced to the printing industry by Frank Romano, Professor Emeritus, School of Print Media, at the College of Imaging Arts and Sciences at Rochester Institute of Technology. However, the concept of merging static document elements and variable document elements predates the term and has seen various implementations ranging from simple desktop 'mail merge', to complex mainframe applications in the financial and banking industry. In the past, the term VDP has been most closely associated with digital printing machines. However, in the past 3 years the application of this technology has spread to web pages, emails, and mobile messaging.

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  Rule-based machine learning

  Rule-based machine learning (RBML) is a term in computer science intended to encompass any machine learning method that identifies, learns, or evolves 'rules' to store, manipulate or apply. The defining characteristic of a rule-based machine learner is the identification and utilization of a set of relational rules that collectively represent the knowledge captured by the system. Rule-based machine learning approaches include learning classifier systems, association rule learning, artificial immune systems, and any other method that relies on a set of rules, each covering contextual knowledge. While rule-based machine learning is conceptually a type of rule-based system, it is distinct from traditional rule-based systems, which are often hand-crafted, and other rule-based decision makers. This is because rule-based machine learning applies some form of learning algorithm such as Rough sets theory to identify and minimise the set of features and to automatically identify useful rules, rather than a human needing to apply prior domain knowledge to manually construct rules and curate a rule set. == Rules == Rules typically take the form of an '{IF:THEN} expression', (e.g. {IF 'condition' THEN 'result'}, or as a more specific example, {IF 'red' AND 'octagon' THEN 'stop-sign}). An individual rule is not in itself a model, since the rule is only applicable when its condition is satisfied. Therefore rule-based machine learning methods typically comprise a set of rules, or knowledge base, that collectively make up the prediction model usually known as decision algorithm. Rules can also be interpreted in various ways depending on the domain knowledge, data types(discrete or continuous) and in combinations. == RIPPER == Repeated incremental pruning to produce error reduction (RIPPER) is a propositional rule learner proposed by William W. Cohen as an optimized version of IREP.

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  Extremal Ensemble Learning

  Extremal Ensemble Learning (EEL) is a machine learning algorithmic paradigm for graph partitioning. EEL creates an ensemble of partitions and then uses information contained in the ensemble to find new and improved partitions. The ensemble evolves and learns how to form improved partitions through extremal updating procedure. The final solution is found by achieving consensus among its member partitions about what the optimal partition is. == Reduced-Network Extremal Ensemble Learning (RenEEL) == A particular implementation of the EEL paradigm is the Reduced-Network Extremal Ensemble Learning (RenEEL) scheme for partitioning a graph. RenEEL uses consensus across many partitions in an ensemble to create a reduced network that can be efficiently analyzed to find more accurate partitions. These better quality partitions are subsequently used to update the ensemble. An algorithm that utilizes the RenEEL scheme is currently the best algorithm for finding the graph partition with maximum modularity, which is an NP-hard problem.

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  Inductive logic programming

  Inductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples, background knowledge and hypotheses. The term "inductive" here refers to philosophical (i.e. suggesting a theory to explain observed facts) rather than mathematical (i.e. proving a property for all members of a well-ordered set) induction. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesised logic program which entails all the positive and none of the negative examples. Schema: positive examples + negative examples + background knowledge ⇒ hypothesis. Bioinformatics and drug design have been highlighted as a principal application area of inductive logic programming techniques. == History == Building on earlier work on Inductive inference, Gordon Plotkin was the first to formalise induction in a clausal setting around 1970, adopting an approach of generalising from examples. In 1981, Ehud Shapiro introduced several ideas that would shape the field in his new approach of model inference, an algorithm employing refinement and backtracing to search for a complete axiomatisation of given examples. His first implementation was the Model Inference System in 1981: a Prolog program that inductively inferred Horn clause logic programs from positive and negative examples. The term Inductive Logic Programming was first introduced in a paper by Stephen Muggleton in 1990, defined as the intersection of machine learning and logic programming. Muggleton and Wray Buntine introduced predicate invention and inverse resolution in 1988. Several inductive logic programming systems that proved influential appeared in the early 1990s. FOIL, introduced by Ross Quinlan in 1990 was based on upgrading propositional learning algorithms AQ and ID3. Golem, introduced by Muggleton and Feng in 1990, went back to a restricted form of Plotkin's least generalisation algorithm. The Progol system, introduced by Muggleton in 1995, first implemented inverse entailment, and inspired many later systems. Aleph, a descendant of Progol introduced by Ashwin Srinivasan in 2001, is still one of the most widely used systems as of 2022. At around the same time, the first practical applications emerged, particularly in bioinformatics, where by 2000 inductive logic programming had been successfully applied to drug design, carcinogenicity and mutagenicity prediction, and elucidation of the structure and function of proteins. Unlike the focus on automatic programming inherent in the early work, these fields used inductive logic programming techniques from a viewpoint of relational data mining. The success of those initial applications and the lack of progress in recovering larger traditional logic programs shaped the focus of the field. Recently, classical tasks from automated programming have moved back into focus, as the introduction of meta-interpretative learning makes predicate invention and learning recursive programs more feasible. This technique was pioneered with the Metagol system introduced by Muggleton, Dianhuan Lin, Niels Pahlavi and Alireza Tamaddoni-Nezhad in 2014. This allows ILP systems to work with fewer examples, and brought successes in learning string transformation programs, answer set grammars and general algorithms. == Setting == Inductive logic programming has adopted several different learning settings, the most common of which are learning from entailment and learning from interpretations. In both cases, the input is provided in the form of background knowledge B, a logical theory (commonly in the form of clauses used in logic programming), as well as positive and negative examples, denoted E + {\textstyle E^{+}} and E − {\textstyle E^{-}} respectively. The output is given as a hypothesis H, itself a logical theory that typically consists of one or more clauses. The two settings differ in the format of examples presented. === Learning from entailment === As of 2022, learning from entailment is by far the most popular setting for inductive logic programming. In this setting, the positive and negative examples are given as finite sets E + {\textstyle E^{+}} and E − {\textstyle E^{-}} of positive and negated ground literals, respectively. A correct hypothesis H is a set of clauses satisfying the following requirements, where the turnstile symbol ⊨ {\displaystyle \models } stands for logical entailment: Completeness: B ∪ H ⊨ E + Consistency: B ∪ H ∪ E − ⊭ false {\displaystyle {\begin{array}{llll}{\text{Completeness:}}&B\cup H&\models &E^{+}\\{\text{Consistency: }}&B\cup H\cup E^{-}&\not \models &{\textit {false}}\end{array}}} Completeness requires any generated hypothesis H to explain all positive examples E + {\textstyle E^{+}} , and consistency forbids generation of any hypothesis H that is inconsistent with the negative examples E − {\textstyle E^{-}} , both given the background knowledge B. In Muggleton's setting of concept learning, "completeness" is referred to as "sufficiency", and "consistency" as "strong consistency". Two further conditions are added: "Necessity", which postulates that B does not entail E + {\textstyle E^{+}} , does not impose a restriction on H, but forbids any generation of a hypothesis as long as the positive facts are explainable without it. "Weak consistency", which states that no contradiction can be derived from B ∧ H {\textstyle B\land H} , forbids generation of any hypothesis H that contradicts the background knowledge B. Weak consistency is implied by strong consistency; if no negative examples are given, both requirements coincide. Weak consistency is particularly important in the case of noisy data, where completeness and strong consistency cannot be guaranteed. === Learning from interpretations === In learning from interpretations, the positive and negative examples are given as a set of complete or partial Herbrand structures, each of which are themselves a finite set of ground literals. Such a structure e is said to be a model of the set of clauses B ∪ H {\textstyle B\cup H} if for any substitution θ {\textstyle \theta } and any clause h e a d ← b o d y {\textstyle \mathrm {head} \leftarrow \mathrm {body} } in B ∪ H {\textstyle B\cup H} such that b o d y θ ⊆ e {\textstyle \mathrm {body} \theta \subseteq e} , h e a d θ ⊆ e {\displaystyle \mathrm {head} \theta \subseteq e} also holds. The goal is then to output a hypothesis that is complete, meaning every positive example is a model of B ∪ H {\textstyle B\cup H} , and consistent, meaning that no negative example is a model of B ∪ H {\textstyle B\cup H} . == Approaches to ILP == An inductive logic programming system is a program that takes as an input logic theories B , E + , E − {\displaystyle B,E^{+},E^{-}} and outputs a correct hypothesis H with respect to theories B , E + , E − {\displaystyle B,E^{+},E^{-}} . A system is complete if and only if for any input logic theories B , E + , E − {\displaystyle B,E^{+},E^{-}} any correct hypothesis H with respect to these input theories can be found with its hypothesis search procedure. Inductive logic programming systems can be roughly divided into two classes, search-based and meta-interpretative systems. Search-based systems exploit that the space of possible clauses forms a complete lattice under the subsumption relation, where one clause C 1 {\textstyle C_{1}} subsumes another clause C 2 {\textstyle C_{2}} if there is a substitution θ {\textstyle \theta } such that C 1 θ {\textstyle C_{1}\theta } , the result of applying θ {\textstyle \theta } to C 1 {\textstyle C_{1}} , is a subset of C 2 {\textstyle C_{2}} . This lattice can be traversed either bottom-up or top-down. === Bottom-up search === Bottom-up methods to search the subsumption lattice have been investigated since Plotkin's first work on formalising induction in clausal logic in 1970. Techniques used include least general generalisation, based on anti-unification, and inverse resolution, based on inverting the resolution inference rule. ==== Least general generalisation ==== A least general generalisation algorithm takes as input two clauses C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} and outputs the least general generalisation of C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} , that is, a clause C {\textstyle C} that subsumes C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} , and that is subsumed by every other clause that subsumes C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} . The least general generalisation can be computed by first computing all selections from C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} , which are pairs of literals ( L , M ) ∈ ( C 1 × C 2 ) {\displaystyle (L,M)\in (C_{1}\times C_{2})} sharing the same predicate symbol and negated/unnegated status. Then, the least general generalisation is obtained as the disjunction of the least general generalisations of the indi

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  AppValley

  AppValley is an independent American digital distribution service operated and trademarked by AppValley LLC. It serves as an alternative app store for the iOS mobile operating system, which allows users to download applications that are not available on the App Store, most commonly tweaked "++" apps, jailbreak apps, and apps including paid apps on the app store. == Legality == AppValley is among several services that violate enterprise developer certificates from Apple. The terms under which these are granted make clear that they are for companies who wish to distribute apps to their employees. AppValley uses these certificates to distribute software directly to non-employees, thereby bypassing the AppStore. AppValley's conduct had implications in U.S. sanctioned markets like Iran, Iraq, North Korea, Cuba, and Venezuela, which have all been subject to commercial sanctions. Among the software offered by AppValley and other services is pirated software, including paid apps on the app store and premium versions of Instagram, Spotify, Pokémon Go, and others. For instance, AppValley distributes an ad-free version of the music streaming app Spotify even on the free tier. == History == The website was founded in May 2017, releasing late that month with a very basic version of the app. There were less than 100 apps available for download at this time. On Jan 19, 2018, a new version dubbed AppValley 2.0 was released bringing dark mode, more categories, a search, and a much faster interface. On February 14, 2019, a Chinese partner "Jason Wu" allegedly took control of the main Twitter account and domain, causing the original AppValley developers to migrate to the domain app-valley.vip and the Twitter account handle @App_Valley_vip. As of September 2024, the app-valley.vip domain now redirects to appvalley.signulous.com. Today, AppValley continues to offer an alternative to Apple's App Store where app developers can publish their applications. == Features == AppValley is a mobile app installer which can also support iOS version that can be installed and downloaded on the mobile or the devices of the people who wish to get access to many different applications available. AppValley also contains apps that have been modified or tweaked for user preferences, and allows the user to by pass national restrictions on the use of apps, without having to resort to jailbreaking. As of June 2, 2020, there are over 1300 apps available for download.

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  Junction tree algorithm

  The junction tree algorithm (also known as 'Clique Tree') is a method used in machine learning to extract marginalization in general graphs. In essence, it entails performing belief propagation on a modified graph called a junction tree. The graph is called a tree because it branches into different sections of data; nodes of variables are the branches. The basic premise is to eliminate cycles by clustering them into single nodes. Multiple extensive classes of queries can be compiled at the same time into larger structures of data. There are different algorithms to meet specific needs and for what needs to be calculated. Inference algorithms gather new developments in the data and calculate it based on the new information provided. == Junction tree algorithm == === Hugin algorithm === If the graph is directed then moralize it to make it un-directed. Introduce the evidence. Triangulate the graph to make it chordal. Construct a junction tree from the triangulated graph (we will call the vertices of the junction tree "supernodes"). Propagate the probabilities along the junction tree (via belief propagation) Note that this last step is inefficient for graphs of large treewidth. Computing the messages to pass between supernodes involves doing exact marginalization over the variables in both supernodes. Performing this algorithm for a graph with treewidth k will thus have at least one computation which takes time exponential in k. It is a message passing algorithm. The Hugin algorithm takes fewer computations to find a solution compared to Shafer-Shenoy. === Shafer-Shenoy algorithm === Computed recursively Multiple recursions of the Shafer-Shenoy algorithm results in Hugin algorithm Found by the message passing equation Separator potentials are not stored The Shafer-Shenoy algorithm is the sum product of a junction tree. It is used because it runs programs and queries more efficiently than the Hugin algorithm. The algorithm makes calculations for conditionals for belief functions possible. Joint distributions are needed to make local computations happen. === Underlying theory === The first step concerns only Bayesian networks, and is a procedure to turn a directed graph into an undirected one. We do this because it allows for the universal applicability of the algorithm, regardless of direction. The second step is setting variables to their observed value. This is usually needed when we want to calculate conditional probabilities, so we fix the value of the random variables we condition on. Those variables are also said to be clamped to their particular value. The third step is to ensure that graphs are made chordal if they aren't already chordal. This is the first essential step of the algorithm. It makes use of the following theorem: Theorem: For an undirected graph, G, the following properties are equivalent: Graph G is triangulated. The clique graph of G has a junction tree. There is an elimination ordering for G that does not lead to any added edges. Thus, by triangulating a graph, we make sure that the corresponding junction tree exists. A usual way to do this, is to decide an elimination order for its nodes, and then run the Variable elimination algorithm. The variable elimination algorithm states that the algorithm must be run each time there is a different query. This will result to adding more edges to the initial graph, in such a way that the output will be a chordal graph. All chordal graphs have a junction tree. The next step is to construct the junction tree. To do so, we use the graph from the previous step, and form its corresponding clique graph. Now the next theorem gives us a way to find a junction tree: Theorem: Given a triangulated graph, weight the edges of the clique graph by their cardinality, |A∩B|, of the intersection of the adjacent cliques A and B. Then any maximum-weight spanning tree of the clique graph is a junction tree. So, to construct a junction tree we just have to extract a maximum weight spanning tree out of the clique graph. This can be efficiently done by, for example, modifying Kruskal's algorithm. The last step is to apply belief propagation to the obtained junction tree. Usage: A junction tree graph is used to visualize the probabilities of the problem. The tree can become a binary tree to form the actual building of the tree. A specific use could be found in auto encoders, which combine the graph and a passing network on a large scale automatically. === Inference Algorithms === Loopy belief propagation: A different method of interpreting complex graphs. The loopy belief propagation is used when an approximate solution is needed instead of the exact solution. It is an approximate inference. Cutset conditioning: Used with smaller sets of variables. Cutset conditioning allows for simpler graphs that are easier to read but are not exact.

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  LamaH

  LamaH (Large-Sample Data for Hydrology and Environmental Sciences) is a cross-state initiative for unified data preparation and collection in the field of catchment hydrology. Hydrological datasets, for example, are an integral component for creating flood forecasting models. == Features == LamaH datasets always consist of a combination of meteorological time series (e.g., precipitation, temperature) and hydrologically relevant catchment attributes (e.g., elevation, slope, forest area, soil, bedrock) aggregated over the respective catchment as well as associated hydrological time series at the catchment outlet (discharge). By evaluating the large and heterogeneous sample (large-sample) of catchments, it is possible to gain insights into the hydrological cycle that would probably not be achievable with local and small-scale studies. The structure of the dataset allows an evaluation based on machine learning methods (deep learning). The accompanying paper explains not only the data preparation but also any limitations, uncertainties and possible applications. == Difference to CAMELS == The LamaH datasets are quite similar to the CAMELS datasets, but additionally feature: Further basin delineations (based on intermediate catchments) and attributes (e.g. flow distance and altitude difference between two topologically adjacent discharge gauges), enabling the setup of an interconnected hydrological network Attributes for classifying catchments and runoff gauges according to the degree and type of (anthropogenic) influence == Availability == LamaH datasets are available for the following regions: Central Europe (Austria and its hydrological upstream areas in Germany, Czech Republic, Switzerland, Slovakia, Italy, Liechtenstein, Slovenia and Hungary) / 859 catchments CAMELS datasets are available for (ranked by publication date): Contiguous USA (exclusive Alaska and Hawaii) / 671 catchments Chile / 516 catchments Brazil / 897 catchments Great Britain / 671 catchments Australia / 222 catchments Both the CAMELS and LamaH datasets are licensed with Creative Commons and are therefore available barrier-free for the public.

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  Absorbing Markov chain

  In the mathematical theory of probability, an absorbing Markov chain is a Markov chain in which every state can reach an absorbing state. An absorbing state is a state that, once entered, cannot be left. Like general Markov chains, there can be continuous-time absorbing Markov chains with an infinite state space. However, this article concentrates on the discrete-time discrete-state-space case. == Formal definition == A Markov chain is an absorbing chain if there is at least one absorbing state and it is possible to go from any state to at least one absorbing state in a finite number of steps. In an absorbing Markov chain, a state that is not absorbing is called transient. === Canonical form === Let an absorbing Markov chain with transition matrix P have t transient states and r absorbing states. The rows of P represent sources, while columns represent destinations. By ordering the transient states before the absorbing states, it can be assumed that P has the form P = [ Q R 0 I r ] , {\displaystyle P={\begin{bmatrix}Q&R\\\mathbf {0} &I_{r}\end{bmatrix}},} where Q is a t-by-t matrix, R is a nonzero t-by-r matrix, 0 is an r-by-t zero matrix, and Ir is the r-by-r identity matrix. Thus, Q describes the probability of transitioning from some transient state to another while R describes the probability of transitioning from some transient state to some absorbing state. The probability of transitioning from i to j in exactly k steps is the (i,j)-entry of Pk, further computed below. When considering only transient states, the probability is found in the upper left of Pk, the (i,j)-entry of Qk. == Fundamental matrix == === Expected number of visits to a transient state === A basic property about an absorbing Markov chain is the expected number of visits to a transient state j starting from a transient state i (before being absorbed). This can be established to be given by the (i, j) entry of so-called fundamental matrix N, obtained by summing Qk for all k (from 0 to ∞). It can be proven that N := ∑ k = 0 ∞ Q k = ( I t − Q ) − 1 , {\displaystyle N:=\sum _{k=0}^{\infty }Q^{k}=(I_{t}-Q)^{-1},} where It is the t-by-t identity matrix. The computation of this formula is the matrix equivalent of the geometric series of scalars, ∑ k = 0 ∞ q k = 1 1 − q {\displaystyle {\textstyle \sum }_{k=0}^{\infty }q^{k}={\tfrac {1}{1-q}}} . With the matrix N in hand, also other properties of the Markov chain are easy to obtain. === Expected number of steps before being absorbed === The expected number of steps before being absorbed in any absorbing state, when starting in transient state i can be computed via a sum over transient states. The value is given by the ith entry of the vector t := N 1 , {\displaystyle \mathbf {t} :=N\mathbf {1} ,} where 1 is a length-t column vector whose entries are all 1. === Absorbing probabilities === By induction, P k = [ Q k ( I t − Q k ) N R 0 I r ] . {\displaystyle P^{k}={\begin{bmatrix}Q^{k}&(I_{t}-Q^{k})NR\\\mathbf {0} &I_{r}\end{bmatrix}}.} The probability of eventually being absorbed in the absorbing state j when starting from transient state i is given by the (i,j)-entry of the matrix B := N R {\displaystyle B:=NR} . The number of columns of this matrix equals the number of absorbing states r. An approximation of those probabilities can also be obtained directly from the (i,j)-entry of P k {\displaystyle P^{k}} for a large enough value of k, when i is the index of a transient, and j the index of an absorbing state. This is because ( lim k → ∞ P k ) i , t + j = B i , j {\displaystyle \left(\lim _{k\to \infty }P^{k}\right)_{i,t+j}=B_{i,j}} . === Transient visiting probabilities === The probability of visiting transient state j when starting at a transient state i is the (i,j)-entry of the matrix H := ( N − I t ) ( N dg ) − 1 , {\displaystyle H:=(N-I_{t})(N_{\operatorname {dg} })^{-1},} where Ndg is the diagonal matrix with the same diagonal as N. === Variance on number of transient visits === The variance on the number of visits to a transient state j with starting at a transient state i (before being absorbed) is the (i,j)-entry of the matrix N 2 := N ( 2 N dg − I t ) − N sq , {\displaystyle N_{2}:=N(2N_{\operatorname {dg} }-I_{t})-N_{\operatorname {sq} },} where Nsq is the Hadamard product of N with itself (i.e. each entry of N is squared). === Variance on number of steps === The variance on the number of steps before being absorbed when starting in transient state i is the ith entry of the vector ( 2 N − I t ) t − t sq , {\displaystyle (2N-I_{t})\mathbf {t} -\mathbf {t} _{\operatorname {sq} },} where tsq is the Hadamard product of t with itself (i.e., as with Nsq, each entry of t is squared). == Examples == === String generation === Consider the process of repeatedly flipping a fair coin until the sequence (heads, tails, heads) appears. This process is modeled by an absorbing Markov chain with transition matrix P = [ 1 / 2 1 / 2 0 0 0 1 / 2 1 / 2 0 1 / 2 0 0 1 / 2 0 0 0 1 ] . {\displaystyle P={\begin{bmatrix}1/2&1/2&0&0\\0&1/2&1/2&0\\1/2&0&0&1/2\\0&0&0&1\end{bmatrix}}.} The first state represents the empty string, the second state the string "H", the third state the string "HT", and the fourth state the string "HTH". Although in reality, the coin flips cease after the string "HTH" is generated, the perspective of the absorbing Markov chain is that the process has transitioned into the absorbing state representing the string "HTH" and, therefore, cannot leave. For this absorbing Markov chain, the fundamental matrix is N = ( I − Q ) − 1 = ( [ 1 0 0 0 1 0 0 0 1 ] − [ 1 / 2 1 / 2 0 0 1 / 2 1 / 2 1 / 2 0 0 ] ) − 1 = [ 1 / 2 − 1 / 2 0 0 1 / 2 − 1 / 2 − 1 / 2 0 1 ] − 1 = [ 4 4 2 2 4 2 2 2 2 ] . {\displaystyle {\begin{aligned}N&=(I-Q)^{-1}=\left({\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}}-{\begin{bmatrix}1/2&1/2&0\\0&1/2&1/2\\1/2&0&0\end{bmatrix}}\right)^{-1}\\[4pt]&={\begin{bmatrix}1/2&-1/2&0\\0&1/2&-1/2\\-1/2&0&1\end{bmatrix}}^{-1}={\begin{bmatrix}4&4&2\\2&4&2\\2&2&2\end{bmatrix}}.\end{aligned}}} The expected number of steps starting from each of the transient states is t = N 1 = [ 4 4 2 2 4 2 2 2 2 ] [ 1 1 1 ] = [ 10 8 6 ] . {\displaystyle \mathbf {t} =N\mathbf {1} ={\begin{bmatrix}4&4&2\\2&4&2\\2&2&2\end{bmatrix}}{\begin{bmatrix}1\\1\\1\end{bmatrix}}={\begin{bmatrix}10\\8\\6\end{bmatrix}}.} Therefore, the expected number of coin flips before observing the sequence (heads, tails, heads) is 10, the entry for the state representing the empty string. === Games of chance === Games based entirely on chance can be modeled by an absorbing Markov chain. A classic example of this is the ancient Indian board game Snakes and Ladders. The graph on the left plots the probability mass in the lone absorbing state that represents the final square as the transition matrix is raised to larger and larger powers. To determine the expected number of turns to complete the game, compute the vector t as described above and examine tstart, which is approximately 39.2. === Infectious disease testing === Infectious disease testing, either of blood products or in medical clinics, is often taught as an example of an absorbing Markov chain. The public U.S. Centers for Disease Control and Prevention (CDC) model for HIV and for hepatitis B, for example, illustrates the property that absorbing Markov chains can lead to the detection of disease, versus the loss of detection through other means. In the standard CDC model, the Markov chain has five states, a state in which the individual is uninfected, then a state with infected but undetectable virus, a state with detectable virus, and absorbing states of having quit/been lost from the clinic, or of having been detected (the goal). The typical rates of transition between the Markov states are the probability p per unit time of being infected with the virus, w for the rate of window period removal (time until virus is detectable), q for quit/loss rate from the system, and d for detection, assuming a typical rate λ {\displaystyle \lambda } at which the health system administers tests of the blood product or patients in question. It follows that we can "walk along" the Markov model to identify the overall probability of detection for a person starting as undetected, by multiplying the probabilities of transition to each next state of the model as: p ( p + q ) w ( w + q ) d ( d + q ) {\displaystyle {\frac {p}{(p+q)}}{\frac {w}{(w+q)}}{\frac {d}{(d+q)}}} . The subsequent total absolute number of false negative tests—the primary CDC concern—would then be the rate of tests, multiplied by the probability of reaching the infected but undetectable state, times the duration of staying in the infected undetectable state: p ( p + q ) 1 ( w + q ) λ {\displaystyle {\frac {p}{(p+q)}}{\frac {1}{(w+q)}}\lambda } .

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  Automatic scorer

  An automatic scorer is the computerized scoring system to keep track of scoring in ten-pin bowling. It was introduced en masse in bowling alleys in the 1970s and combined with mechanical pinsetters to detect overturned pins. By eliminating the need for manual score-keeping, these systems have introduced new bowlers into the game who otherwise would not participate because they had to count the score themselves, as many do not understand the mathematical formula involved in bowler scoring. At first, people were skeptical about whether a computer could keep an accurate score. In the twenty-first century, automatic scorers are used in most bowling centers around the world. The three manufacturers of these specialty computers have been Brunswick Bowling, AMF Bowling (later QubicaAMF), and RCA. == History == Automatic equipment is considered a cornerstone of the modern bowling center. The traditional bowling center of the early 20th century was advanced in automation when the pinsetter person ("pin boy"), who set back up by hand the bowled down pins, was replaced by a machine that automatically replaced the pins in their proper play positions. This machine came out in the 1950s. A detection system was developed from the pinsetter mechanism in the 1960s that could tell which pins had been knocked down, and that information could be transferred to a digital computer. Automatic electronic scoring was first conceived by Robert Reynolds, who was described by a newspaper story at the time as "a West Coast electronics calculator expert." He worked with the technical staff of Brunswick Bowling to develop it. The goal was realized in the late 1960s when a specialized computer was designed for the purpose of automatic scorekeeping for bowling. The field test for the automatic scorer took place at Village Lanes bowling center, Chicago in 1967. The scoring machine received approval for official use by the American Bowling Congress in August of that year. They were first used in national official league gaming on October 10, 1967. In November, Brunswick announced that they were accepting orders for the new digital computer, which cost around $3,000 per bowling lane. Bowling centers that installed these new automatic scoring devices in the 1970s charged a ten cents extra per line of scoring for the convenience. == Description == Each Automatic Scorer computer unit kept score for four lanes. It had two bowler identification panels serving two lanes each. The bowler pushed it into his named position when his turn came up so the computer knew who was bowling and score accordingly. After the bowler rolled the bowling ball down the lane and knocked down pins, the pinsetter detected which pins were down and relayed this information back to the computer for scoring. The result was then printed on a scoresheet and projected overhead onto a large screen for all to see. The Automatic Scorer digital computer was mathematically accurate, however the detection system at the pinsetter mechanism sometimes reported the wrong number of pins knocked down. The computer could be corrected manually for any errors in the system; similarly, human errors, such as neglecting to move the bowler identification mechanism, could be corrected for by manual action. The scorer could take into account bowlers' handicaps and could adjust for late-arriving bowlers. The automatic scorer is directly connected to the foul detection unit. As a result, foul line violations are automatically scored. Brunswick had put ten years of research and development into the Automatic Scorer, and by 1972 there were over 500 of these computers installed in bowling centers around the world. AMF Bowling, competitor to Brunswick, entered into the automatic scorer computer field during the 1970s and their systems were installed into their brand of bowling centers. By 1974, RCA was also making these computers for automatic scoring. == Reception and further developments == The purposes of the computerized scoring were to avoid errors by human scorers and to prevent cheating. It had the side benefit of speeding up the progress of the game and introducing new bowlers to the game. Score-keeping for bowling is based on a formula that many new to bowling were not familiar with and thought difficult to learn. These casual bowlers unfamiliar with the formula thought the scores given by the computers were confusing. Some bowlers were not comfortable with automatic scorers when they were introduced in the 1970s, so kept score using the traditional method on paper score sheets. The introduction of this device increased the popularity of the sport. Automatic scorers came to be considered a normal part of modern bowling installations worldwide, with owners and managers saying that bowlers expect such equipment to be present in bowling establishments and that business increased following their introduction. Brunswick introduced a color television style automatic scorer in 1983. Bowling center owners could use these style automatic scorers for advertising, management, videos, and live television. By the 2010s, these types of electronic visual displays could show bowler avatars and social media connections to publicize the bowlers' scores. Some are capable of being extended entertainment systems of games for children and adults. Some scoring systems support variations on traditional bowling, such as different kinds of bingo games where certain pins have to be knocked down at certain times or practice regimes where certain spares have to be accomplished. By this point, QubicaAMF Worldwide, an outgrowth of AMF, was one of the leading providers of bowling scoring equipment.

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  Tensor sketch

  In statistics, machine learning and algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors that have tensor structure. Such a sketch can be used to speed up explicit kernel methods, bilinear pooling in neural networks and is a cornerstone in many numerical linear algebra algorithms. == Mathematical definition == Mathematically, a dimensionality reduction or sketching matrix is a matrix M ∈ R k × d {\displaystyle M\in \mathbb {R} ^{k\times d}} , where k < d {\displaystyle k Read more →

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  Automated Pain Recognition

  Automated Pain Recognition (APR) is a method for objectively measuring pain and at the same time represents an interdisciplinary research area that comprises elements of medicine, psychology, psychobiology, and computer science. The focus is on computer-aided objective recognition of pain, implemented on the basis of machine learning. Automated pain recognition allows for the valid, reliable detection and monitoring of pain in people who are unable to communicate verbally. The underlying machine learning processes are trained and validated in advance by means of unimodal or multimodal body signals. Signals used to detect pain may include facial expressions or gestures and may also be of a (psycho-)physiological or paralinguistic nature. To date, the focus has been on identifying pain intensity, but visionary efforts are also being made to recognize the quality, site, and temporal course of pain. However, the clinical implementation of this approach is a controversial topic in the field of pain research. Critics of automated pain recognition argue that pain diagnosis can only be performed subjectively by humans. == Background == Pain diagnosis under conditions where verbal reporting is restricted - such as in verbally and/or cognitively impaired people or in patients who are sedated or mechanically ventilated - is based on behavioral observations by trained professionals. However, all known observation procedures (e.g., Zurich Observation Pain Assessment (ZOPA)); Pain Assessment in Advanced Dementia Scale (PAINAD) require a great deal of specialist expertise. These procedures can be made more difficult by perception- and interpretation-related misjudgments on the part of the observer. With regard to the differences in design, methodology, evaluation sample, and conceptualization of the phenomenon of pain, it is difficult to compare the quality criteria of the various tools. Even if trained personnel could theoretically record pain intensity several times a day using observation instruments, it would not be possible to measure it every minute or second. In this respect, the goal of automated pain recognition is to use valid, robust pain response patterns that can be recorded multimodally for a temporally dynamic, high-resolution, automated pain intensity recognition system. == Procedure == For automated pain recognition, pain-relevant parameters are usually recorded using non-invasive sensor technology, which captures data on the (physical) responses of the person in pain. This can be achieved with camera technology that captures facial expressions, gestures, or posture, while audio sensors record paralinguistic features. (Psycho-)physiological information such as muscle tone and heart rate can be collected via biopotential sensors (electrodes). Pain recognition requires the extraction of meaningful characteristics or patterns from the data collected. This is achieved using machine learning techniques that are able to provide an assessment of the pain after training (learning), e.g., "no pain," "mild pain," or "severe pain." == Parameters == Although the phenomenon of pain comprises different components (sensory discriminative, affective (emotional), cognitive, vegetative, and (psycho-)motor), automated pain recognition currently relies on the measurable parameters of pain responses. These can be divided roughly into the two main categories of "physiological responses" and "behavioral responses". === Physiological responses === In humans, pain almost always initiates autonomic nervous processes that are reflected measurably in various physiological signals. ==== Physiological signals ==== Measurements can include electrodermal activity (EDA, also skin conductance), electromyography (EMG), electrocardiogram (ECG), blood volume pulse (BVP), electroencephalogram (EEG), respiration, and body temperature, which are regulatory mechanisms of the sympathetic and parasympathetic systems. Physiological signals are mainly recorded using special non-invasive surface electrodes (for EDA, EMG, ECG, and EEG), a blood volume pulse sensor (BVP), a respiratory belt (respiration), and a thermal sensor (body temperature). Endocrinological and immunological parameters can also be recorded, but this requires measures that are somewhat invasive (e.g., blood sampling). === Behavioral responses === Behavioral responses to pain fulfil two functions: protection of the body (e.g., through protective reflexes) and external communication of the pain (e.g., as a cry for help). The responses are particularly evident in facial expressions, gestures, and paralinguistic features. ==== Facial expressions ==== Behavioral signals captured comprise facial expression patterns (expressive behavior), which are measured with the aid of video signals. Facial expression recognition is based on the everyday clinical observation that pain often manifests itself in the patient's facial expressions but that this is not necessarily always the case, since facial expressions can be inhibited through self-control. Despite the possibility that facial expressions may be influenced consciously, facial expression behavior represents an essential source of information for pain diagnosis and is thus also a source of information for automatic pain recognition. One advantage of video-based facial expression recognition is the contact-free measurement of the face, provided that it can be captured on video, which is not possible in every position (e.g., lying face down) or may be limited by bandages covering the face. Facial expression analysis relies on rapid, spontaneous, and temporary changes in neuromuscular activity that lead to visually detectable changes in the face. ==== Gestures ==== Gestures are also captured predominantly using non-contact camera technology. Motor pain responses vary and are strongly dependent on the type and cause of the pain. They range from abrupt protective reflexes (e.g., spontaneous retraction of extremities or doubling up) to agitation (pathological restlessness) and avoidance behavior (hesitant, cautious movements). ==== Paralinguistic features of language ==== Among other things, pain leads to nonverbal linguistic behavior that manifests itself in sounds such as sighing, gasping, moaning, whining, etc. Paralinguistic features are usually recorded using highly sensitive microphones. == Algorithms == After the recording, pre-processing (e.g., filtering), and extraction of relevant features, an optional information fusion can be performed. During this process, modalities from different signal sources are merged to generate new or more precise knowledge. The pain is classified using machine learning processes. The method chosen has a significant influence on the recognition rate and depends greatly on the quality and granularity of the underlying data. Similar to the field of affective computing, the following classifiers are currently being used: Support Vector Machine (SVM): The goal of an SVM is to find a clearly defined optimal hyperplane with the greatest minimal distance to two (or more) classes to be separated. The hyperplane acts as a decision function for classifying an unknown pattern. Random Forest (RF): RF is based on the composition of random, uncorrelated decision trees. An unknown pattern is judged individually by each tree and assigned to a class. The final classification of the patterns by the RF is then based on a majority decision. k-Nearest Neighbors (k-NN): The k-NN algorithm classifies an unknown object using the class label that most commonly classifies the k neighbors closest to it. Its neighbors are determined using a selected similarity measure (e.g., Euclidean distance, Jaccard coefficient, etc.). Artificial neural networks (ANNs): ANNs are inspired by biological neural networks and model their organizational principles and processes in a very simplified manner. Class patterns are learned by adjusting the weights of the individual neuronal connections. == Databases == In order to classify pain in a valid manner, it is necessary to create representative, reliable, and valid pain databases that are available to the machine learner for training. An ideal database would be sufficiently large and would consist of natural (not experimental), high-quality pain responses. However, natural responses are difficult to record and can only be obtained to a limited extent; in most cases they are characterized by suboptimal quality. The databases currently available therefore contain experimental or quasi-experimental pain responses, and each database is based on a different pain model. The following list shows a selection of the most relevant pain databases (last updated: April 2020): UNBC-McMaster Shoulder Pain BioVid Heat Pain EmoPain SenseEmotion X-ITE Pain

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