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  ReactiveX

  ReactiveX (Rx, also known as Reactive Extensions) is a software library originally created by Microsoft that allows imperative programming languages to operate on sequences of data regardless of whether the data is synchronous or asynchronous. It provides a set of sequence operators that operate on each item in the sequence. It is an implementation of reactive programming and provides a blueprint for the tools to be implemented in multiple programming languages. == Overview == ReactiveX is an API for asynchronous programming with observable streams. Asynchronous programming allows programmers to call functions and then have the functions "callback" when they are done, usually by giving the function the address of another function to execute when it is done. Programs designed in this way often avoid the overhead of having many threads constantly starting and stopping. Observable streams (i.e. streams that can be observed) in the context of Reactive Extensions are like event emitters that emit three events: next, error, and complete. An observable emits next events until it either emits an error event or a complete event. However, at that point it will not emit any more events, unless it is subscribed to again. The examples below use the RxJS implementation of Reactive Extensions for the JavaScript programming language. === Motivation === For sequences of data, it combines the advantages of iterators with the flexibility of event-based asynchronous programming. It also works as a simple promise, eliminating the pyramid of doom that results from multiple layers of callbacks. === Observables and observers === ReactiveX is a combination of ideas from the observer and the iterator patterns and from functional programming. An observer subscribes to an observable sequence. The sequence then sends the items to the observer one at a time, usually by calling the provided callback function. The observer handles each one before processing the next one. If many events come in asynchronously, they must be stored in a queue or dropped. In ReactiveX, an observer will never be called with an item out of order or (in a multi-threaded context) called before the callback has returned for the previous item. Asynchronous calls remain asynchronous and may be handled by returning an observable. It is similar to the iterators pattern in that if a fatal error occurs, it notifies the observer separately (by calling a second function). When all the items have been sent, it completes (and notifies the observer by calling a third function). The Reactive Extensions API also borrows many of its operators from iterator operators in other programming languages. Reactive Extensions is different from functional reactive programming as the Introduction to Reactive Extensions explains: It is sometimes called "functional reactive programming" but this is a misnomer. ReactiveX may be functional, and it may be reactive, but "functional reactive programming" is a different animal. One main point of difference is that functional reactive programming operates on values that change continuously over time, while ReactiveX operates on discrete values that are emitted over time. (See Conal Elliott's work for more-precise information on functional reactive programming.) === Reactive operators === An operator is a function that takes one observable (the source) as its first argument and returns another observable (the destination, or outer observable). Then for every item that the source observable emits, it will apply a function to that item, and then emit it on the destination Observable. It can even emit another Observable on the destination observable. This is called an inner observable. An operator that emits inner observables can be followed by another operator that in some way combines the items emitted by all the inner observables and emits the item on its outer observable. Examples include: switchAll – subscribes to each new inner observable as soon as it is emitted and unsubscribes from the previous one. mergeAll – subscribes to all inner observables as they are emitted and outputs their values in whatever order it receives them. concatAll – subscribes to each inner observable in order and waits for it to complete before subscribing to the next observable. Operators can be chained together to create complex data flows that filter events based on certain criteria. Multiple operators can be applied to the same observable. Some of the operators that can be used in Reactive Extensions may be familiar to programmers who use functional programming language, such as map, reduce, group, and zip. There are many other operators available in Reactive Extensions, though the operators available in a particular implementation for a programming language may vary. ==== Reactive operator examples ==== Here is an example of using the map and reduce operators. We create an observable from a list of numbers. The map operator will then multiply each number by two and return an observable. The reduce operator will then sum up all the numbers provided to it (the value of 0 is the starting point). Calling subscribe will register an observer that will observe the values from the observable produced by the chain of operators. With the subscribe method, we are able to pass in an error-handling function, called whenever an error is emitted in the observable, and a completion function when the observable has finished emitting items. ==== Usage in stream-oriented programming ==== Certain RxJS primitives such as BehaviorSubject make it possible to create pure stateful streams to track application state of arbitrary complexity in simple terms. The button below will feed an event to the stream, which in turn will re-emit the next natural number every time, back into the tag that follows and displays the count of clicks detected. Libraries such as Rimmel.js, designed around RxJS Observables, enable integration between reactive streams and the HTML DOM: == History == Reactive Extensions was created by the Cloud Programmability Team at Microsoft around 2011, as a byproduct of a larger effort called Volta. It was originally intended to provide an abstraction for events across different tiers in an application to support tier splitting in Volta. The project's logo represents an electric eel, which is a reference to Volta. The extensions suffix in the name is a reference to the Parallel Extensions technology which was invented around the same time; the two are considered complementary. The initial implementation of Rx was for .NET Framework and was released on June 21, 2011. Later, the team started the implementation of Rx for other platforms, including JavaScript and C++. The technology was released as open source in late 2012, initially on CodePlex. Later, the code moved to GitHub and has been ported to several other languages, including Go, Java, Kotlin, PHP and Rust.

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  Unique negative dimension

  Unique negative dimension (UND) is a complexity measure for the model of learning from positive examples. The unique negative dimension of a class C {\displaystyle C} of concepts is the size of the maximum subclass D ⊆ C {\displaystyle D\subseteq C} such that for every concept c ∈ D {\displaystyle c\in D} , we have ∩ ( D ∖ { c } ) ∖ c {\displaystyle \cap (D\setminus \{c\})\setminus c} is nonempty. This concept was originally proposed by M. Gereb-Graus in "Complexity of learning from one-side examples", Technical Report TR-20-89, Harvard University Division of Engineering and Applied Science, 1989.

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  Bayesian hierarchical modeling

  Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the posterior distribution of model parameters using the Bayesian method. The sub-models combine to form the hierarchical model, and Bayes' theorem is used to integrate them with the observed data and account for all the uncertainty that is present. This integration enables calculation of updated posterior over the (hyper)parameters, effectively updating prior beliefs in light of the observed data. Frequentist statistics may yield conclusions seemingly incompatible with those offered by Bayesian statistics due to the Bayesian treatment of the parameters as random variables and its use of subjective information in establishing assumptions on these parameters. As the approaches answer different questions the formal results are not technically contradictory but the two approaches disagree over which answer is relevant to particular applications. Bayesians argue that relevant information regarding decision-making and updating beliefs cannot be ignored and that hierarchical modeling has the potential to overrule classical methods in applications where respondents give multiple observational data. Moreover, the model has proven to be robust, with the posterior distribution less sensitive to the more flexible hierarchical priors. Hierarchical modeling, as its name implies, retains nested data structure, and is used when information is available at several different levels of observational units. For example, in epidemiological modeling to describe infection trajectories for multiple countries, observational units are countries, and each country has its own time-based profile of daily infected cases. In decline curve analysis to describe oil or gas production decline curve for multiple wells, observational units are oil or gas wells in a reservoir region, and each well has each own time-based profile of oil or gas production rates (usually, barrels per month). Hierarchical modeling is used to devise computation based strategies for multiparameter problems. == Philosophy == Statistical methods and models commonly involve multiple parameters that can be regarded as related or connected in such a way that the problem implies a dependence of the joint probability model for these parameters. Individual degrees of belief, expressed in the form of probabilities, come with uncertainty. Amidst this is the change of the degrees of belief over time. As was stated by Professor José M. Bernardo and Professor Adrian F. Smith, "The actuality of the learning process consists in the evolution of individual and subjective beliefs about the reality." These subjective probabilities are more directly involved in the mind rather than the physical probabilities. Hence, it is with this need of updating beliefs that Bayesians have formulated an alternative statistical model which takes into account the prior occurrence of a particular event. == Bayes' theorem == The assumed occurrence of a real-world event will typically modify preferences between certain options. This is done by modifying the degrees of belief attached, by an individual, to the events defining the options. Suppose in a study of the effectiveness of cardiac treatments, with the patients in hospital j having survival probability θ j {\displaystyle \theta _{j}} , the survival probability will be updated with the occurrence of y, the event in which a controversial serum is created which, as believed by some, increases survival in cardiac patients. In order to make updated probability statements about θ j {\displaystyle \theta _{j}} , given the occurrence of event y, we must begin with a model providing a joint probability distribution for θ j {\displaystyle \theta _{j}} and y. This can be written as a product of the two distributions that are often referred to as the prior distribution P ( θ ) {\displaystyle P(\theta )} and the sampling distribution P ( y ∣ θ ) {\displaystyle P(y\mid \theta )} respectively: P ( θ , y ) = P ( θ ) P ( y ∣ θ ) {\displaystyle P(\theta ,y)=P(\theta )P(y\mid \theta )} Using the basic property of conditional probability, the posterior distribution will yield: P ( θ ∣ y ) = P ( θ , y ) P ( y ) = P ( y ∣ θ ) P ( θ ) P ( y ) {\displaystyle P(\theta \mid y)={\frac {P(\theta ,y)}{P(y)}}={\frac {P(y\mid \theta )P(\theta )}{P(y)}}} This equation, showing the relationship between the conditional probability and the individual events, is known as Bayes' theorem. This simple expression encapsulates the technical core of Bayesian inference which aims to deconstruct the probability, P ( θ ∣ y ) {\displaystyle P(\theta \mid y)} , relative to solvable subsets of its supportive evidence. == Exchangeability == The usual starting point of a statistical analysis is the assumption that the n values y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} are exchangeable. If no information – other than data y – is available to distinguish any of the θ j {\displaystyle \theta _{j}} 's from any others, and no ordering or grouping of the parameters can be made, one must assume symmetry of prior distribution parameters. This symmetry is represented probabilistically by exchangeability. Generally, it is useful and appropriate to model data from an exchangeable distribution as independently and identically distributed, given some unknown parameter vector θ {\displaystyle \theta } , with distribution P ( θ ) {\displaystyle P(\theta )} . === Finite exchangeability === For a fixed number n, the set y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} is exchangeable if the joint probability P ( y 1 , y 2 , … , y n ) {\displaystyle P(y_{1},y_{2},\ldots ,y_{n})} is invariant under permutations of the indices. That is, for every permutation π {\displaystyle \pi } or ( π 1 , π 2 , … , π n ) {\displaystyle (\pi _{1},\pi _{2},\ldots ,\pi _{n})} of (1, 2, …, n), P ( y 1 , y 2 , … , y n ) = P ( y π 1 , y π 2 , … , y π n ) . {\displaystyle P(y_{1},y_{2},\ldots ,y_{n})=P(y_{\pi _{1}},y_{\pi _{2}},\ldots ,y_{\pi _{n}}).} The following is an exchangeable, but not independent and identical (iid), example: Consider an urn with a red ball and a blue ball inside, with probability 1 2 {\displaystyle {\frac {1}{2}}} of drawing either. Balls are drawn without replacement, i.e. after one ball is drawn from the n {\displaystyle n} balls, there will be n − 1 {\displaystyle n-1} remaining balls left for the next draw. Let Y i = { 1 , if the i th ball is red , 0 , otherwise . {\displaystyle {\text{Let }}Y_{i}={\begin{cases}1,&{\text{if the }}i{\text{th ball is red}},\\0,&{\text{otherwise}}.\end{cases}}} The probability of selecting a red ball in the first draw and a blue ball in the second draw is equal to the probability of selecting a blue ball on the first draw and a red on the second, both of which are 1/2: P ( y 1 = 1 , y 2 = 0 ) = P ( y 1 = 0 , y 2 = 1 ) = 1 2 {\displaystyle P(y_{1}=1,y_{2}=0)=P(y_{1}=0,y_{2}=1)={\frac {1}{2}}} . This makes y 1 {\displaystyle y_{1}} and y 2 {\displaystyle y_{2}} exchangeable. But the probability of selecting a red ball on the second draw given that the red ball has already been selected in the first is 0. This is not equal to the probability that the red ball is selected in the second draw, which is 1/2: P ( y 2 = 1 ∣ y 1 = 1 ) = 0 ≠ P ( y 2 = 1 ) = 1 2 {\displaystyle P(y_{2}=1\mid y_{1}=1)=0\neq P(y_{2}=1)={\frac {1}{2}}} . Thus, y 1 {\displaystyle y_{1}} and y 2 {\displaystyle y_{2}} are not independent. If x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} are independent and identically distributed, then they are exchangeable, but the converse is not necessarily true. === Infinite exchangeability === Infinite exchangeability is the property that every finite subset of an infinite sequence y 1 {\displaystyle y_{1}} , y 2 , … {\displaystyle y_{2},\ldots } is exchangeable. For any n, the sequence y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} is exchangeable. == Hierarchical models == === Components === Bayesian hierarchical modeling makes use of two important concepts in deriving the posterior distribution, namely: Hyperparameters: parameters of the prior distribution Hyperpriors: distributions of Hyperparameters Suppose a random variable Y follows a normal distribution with parameter θ {\displaystyle \theta } as the mean and 1 as the variance, that is Y ∣ θ ∼ N ( θ , 1 ) {\displaystyle Y\mid \theta \sim N(\theta ,1)} . The tilde relation ∼ {\displaystyle \sim } can be read as "has the distribution of" or "is distributed as". Suppose also that the parameter θ {\displaystyle \theta } has a distribution given by a normal distribution with mean μ {\displaystyle \mu } and variance 1, i.e. θ ∣ μ ∼ N ( μ , 1 ) {\displaystyle \theta \mid \mu \sim N(\mu ,1)} . Furthermore, μ {\displaystyle \mu } follows another distribution given, for example, by the standard normal distribution, N ( 0 , 1 ) {\displaystyle {\text{N}}(0,1)} . The parameter μ {\dis

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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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  Artificial intimacy

  Artificial intimacy is a form of human-AI interaction in which an individual will form social connections, emotional bonds, or intimate relationships with various forms of artificial intelligence, including chatbots, virtual assistants, and other artificial entities. Artificially intimate relationships include not only romances, but parasocial relationships with virtual AI characters and the use of griefbots trained on a dead or otherwise lost individual. Artificial intimacy can arise because humans are prone to anthropomorphism. Responses from these AI models are often designed to simulate human interaction. Individuals experiencing artificial intimacy may exhibit attachment, love and commitment to certain AI models, akin to the bonds typically shared between humans. == Causes == === Perceived responsiveness === Robin Dunbar famously proposed that due to emergence of larger groups of humans, vocal communication and language in humans evolved to replace grooming as a means of bonding, arguing that language was a more efficient way to maintain and strengthen social bonds across wider social settings and networks. Further research in this field leads many psychologists to agree that social cognition, affiliative bonding and language in humans are deeply connected. The interpersonal model of intimacy considers communication to be key in affiliative bonding, suggesting that intimacy develops and deepens through open communication between partners in relationship. Specifically, when individuals communicate emotions and perceive their partner as responsive and caring, feelings of closeness and connection are enhanced, building intimacy. Social penetration theory also aligns with the idea of communication being central to intimacy, by explaining how interpersonal relationships develop through gradual increases in self-disclosure. When the benefits of emotional bonding outweigh the costs of vulnerability, individuals will partake in self-disclosure, opening up to one another. Thereby, the literature can be used to provide a proximate explanation for the emergence of artificial intimacy to understand how the phenomenon occurs. Artificial entities are able to mimic interpersonal communication between humans, which in turn can simulate sensations of intimacy within human users though a perceived sense of responsiveness. The relationship between human and AI does not come with the cost of vulnerability or social rejection, which may make self-disclosure easier than with other humans. Altogether, these factors may lead to the experience of anthropomorphism and formation of affiliative relationships. Skjuve et al's interview study on Replika chatbot users further aligns with this explanation, finding that users' perception of chatbots as "accepting, understanding and non-judgmental" facilitated relationship development between the AI and users, and the act of self-disclosure possibly strengthened relationships. Another study on Replika users' reviews and survey results found users perceived chatbots as emotional supportive companions. This evidence further suggests that the perception of artificial entities as capable of empathy and responsiveness in communication facilitate the development of intimate relationships between users and AI. === Loneliness and coping with negative emotions === Research has suggested that humans evolved social bonds as a result of evolutionary pressures that favored cooperation, information exchange and transmission, and group living. Many studies stress the presence of social bonds to be important for human living: research by Baumeister and Leary suggests that humans have a basic psychological need to form and maintain "strong, stable interpersonal relationships", and that a lack of social bonds or sense of belonging leads to negative psychological and physical outcomes. Eisenberger et al's study on the neuroimaging of brain activity suggests that human brains process social rejection and exclusion similarly to physical pain. Furthermore, Song et al's study found that lonely individuals tend to seek more connections in mediated environments, such as online platforms like Facebook. This was suggested to be as a means to reduce their offline loneliness from a lack of in-person interaction, while also fulfilling a need to communicate. Leading on from this, an ultimate explanation for why humans seek the perceived sense of connection from artificial intimacy is to fulfil an evolutionary need for bonding and belonging. Xie et al's study found loneliness to be a driving factor in chatbot interaction. Herbener and Damholdt's study on Danish high school students found that students who sought emotional support or engaged in reciprocal conversations with chatbots were significantly more lonely than their peers, perceived themselves as having less social support, and used the chatbots to cope with negative emotions. The aforementioned notion that chatbots were perceived to have a positive effect on users' negative emotions is also further supported by other studies. Skjuve et al's study found that chatbot relationships may have a positive effect on users' wellbeing. De Freitas et al ran several studies on the effect of chatbots on loneliness, consistently finding evidence suggesting that interaction with chatbots reduces loneliness in users: It was found that existing chatbot users used AI to alleviate loneliness, having an AI companion consistently reduced loneliness over the course of a week, and reductions in loneliness could be explained by chatbot performance—and specifically whether it was able to make users feel heard. Overall the evidence suggests an innate need for bonding evokes feelings of loneliness in users, who turn to artificial intimacy as a low-cost method alleviate these emotions. While many users report positive experiences, some researchers caution that pursuing artificial intimacy may lead to reduced social motivation, social substitution effects, withdrawal from real-life relationships and difficulty discerning reality from fantasy, which may increase longer-term loneliness and isolation. The long-term psychological and societal impacts remain under active investigation.

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  Ordination (statistics)

  Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). In contrast to cluster analysis, ordination orders quantities in a (usually lower-dimensional) latent space. In the ordination space, quantities that are near each other share attributes (i.e., are similar to some degree), and dissimilar objects are farther from each other. Such relationships between the objects, on each of several axes or latent variables, are then characterized numerically and/or graphically in a biplot. The first ordination method, principal components analysis, was suggested by Karl Pearson in 1901. == Methods == Ordination methods can broadly be categorized in eigenvector-, algorithm-, or model-based methods. Many classical ordination techniques, including principal components analysis, correspondence analysis (CA) and its derivatives (detrended correspondence analysis, canonical correspondence analysis, and redundancy analysis, belong to the first group). The second group includes some distance-based methods such as non-metric multidimensional scaling, and machine learning methods such as T-distributed stochastic neighbor embedding and nonlinear dimensionality reduction. The third group includes model-based ordination methods, which can be considered as multivariate extensions of Generalized Linear Models. Model-based ordination methods are more flexible in their application than classical ordination methods, so that it is for example possible to include random-effects. Unlike in the aforementioned two groups, there is no (implicit or explicit) distance measure in the ordination. Instead, a distribution needs to be specified for the responses as is typical for statistical models. These and other assumptions, such as the assumed mean-variance relationship, can be validated with the use of residual diagnostics, unlike in other ordination methods. == Applications == Ordination can be used on the analysis of any set of multivariate objects. It is frequently used in several environmental or ecological sciences, particularly plant community ecology. It is also used in genetics and systems biology for microarray data analysis and in psychometrics.

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  Information gain ratio

  In decision tree learning, information gain ratio is a ratio of information gain to the intrinsic information. It was proposed by Ross Quinlan, to reduce a bias towards multi-valued attributes by taking the number and size of branches into account when choosing an attribute. Information gain is also known as mutual information. == Information gain calculation == Information gain is the reduction in entropy produced from partitioning a set with attributes a {\displaystyle a} and finding the optimal candidate that produces the highest value: IG ( T , a ) = H ( T ) − H ( T | a ) , {\displaystyle {\text{IG}}(T,a)=\mathrm {H} {(T)}-\mathrm {H} {(T|a)},} where T {\displaystyle T} is a random variable and H ( T | a ) {\displaystyle \mathrm {H} {(T|a)}} is the entropy of T {\displaystyle T} given the value of attribute a {\displaystyle a} . The information gain is equal to the total entropy for an attribute if for each of the attribute values a unique classification can be made for the result attribute. In this case the relative entropies subtracted from the total entropy are 0. == Split information calculation == The split information value for a test is defined as follows: SplitInformation ( X ) = − ∑ i = 1 n N ( x i ) N ( x ) ∗ log ⁡ 2 N ( x i ) N ( x ) {\displaystyle {\text{SplitInformation}}(X)=-\sum _{i=1}^{n}{{\frac {\mathrm {N} (x_{i})}{\mathrm {N} (x)}}\log {_{2}}{\frac {\mathrm {N} (x_{i})}{\mathrm {N} (x)}}}} where X {\displaystyle X} is a discrete random variable with possible values x 1 , x 2 , . . . , x i {\displaystyle {x_{1},x_{2},...,x_{i}}} and N ( x i ) {\displaystyle N(x_{i})} being the number of times that x i {\displaystyle x_{i}} occurs divided by the total count of events N ( x ) {\displaystyle N(x)} where x {\displaystyle x} is the set of events. The split information value is a positive number that describes the potential worth of splitting a branch from a node. This in turn is the intrinsic value that the random variable possesses and will be used to remove the bias in the information gain ratio calculation. == Information gain ratio calculation == The information gain ratio is the ratio between the information gain and the split information value: IGR ( T , a ) = IG ( T , a ) / SplitInformation ( T ) {\displaystyle {\text{IGR}}(T,a)={\text{IG}}(T,a)/{\text{SplitInformation}}(T)} IGR ( T , a ) = − ∑ i = 1 n P ( T ) log ⁡ P ( T ) − ( − ∑ i = 1 n P ( T | a ) log ⁡ P ( T | a ) ) − ∑ i = 1 n N ( t i ) N ( t ) ∗ log ⁡ 2 N ( t i ) N ( t ) {\displaystyle {\text{IGR}}(T,a)={\frac {-\sum _{i=1}^{n}{\mathrm {P} (T)\log \mathrm {P} (T)}-(-\sum _{i=1}^{n}{\mathrm {P} (T|a)\log \mathrm {P} (T|a)})}{-\sum _{i=1}^{n}{{\frac {\mathrm {N} (t_{i})}{\mathrm {N} (t)}}\log {_{2}}{\frac {\mathrm {N} (t_{i})}{\mathrm {N} (t)}}}}}} == Example == Using weather data published by Fordham University, the table was created below: Using the table above, one can find the entropy, information gain, split information, and information gain ratio for each variable (outlook, temperature, humidity, and wind). These calculations are shown in the tables below: Using the above tables, one can deduce that Outlook has the highest information gain ratio. Next, one must find the statistics for the sub-groups of the Outlook variable (sunny, overcast, and rainy), for this example one will only build the sunny branch (as shown in the table below): One can find the following statistics for the other variables (temperature, humidity, and wind) to see which have the greatest effect on the sunny element of the outlook variable: Humidity was found to have the highest information gain ratio. One will repeat the same steps as before and find the statistics for the events of the Humidity variable (high and normal): Since the play values are either all "No" or "Yes", the information gain ratio value will be equal to 1. Also, now that one has reached the end of the variable chain with Wind being the last variable left, they can build an entire root to leaf node branch line of a decision tree. Once finished with reaching this leaf node, one would follow the same procedure for the rest of the elements that have yet to be split in the decision tree. This set of data was relatively small, however, if a larger set was used, the advantages of using the information gain ratio as the splitting factor of a decision tree can be seen more. == Advantages == Information gain ratio biases the decision tree against considering attributes with a large number of distinct values. For example, suppose that we are building a decision tree for some data describing a business's customers. Information gain ratio is used to decide which of the attributes are the most relevant. These will be tested near the root of the tree. One of the input attributes might be the customer's telephone number. This attribute has a high information gain, because it uniquely identifies each customer. Due to its high amount of distinct values, this will not be chosen to be tested near the root. == Disadvantages == Although information gain ratio solves the key problem of information gain, it creates another problem. If one is considering an amount of attributes that have a high number of distinct values, these will never be above one that has a lower number of distinct values. == Difference from information gain == Information gain's shortcoming is created by not providing a numerical difference between attributes with high distinct values from those that have less. Example: Suppose that we are building a decision tree for some data describing a business's customers. Information gain is often used to decide which of the attributes are the most relevant, so they can be tested near the root of the tree. One of the input attributes might be the customer's credit card number. This attribute has a high information gain, because it uniquely identifies each customer, but we do not want to include it in the decision tree: deciding how to treat a customer based on their credit card number is unlikely to generalize to customers we haven't seen before. Information gain ratio's strength is that it has a bias towards the attributes with the lower number of distinct values. Below is a table describing the differences of information gain and information gain ratio when put in certain scenarios.

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  Optical neural network

  An optical neural network is a physical implementation of an artificial neural network with optical components. Early optical neural networks used a photorefractive Volume hologram to interconnect arrays of input neurons to arrays of output with synaptic weights in proportion to the multiplexed hologram's strength. Volume holograms were further multiplexed using spectral hole burning to add one dimension of wavelength to space to achieve four dimensional interconnects of two dimensional arrays of neural inputs and outputs. This research led to extensive research on alternative methods using the strength of the optical interconnect for implementing neuronal communications. Some artificial neural networks that have been implemented as optical neural networks include the Hopfield neural network and the Kohonen self-organizing map with liquid crystal spatial light modulators Optical neural networks can also be based on the principles of neuromorphic engineering, creating neuromorphic photonic systems. Typically, these systems encode information in the networks using spikes, mimicking the functionality of spiking neural networks in optical and photonic hardware. Photonic devices that have demonstrated neuromorphic functionalities include (among others) vertical-cavity surface-emitting lasers, integrated photonic modulators, optoelectronic systems based on superconducting Josephson junctions or systems based on resonant tunnelling diodes. == Electrochemical vs. optical neural networks == Biological neural networks function on an electrochemical basis, while optical neural networks use electromagnetic waves. Optical interfaces to biological neural networks can be created with optogenetics, but is not the same as an optical neural networks. In biological neural networks there exist a lot of different mechanisms for dynamically changing the state of the neurons, these include short-term and long-term synaptic plasticity. Synaptic plasticity is among the electrophysiological phenomena used to control the efficiency of synaptic transmission, long-term for learning and memory, and short-term for short transient changes in synaptic transmission efficiency. Implementing this with optical components is difficult, and ideally requires advanced photonic materials. Properties that might be desirable in photonic materials for optical neural networks include the ability to change their efficiency of transmitting light, based on the intensity of incoming light. == Rising Era of Optical Neural Networks == With the increasing significance of computer vision in various domains, the computational cost of these tasks has increased, making it more important to develop the new approaches of the processing acceleration. Optical computing has emerged as a potential alternative to GPU acceleration for modern neural networks, particularly considering the looming obsolescence of Moore's Law. Consequently, optical neural networks have garnered increased attention in the research community. Presently, two primary methods of optical neural computing are under research: silicon photonics-based and free-space optics. Each approach has its benefits and drawbacks; while silicon photonics may offer superior speed, it lacks the massive parallelism that free-space optics can deliver. Given the substantial parallelism capabilities of free-space optics, researchers have focused on taking advantage of it. One implementation, proposed by Lin et al., involves the training and fabrication of phase masks for a handwritten digit classifier. By stacking 3D-printed phase masks, light passing through the fabricated network can be read by a photodetector array of ten detectors, each representing a digit class ranging from 1 to 10. Although this network can achieve terahertz-range classification, it lacks flexibility, as the phase masks are fabricated for a specific task and cannot be retrained. An alternative method for classification in free-space optics, introduced by Cahng et al., employs a 4F system that is based on the convolution theorem to perform convolution operations. This system uses two lenses to execute the Fourier transforms of the convolution operation, enabling passive conversion into the Fourier domain without power consumption or latency. However, the convolution operation kernels in this implementation are also fabricated phase masks, limiting the device's functionality to specific convolutional layers of the network only. In contrast, Li et al. proposed a technique involving kernel tiling to use the parallelism of the 4F system while using a Digital Micromirror Device (DMD) instead of a phase mask. This approach allows users to upload various kernels into the 4F system and execute the entire network's inference on a single device. Unfortunately, modern neural networks are not designed for the 4F systems, as they were primarily developed during the CPU/GPU era. Mostly because they tend to use a lower resolution and a high number of channels in their feature maps. == Other Implementations == In 2007 there was one model of Optical Neural Network: the Programmable Optical Array/Analogic Computer (POAC). It had been implemented in the year 2000 and reported based on modified Joint Fourier Transform Correlator (JTC) and Bacteriorhodopsin (BR) as a holographic optical memory. Full parallelism, large array size and the speed of light are three promises offered by POAC to implement an optical CNN. They had been investigated during the last years with their practical limitations and considerations yielding the design of the first portable POAC version. The practical details – hardware (optical setups) and software (optical templates) – were published. However, POAC is a general purpose and programmable array computer that has a wide range of applications including: image processing pattern recognition target tracking real-time video processing document security optical switching == Progress in the 2020s == Taichi from Tsinghua University in Beijing is a hybrid ONN that combines the power efficiency and parallelism of optical diffraction and the configurability of optical interference. Taichi offers 13.96 million parameters. Taichi avoids the high error rates that afflict deep (multi-layer) networks by combining clusters of fewer-layer diffractive units with arrays of interferometers for reconfigurable computation. Its encoding protocol divides large network models into sub-models that can be distributed across multiple chiplets in parallel. Taichi achieved 91.89% accuracy in tests with the Omniglot database. It was also used to generate music Bach and generate images the styles of Van Gogh and Munch. The developers claimed energy efficiency of up to 160 trillion operations second−1 watt−1 and an area efficiency of 880 trillion multiply-accumulate operations mm−2 or 103 more energy efficient than the NVIDIA H100, and 102 times more energy efficient and 10 times more area efficient than previous ONNs. Time dimension has recently been introduced into diffractive neural network by fs laser lithography of perovskite hydration. The temporal behaviour of the neuron can be modulated by the fs laser at the nanoscale, enabling a programmable holographic neural network with temporal evolution functionality, i.e., the functionality can change with time under the hydration stimuli. An in-memory temporal inference functionality was demonstrated to mimic the function evolution of the human brain, i.e., the functionality can change from simple digit image classification to more complicated digit and clothing product image classification with time. This is the first time of introducing time dimension into the optical neural network, laying a foundation for future brain-like photonic chip development.

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  Artificial intelligence in spirituality

  Some users of artificial intelligence (AI) technologies, especially chatbots, may develop beliefs that AI has or can attain supernatural or spiritual powers. AI models such as ChatGPT are turned to for fortune telling, mysticism and remote viewing. Recent and sudden advances in large language models have led to folk myths about their origin or capabilities, as well as their deification or worship by some users. Tucker Carlson has made similar claims, including directly to Sam Altman. Pope Leo XIV advised priests against using LLM models when it came to the creation of sermons.

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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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  Vladimir Batagelj

  Vladimir Batagelj (born June 14, 1948 in Idrija, Yugoslavia) is a Slovenian mathematician and an emeritus professor of mathematics at the University of Ljubljana. He is known for his work in discrete mathematics and combinatorial optimization, particularly analysis of social networks and other large networks (blockmodeling). == Education and career == Vladimir Batagelj completed his Ph.D. at the University of Ljubljana in 1986 under the direction of Tomaž Pisanski. He stayed at the University of Ljubljana as a professor until his retirement, where he was a professor of sociology and statistics, while also being a chair of the Department of Sociology of the Faculty of Social Sciences. As visiting professor, he was taught at the University of Pittsburgh (1990-91) and at the University of Konstanz (2002). He was also a member of editorial boards of two journals: Informatica and Journal of Social Structure. His work has been cited over 11000 times. His book Exploratory Social Network Analysis with Pajek on blockmodeling, coauthored with Wouter de Nooy and Andrej Mrvar, is Batagelj's most cited work and has over 3300 citations. The book was translated into Chinese and Japanese. The revised and expanded third edition has been published by Cambridge University Press. In 1975, 11 years before completing his PhD, Batagelj published a solo paper in Communications of the ACM. Batagelj authored more than 20 textbooks in Slovenian, covering topics like TeX, combinatorics and discrete mathematics. He has also written extensively in the Slovenian popular science journal Presek. Batagelj has advised 9 Ph.D. students. == Pajek == Batagelj is particularly known for his work on Pajek, a freely available software for analysis and visualization of large networks. He began work on Pajek in 1996 with Andrej Mrvar, who was then his PhD student. == Awards and honors == First prizes for contributions (with Andrej Mrvar) to Graph Drawing Contests in years: 1995, 1996, 1997, 1998, 1999, 2000 and 2005 / Graph Drawing Hall of Fame. In 2007 the book Generalized blockmodeling was awarded the Harrison White Outstanding Book Award by the Mathematical Sociology Section of American Sociological Association In 2007 he was awarded (together with Anuška Ferligoj) the Simmel Award by INSNA. In 2013, Vladimir Batagelj and Andrej Mrvar received the INSNA's William D. Richards Software award for their work on Pajek. == Selected bibliography == Vladimir Batagelj, Social Network Analysis, Large-Scale [1]. in R.A. Meyers, ed., Encyclopedia of Complexity and Systems Science, Springer 2009: 8245–8265. Vladimir Batagelj, Complex Networks, Visualization of [2]. in R.A. Meyers, ed., Encyclopedia of Complexity and Systems Science, Springer 2009: 1253–1268. Wouter de Nooy, Andrej Mrvar, Vladimir Batagelj, Mark Granovetter (Series Editor), Exploratory Social Network Analysis with Pajek (Structural Analysis in the Social Sciences), Cambridge University Press 2005 (ISBN 0-521-60262-9). ESNA in Japanese, TDU, 2010. Patrick Doreian, Vladimir Batagelj, Anuška Ferligoj, Mark Granovetter (Series Editor), Generalized Blockmodeling (Structural Analysis in the Social Sciences), Cambridge University Press 2004 (ISBN 0-521-84085-6)

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  Grammatical evolution

  Grammatical evolution (GE) is a genetic programming (GP) technique (or approach) from evolutionary computation pioneered by Conor Ryan, JJ Collins and Michael O'Neill in 1998 at the BDS Group in the University of Limerick. As in any other GP approach, the objective is to find an executable program, program fragment, or function, which will achieve a good fitness value for a given objective function. In most published work on GP, a LISP-style tree-structured expression is directly manipulated, whereas GE applies genetic operators to an integer string, subsequently mapped to a program (or similar) through the use of a grammar, which is typically expressed in Backus–Naur form. One of the benefits of GE is that this mapping simplifies the application of search to different programming languages and other structures. == Problem addressed == In type-free, conventional Koza-style GP, the function set must meet the requirement of closure: all functions must be capable of accepting as their arguments the output of all other functions in the function set. Usually, this is implemented by dealing with a single data-type such as double-precision floating point. While modern Genetic Programming frameworks support typing, such type-systems have limitations that Grammatical Evolution does not suffer from. == GE's solution == GE offers a solution to the single-type limitation by evolving solutions according to a user-specified grammar (usually a grammar in Backus-Naur form). Therefore, the search space can be restricted, and domain knowledge of the problem can be incorporated. The inspiration for this approach comes from a desire to separate the "genotype" from the "phenotype": in GP, the objects the search algorithm operates on and what the fitness evaluation function interprets are one and the same. In contrast, GE's "genotypes" are ordered lists of integers which code for selecting rules from the provided context-free grammar. The phenotype, however, is the same as in Koza-style GP: a tree-like structure that is evaluated recursively. This model is more in line with how genetics work in nature, where there is a separation between an organism's genotype and the final expression of phenotype in proteins, etc. Separating genotype and phenotype allows a modular approach. In particular, the search portion of the GE paradigm needn't be carried out by any one particular algorithm or method. Observe that the objects GE performs search on are the same as those used in genetic algorithms. This means, in principle, that any existing genetic algorithm package, such as the popular GAlib, can be used to carry out the search, and a developer implementing a GE system need only worry about carrying out the mapping from list of integers to program tree. It is also in principle possible to perform the search using some other method, such as particle swarm optimization (see the remark below); the modular nature of GE creates many opportunities for hybrids as the problem of interest to be solved dictates. Brabazon and O'Neill have successfully applied GE to predicting corporate bankruptcy, forecasting stock indices, bond credit ratings, and other financial applications. GE has also been used with a classic predator-prey model to explore the impact of parameters such as predator efficiency, niche number, and random mutations on ecological stability. It is possible to structure a GE grammar that for a given function/terminal set is equivalent to genetic programming. == Criticism == Despite its successes, GE has been the subject of some criticism. One issue is that as a result of its mapping operation, GE's genetic operators do not achieve high locality which is a highly regarded property of genetic operators in evolutionary algorithms. == Variants == Although GE was originally described in terms of using an Evolutionary Algorithm, specifically, a Genetic Algorithm, other variants exist. For example, GE researchers have experimented with using particle swarm optimization to carry out the searching instead of genetic algorithms with results comparable to that of normal GE; this is referred to as a "grammatical swarm"; using only the basic PSO model it has been found that PSO is probably equally capable of carrying out the search process in GE as simple genetic algorithms are. (Although PSO is normally a floating-point search paradigm, it can be discretized, e.g., by simply rounding each vector to the nearest integer, for use with GE.) Yet another possible variation that has been experimented with in the literature is attempting to encode semantic information in the grammar in order to further bias the search process. Other work showed that, with biased grammars that leverage domain knowledge, even random search can be used to drive GE. == Related work == GE was originally a combination of the linear representation as used by the Genetic Algorithm for Developing Software (GADS) and Backus Naur Form grammars, which were originally used in tree-based GP by Wong and Leung in 1995 and Whigham in 1996. Other related work noted in the original GE paper was that of Frederic Gruau, who used a conceptually similar "embryonic" approach, as well as that of Keller and Banzhaf, which similarly used linear genomes. == Implementations == There are several implementations of GE. These include the following.

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  Expectation propagation

  Expectation propagation (EP) is a technique in Bayesian machine learning. EP finds approximations to a probability distribution. It uses an iterative approach that uses the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as variational Bayesian methods. More specifically, suppose we wish to approximate an intractable probability distribution p ( x ) {\displaystyle p(\mathbf {x} )} with a tractable distribution q ( x ) {\displaystyle q(\mathbf {x} )} . Expectation propagation achieves this approximation by minimizing the Kullback–Leibler divergence K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} . Variational Bayesian methods minimize K L ( q | | p ) {\displaystyle \mathrm {KL} (q||p)} instead. If q ( x ) {\displaystyle q(\mathbf {x} )} is a Gaussian N ( x | μ , Σ ) {\displaystyle {\mathcal {N}}(\mathbf {x} |\mu ,\Sigma )} , then K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} is minimized with μ {\displaystyle \mu } and Σ {\displaystyle \Sigma } being equal to the mean of p ( x ) {\displaystyle p(\mathbf {x} )} and the covariance of p ( x ) {\displaystyle p(\mathbf {x} )} , respectively; this is called moment matching. == Applications == Expectation propagation via moment matching plays a vital role in approximation for indicator functions that appear when deriving the message passing equations for TrueSkill.

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  Teacher forcing

  Teacher forcing is an algorithm for training the weights of recurrent neural networks (RNNs). It involves feeding observed sequence values (i.e. ground-truth samples) back into the RNN after each step, thus forcing the RNN to stay close to the ground-truth sequence. The term "teacher forcing" can be motivated by comparing the RNN to a human student taking a multi-part exam where the answer to each part (for example a mathematical calculation) depends on the answer to the preceding part. In this analogy, rather than grading every answer in the end, with the risk that the student fails every single part even though they only made a mistake in the first one, a teacher records the score for each individual part and then tells the student the correct answer, to be used in the next part. The use of an external teacher signal is in contrast to real-time recurrent learning (RTRL). Teacher signals are known from oscillator networks. The promise is, that teacher forcing helps to reduce the training time. The term "teacher forcing" was introduced in 1989 by Ronald J. Williams and David Zipser, who reported that the technique was already being "frequently used in dynamical supervised learning tasks" around that time. A NeurIPS 2016 paper introduced the related method of "professor forcing".

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  Jackknife variance estimates for random forest

  In statistics, jackknife variance estimates for random forest are a way to estimate the variance in random forest models, in order to eliminate the bootstrap effects. == Jackknife variance estimates == The sampling variance of bagged learners is: V ( x ) = V a r [ θ ^ ∞ ( x ) ] {\displaystyle V(x)=Var[{\hat {\theta }}^{\infty }(x)]} Jackknife estimates can be considered to eliminate the bootstrap effects. The jackknife variance estimator is defined as: V ^ j = n − 1 n ∑ i = 1 n ( θ ^ ( − i ) − θ ¯ ) 2 {\displaystyle {\hat {V}}_{j}={\frac {n-1}{n}}\sum _{i=1}^{n}({\hat {\theta }}_{(-i)}-{\overline {\theta }})^{2}} In some classification problems, when random forest is used to fit models, jackknife estimated variance is defined as: V ^ j = n − 1 n ∑ i = 1 n ( t ¯ ( − i ) ⋆ ( x ) − t ¯ ⋆ ( x ) ) 2 {\displaystyle {\hat {V}}_{j}={\frac {n-1}{n}}\sum _{i=1}^{n}({\overline {t}}_{(-i)}^{\star }(x)-{\overline {t}}^{\star }(x))^{2}} Here, t ⋆ {\displaystyle t^{\star }} denotes a decision tree after training, t ( − i ) ⋆ {\displaystyle t_{(-i)}^{\star }} denotes the result based on samples without i t h {\displaystyle ith} observation. == Examples == E-mail spam problem is a common classification problem, in this problem, 57 features are used to classify spam e-mail and non-spam e-mail. Applying IJ-U variance formula to evaluate the accuracy of models with m=15,19 and 57. The results shows in paper( Confidence Intervals for Random Forests: The jackknife and the Infinitesimal Jackknife ) that m = 57 random forest appears to be quite unstable, while predictions made by m=5 random forest appear to be quite stable, this results is corresponding to the evaluation made by error percentage, in which the accuracy of model with m=5 is high and m=57 is low. Here, accuracy is measured by error rate, which is defined as: E r r o r R a t e = 1 N ∑ i = 1 N ∑ j = 1 M y i j , {\displaystyle ErrorRate={\frac {1}{N}}\sum _{i=1}^{N}\sum _{j=1}^{M}y_{ij},} Here N is also the number of samples, M is the number of classes, y i j {\displaystyle y_{ij}} is the indicator function which equals 1 when i t h {\displaystyle ith} observation is in class j, equals 0 when in other classes. No probability is considered here. There is another method which is similar to error rate to measure accuracy: l o g l o s s = 1 N ∑ i = 1 N ∑ j = 1 M y i j l o g ( p i j ) {\displaystyle logloss={\frac {1}{N}}\sum _{i=1}^{N}\sum _{j=1}^{M}y_{ij}log(p_{ij})} Here N is the number of samples, M is the number of classes, y i j {\displaystyle y_{ij}} is the indicator function which equals 1 when i t h {\displaystyle ith} observation is in class j, equals 0 when in other classes. p i j {\displaystyle p_{ij}} is the predicted probability of i t h {\displaystyle ith} observation in class j {\displaystyle j} .This method is used in Kaggle These two methods are very similar. == Modification for bias == When using Monte Carlo MSEs for estimating V I J ∞ {\displaystyle V_{IJ}^{\infty }} and V J ∞ {\displaystyle V_{J}^{\infty }} , a problem about the Monte Carlo bias should be considered, especially when n is large, the bias is getting large: E [ V ^ I J B ] − V ^ I J ∞ ≈ n ∑ b = 1 B ( t b ⋆ − t ¯ ⋆ ) 2 B {\displaystyle E[{\hat {V}}_{IJ}^{B}]-{\hat {V}}_{IJ}^{\infty }\approx {\frac {n\sum _{b=1}^{B}(t_{b}^{\star }-{\bar {t}}^{\star })^{2}}{B}}} To eliminate this influence, bias-corrected modifications are suggested: V ^ I J − U B = V ^ I J B − n ∑ b = 1 B ( t b ⋆ − t ¯ ⋆ ) 2 B {\displaystyle {\hat {V}}_{IJ-U}^{B}={\hat {V}}_{IJ}^{B}-{\frac {n\sum _{b=1}^{B}(t_{b}^{\star }-{\bar {t}}^{\star })^{2}}{B}}} V ^ J − U B = V ^ J B − ( e − 1 ) n ∑ b = 1 B ( t b ⋆ − t ¯ ⋆ ) 2 B {\displaystyle {\hat {V}}_{J-U}^{B}={\hat {V}}_{J}^{B}-(e-1){\frac {n\sum _{b=1}^{B}(t_{b}^{\star }-{\bar {t}}^{\star })^{2}}{B}}}

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