Model

A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in 16th-century English, and derived via French and Italian ultimately from Latin modulus, 'a measure'. Models can be divided into physical models (e.g. a ship model) and abstract models (e.g. a set of mathematical equations describing the workings of the atmosphere for the purpose of weather forecasting). Abstract or conceptual models are central to philosophy of science. In scholarly research and applied science, a model should not be confused with a theory: while a model seeks only to represent reality with the purpose of better understanding or predicting the world, a theory is more ambitious in that it claims to be an explanation of reality. == Types of model == === Model in specific contexts === As a noun, model has specific meanings in certain fields, derived from its original meaning of "structural design or layout": Model (art), a person posing for an artist, e.g. a 15th-century criminal representing the biblical Judas in Leonardo da Vinci's painting The Last Supper Model (person), a person who serves as a template for others to copy, as in a role model, often in the context of advertising commercial products; e.g. the first fashion model, Marie Vernet Worth in 1853, wife of designer Charles Frederick Worth. Model (product), a particular design of a product as displayed in a catalogue or show room (e.g. Ford Model T, an early car model) Model (organism) a non-human species that is studied to understand biological phenomena in other organisms, e.g. a guinea pig starved of vitamin C to study scurvy, an experiment that would be immoral to conduct on a person Model (mimicry), a species that is mimicked by another species Model (logic), a structure (a set of items, such as natural numbers 1, 2, 3,..., along with mathematical operations such as addition and multiplication, and relations, such as < {\displaystyle <} ) that satisfies a given system of axioms (basic truisms), i.e. that satisfies the statements of a given theory Model (CGI), a mathematical representation of any surface of an object in three dimensions via specialized software Model (MVC), the information-representing internal component of a software, as distinct from its user interface === Physical model === A physical model (most commonly referred to simply as a model but in this context distinguished from a conceptual model) is a smaller or larger physical representation of an object, person or system. The object being modelled may be small (e.g., an atom) or large (e.g., the Solar System) or life-size (e.g., a fashion model displaying clothes for similarly-built potential customers). The geometry of the model and the object it represents are often similar in the sense that one is a rescaling of the other. However, in many cases the similarity is only approximate or even intentionally distorted. Sometimes the distortion is systematic, e.g., a fixed scale horizontally and a larger fixed scale vertically when modelling topography to enhance a region's mountains. An architectural model permits visualization of internal relationships within the structure or external relationships of the structure to the environment. Another use is as a toy. Instrumented physical models are an effective way of investigating fluid flows for engineering design. Physical models are often coupled with computational fluid dynamics models to optimize the design of equipment and processes. This includes external flow such as around buildings, vehicles, people, or hydraulic structures. Wind tunnel and water tunnel testing is often used for these design efforts. Instrumented physical models can also examine internal flows, for the design of ductwork systems, pollution control equipment, food processing machines, and mixing vessels. Transparent flow models are used in this case to observe the detailed flow phenomenon. These models are scaled in terms of both geometry and important forces, for example, using Froude number or Reynolds number scaling (see Similitude). In the pre-computer era, the UK economy was modelled with the hydraulic model MONIAC, to predict for example the effect of tax rises on employment. === Conceptual model === A conceptual model is a theoretical representation of a system, e.g. a set of mathematical equations attempting to describe the workings of the atmosphere for the purpose of weather forecasting. It consists of concepts used to help understand or simulate a subject the model represents. Abstract or conceptual models are central to philosophy of science, as almost every scientific theory effectively embeds some kind of model of the physical or human sphere. In some sense, a physical model "is always the reification of some conceptual model; the conceptual model is conceived ahead as the blueprint of the physical one", which is then constructed as conceived. Thus, the term refers to models that are formed after a conceptualization or generalization process. === Examples === Conceptual model (computer science), an agreed representation of entities and their relationships, to assist in developing software Economic model, a theoretical construct representing economic processes Language model, a probabilistic model of a natural language, used for speech recognition, language generation, and information retrieval Large language models are artificial neural networks used for generative artificial intelligence (AI), e.g. ChatGPT Mathematical model, a description of a system using mathematical concepts and language Statistical model, a mathematical model that usually specifies the relationship between one or more random variables and other non-random variables Model (CGI), a mathematical representation of any surface of an object in three dimensions via specialized software Medical model, a proposed "set of procedures in which all doctors are trained" Mental model, in psychology, an internal representation of external reality Model (logic), a set along with a collection of finitary operations, and relations that are defined on it, satisfying a given collection of axioms Model (MVC), information-representing component of a software, distinct from the user interface (the "view"), both linked by the "controller" component, in the context of the model–view–controller software design Model act, a law drafted centrally to be disseminated and proposed for enactment in multiple independent legislatures Standard model (disambiguation) == Properties of models, according to general model theory == According to Herbert Stachowiak, a model is characterized by at least three properties: 1. Mapping A model always is a model of something—it is an image or representation of some natural or artificial, existing or imagined original, where this original itself could be a model. 2. Reduction In general, a model will not include all attributes that describe the original but only those that appear relevant to the model's creator or user. 3. Pragmatism A model does not relate unambiguously to its original. It is intended to work as a replacement for the original a) for certain subjects (for whom?) b) within a certain time range (when?) c) restricted to certain conceptual or physical actions (what for?). For example, a street map is a model of the actual streets in a city (mapping), showing the course of the streets while leaving out, say, traffic signs and road markings (reduction), made for pedestrians and vehicle drivers for the purpose of finding one's way in the city (pragmatism). Additional properties have been proposed, like extension and distortion as well as validity. The American philosopher Michael Weisberg differentiates between concrete and mathematical models and proposes computer simulations (computational models) as their own class of models. == Uses of models == According to Bruce Edmonds, there are at least 5 general uses for models: Prediction: reliably anticipating unknown data, including data within the domain of the training data (interpolation), and outside the domain (extrapolation) Explanation: establishing plausible chains of causality by proposing mechanisms that can explain patterns seen in data Theoretical exposition: discovering or proposing new hypotheses, or refuting existing hypotheses about the behaviour of the system being modelled Description: representing important aspects of the system being modelled Illustration: communicating an idea or explanation

CloudSim

CloudSim is a framework for modeling and simulation of cloud computing infrastructures and services. Originally built primarily at the Cloud Computing and Distributed Systems (CLOUDS) Laboratory, the University of Melbourne, Australia, CloudSim has become one of the most popular open source cloud simulators in the research and academia. CloudSim is completely written in Java. The latest version of CloudSim is CloudSim v6.0.0-beta on GitHub. Cloudsim is suitable for implementing simulations scenarios based on Infrastructure as a service as well as with latest version Platform as a service, so get started here == CloudSim extensions == Initially developed as a stand-alone cloud simulator, CloudSim has further been extended by independent researchers. GPUCloudSim is an enhanced CloudSim tool for modeling GPU-based cloud infrastructures and data centers. It offers simulations for multi-GPU setups, customizable GPU policies, GPU remoting, etc. It also examines performance impacts and interactions within virtualized GPU environments. CloudSim Plus is a totally re-engineered CloudSim fork providing general-purpose cloud computing simulation and exclusive features such as: multi-cloud simulations, vertical and horizontal VM scaling, host fault injection and recovery, joint power- and network-aware simulations and more. Though CloudSim itself does not have a graphical user interface, extensions such as CloudReports offer a GUI for CloudSim simulations. CloudSimEx extends CloudSim by adding MapReduce simulation capabilities and parallel simulations. Cloud2Sim extends CloudSim to execute on multiple distributed servers, by leveraging Hazelcast distributed execution framework. RECAP DES extends the CloudSim Plus framework to model synchronous hierarchical architectures (such as ElasticSearch). ThermoSim extends CloudSim toolkit by incorporating thermal characteristics, and uses Deep learning-based temperature predictor for cloud nodes.

Bayesian programming

Bayesian programming is a formalism and a methodology for having a technique to specify probabilistic models and solve problems when less than the necessary information is available. Edwin T. Jaynes proposed that probability could be considered as an alternative and an extension of logic for rational reasoning with incomplete and uncertain information. In his founding book Probability Theory: The Logic of Science he developed this theory and proposed what he called "the robot," which was not a physical device, but an inference engine to automate probabilistic reasoning—a kind of Prolog for probability instead of logic. Bayesian programming is a formal and concrete implementation of this "robot". Bayesian programming may also be seen as an algebraic formalism to specify graphical models such as, for instance, Bayesian networks, dynamic Bayesian networks, Kalman filters or hidden Markov models. Indeed, Bayesian programming is more general than Bayesian networks and has a power of expression equivalent to probabilistic factor graphs. == Formalism == A Bayesian program is a means of specifying a family of probability distributions. The constituent elements of a Bayesian program are presented below: Program { Description { Specification ( π ) { Variables Decomposition Forms Identification (based on δ ) Question {\displaystyle {\text{Program}}{\begin{cases}{\text{Description}}{\begin{cases}{\text{Specification}}(\pi ){\begin{cases}{\text{Variables}}\\{\text{Decomposition}}\\{\text{Forms}}\\\end{cases}}\\{\text{Identification (based on }}\delta )\end{cases}}\\{\text{Question}}\end{cases}}} A program is constructed from a description and a question. A description is constructed using some specification ( π {\displaystyle \pi } ) as given by the programmer and an identification or learning process for the parameters not completely specified by the specification, using a data set ( δ {\displaystyle \delta } ). A specification is constructed from a set of pertinent variables, a decomposition and a set of forms. Forms are either parametric forms or questions to other Bayesian programs. A question specifies which probability distribution has to be computed. === Description === The purpose of a description is to specify an effective method of computing a joint probability distribution on a set of variables { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} given a set of experimental data δ {\displaystyle \delta } and some specification π {\displaystyle \pi } . This joint distribution is denoted as: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} . To specify preliminary knowledge π {\displaystyle \pi } , the programmer must undertake the following: Define the set of relevant variables { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} on which the joint distribution is defined. Decompose the joint distribution (break it into relevant independent or conditional probabilities). Define the forms of each of the distributions (e.g., for each variable, one of the list of probability distributions). ==== Decomposition ==== Given a partition of { X 1 , X 2 , … , X N } {\displaystyle \left\{X_{1},X_{2},\ldots ,X_{N}\right\}} containing K {\displaystyle K} subsets, K {\displaystyle K} variables are defined L 1 , ⋯ , L K {\displaystyle L_{1},\cdots ,L_{K}} , each corresponding to one of these subsets. Each variable L k {\displaystyle L_{k}} is obtained as the conjunction of the variables { X k 1 , X k 2 , ⋯ } {\displaystyle \left\{X_{k_{1}},X_{k_{2}},\cdots \right\}} belonging to the k t h {\displaystyle k^{th}} subset. Recursive application of Bayes' theorem leads to: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) = P ( L 1 ∧ ⋯ ∧ L K ∣ δ ∧ π ) = P ( L 1 ∣ δ ∧ π ) × P ( L 2 ∣ L 1 ∧ δ ∧ π ) × ⋯ × P ( L K ∣ L K − 1 ∧ ⋯ ∧ L 1 ∧ δ ∧ π ) {\displaystyle {\begin{aligned}&P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\wedge \cdots \wedge L_{K}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\mid \delta \wedge \pi \right)\times P\left(L_{2}\mid L_{1}\wedge \delta \wedge \pi \right)\times \cdots \times P\left(L_{K}\mid L_{K-1}\wedge \cdots \wedge L_{1}\wedge \delta \wedge \pi \right)\end{aligned}}} Conditional independence hypotheses then allow further simplifications. A conditional independence hypothesis for variable L k {\displaystyle L_{k}} is defined by choosing some variable X n {\displaystyle X_{n}} among the variables appearing in the conjunction L k − 1 ∧ ⋯ ∧ L 2 ∧ L 1 {\displaystyle L_{k-1}\wedge \cdots \wedge L_{2}\wedge L_{1}} , labelling R k {\displaystyle R_{k}} as the conjunction of these chosen variables and setting: P ( L k ∣ L k − 1 ∧ ⋯ ∧ L 1 ∧ δ ∧ π ) = P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid L_{k-1}\wedge \cdots \wedge L_{1}\wedge \delta \wedge \pi \right)=P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} We then obtain: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) = P ( L 1 ∣ δ ∧ π ) × P ( L 2 ∣ R 2 ∧ δ ∧ π ) × ⋯ × P ( L K ∣ R K ∧ δ ∧ π ) {\displaystyle {\begin{aligned}&P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\mid \delta \wedge \pi \right)\times P\left(L_{2}\mid R_{2}\wedge \delta \wedge \pi \right)\times \cdots \times P\left(L_{K}\mid R_{K}\wedge \delta \wedge \pi \right)\end{aligned}}} Such a simplification of the joint distribution as a product of simpler distributions is called a decomposition, derived using the chain rule. This ensures that each variable appears at the most once on the left of a conditioning bar, which is the necessary and sufficient condition to write mathematically valid decompositions. ==== Forms ==== Each distribution P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} appearing in the product is then associated with either a parametric form (i.e., a function f μ ( L k ) {\displaystyle f_{\mu }\left(L_{k}\right)} ) or a question to another Bayesian program P ( L k ∣ R k ∧ δ ∧ π ) = P ( L ∣ R ∧ δ ^ ∧ π ^ ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)=P\left(L\mid R\wedge {\widehat {\delta }}\wedge {\widehat {\pi }}\right)} . When it is a form f μ ( L k ) {\displaystyle f_{\mu }\left(L_{k}\right)} , in general, μ {\displaystyle \mu } is a vector of parameters that may depend on R k {\displaystyle R_{k}} or δ {\displaystyle \delta } or both. Learning takes place when some of these parameters are computed using the data set δ {\displaystyle \delta } . An important feature of Bayesian programming is this capacity to use questions to other Bayesian programs as components of the definition of a new Bayesian program. P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} is obtained by some inferences done by another Bayesian program defined by the specifications π ^ {\displaystyle {\widehat {\pi }}} and the data δ ^ {\displaystyle {\widehat {\delta }}} . This is similar to calling a subroutine in classical programming and provides an easy way to build hierarchical models. === Question === Given a description (i.e., P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} ), a question is obtained by partitioning { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} into three sets: the searched variables, the known variables and the free variables. The 3 variables S e a r c h e d {\displaystyle Searched} , K n o w n {\displaystyle Known} and F r e e {\displaystyle Free} are defined as the conjunction of the variables belonging to these sets. A question is defined as the set of distributions: P ( S e a r c h e d ∣ Known ∧ δ ∧ π ) {\displaystyle P\left(Searched\mid {\text{Known}}\wedge \delta \wedge \pi \right)} made of many "instantiated questions" as the cardinal of K n o w n {\displaystyle Known} , each instantiated question being the distribution: P ( Searched ∣ Known ∧ δ ∧ π ) {\displaystyle P\left({\text{Searched}}\mid {\text{Known}}\wedge \delta \wedge \pi \right)} === Inference === Given the joint distribution P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} , it is always possible to compute any possible question using the following general inference: P ( Searched ∣ Known ∧ δ ∧ π ) = ∑ Free [ P ( Searched ∧ Free ∣ Known ∧ δ ∧ π ) ] = ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] P ( Known ∣ δ ∧ π ) = ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] ∑ Free ∧ Searched [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] = 1 Z × ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] {\displaystyle {\begin{aligned}&P\left({\text{Searched}}\mid {\text{Known}}\wedge \delta \wedge \pi \right)\\={}&\sum _{\text{Free}}\left[P\left({\text{Searched}}\wedge {\text{Free}}\mid {\text{Known}}\wedge \delta \wedge \

H2O (software)

H2O is an open-source, in-memory, distributed machine learning and predictive analytics platform developed by the company H2O.ai (previously 0xdata). The software uses a distributed architecture for parallel processing on standard hardware. It supports algorithms for large-scale data analysis and model deployment. H2O is primarily used by data scientists and developers for statistical modeling and data-driven decision-making. The platform is designed to handle in-memory computations across a distributed computing environment. It offers implementations for numerous statistical and machine learning algorithms, which are accessible through various programming interfaces. The software is released under the Apache License 2.0. == Functionality and features == H2O provides a suite of supervised and unsupervised machine learning algorithms. Its core functions include: Supervised learning: algorithms in the field of statistics, data mining and machine learning such as generalized linear models, random forests, gradient boosting and deep learning are implemented for classification and regression tasks. Unsupervised learning: including K-Means clustering and principal component analysis. Automated machine learning: a features designed to automate the processes of model selection, tuning, and ensemble creation. The software can ingest data from various sources, including the Hadoop Distributed File System, Amazon S3, SQL databases, as well as local file systems. It operates natively on Apache Spark clusters through Sparkling Water. Proponents claim that improved performance is achieved compared to other analysis tools. The software is distributed free of charge, under a business model based on the development of individual applications and support. == Architecture == H2O is primarily written in Java. It uses a distributed architecture that allows the platform to cluster nodes for parallel processing and in-memory storage of data and models. Users interact with the H2O platform through several primary interfaces: Programming language interfaces: APIs are provided for the R and Python programming languages, and various Apache offerings (Apache Hadoop and Spark, as well as Maven). H2O Flow: a graphical web-based interactive computational environment that functions as a notebook interface for data exploration, model building, and scripting. REST-API: allows for integration with other applications and frameworks such as Microsoft Excel or RStudio. With the H2O Machine Learning Integration Nodes, KNIME offers algorithmic workflows. While the algorithm executes, approximate results are displayed, so that users can track the progress and intervene if needed. == History, influences, and extensions == The software project was initiated by the company 0xdata, which later changed its name to H2O.ai. The three Stanford professors Stephen P. Boyd, Robert Tibshirani and Trevor Hastie form a panel that advises H2O on scientific issues. Since its inception, H2O provides open-source machine learning libraries for enterprise use. The core H2O platform is often complemented by offerings from H2O.ai, such as H2O Driverless AI. == Reception == H2O is referenced in peer-reviewed literature regarding automated machine learning (AutoML). The platform has been categorized as a "Leader" and a "Strong Performer" in industry reports by Forrester Research. H2O (the open-source platform) and the associated commercial platform Driverless AI have been recurring winners of InfoWorld's most prestigious awards, including both the Best of Open Source Software ("Bossies") and the Technology of the Year awards.

Confusion matrix

In machine learning, a confusion matrix, also known as error matrix, is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one. In unsupervised learning it is usually called a matching matrix. The term is used specifically in the problem of statistical classification. Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class, or vice versa – both variants are found in the literature. The diagonal of the matrix therefore represents all instances that are correctly predicted. The name stems from the fact that it makes it easy to identify whether the system is confusing two classes (i.e., commonly mislabeling one class as another). The confusion matrix has its origins in human perceptual studies of auditory stimuli. It was adapted for machine learning studies and used by Frank Rosenblatt, among other early researchers, to compare human and machine classifications of visual (and later auditory) stimuli. It is a special kind of contingency table, with two dimensions ("actual" and "predicted"), and identical sets of "classes" in both dimensions (each combination of dimension and class is a variable in the contingency table). == Example == Given a sample of 12 individuals, 8 that have been diagnosed with cancer and 4 that are cancer-free, where individuals with cancer belong to class 1 (positive) and non-cancer individuals belong to class 0 (negative), we can display that data as follows: Assume that we have a classifier that distinguishes between individuals with and without cancer in some way, we can take the 12 individuals and run them through the classifier. The classifier then makes 9 accurate predictions and misses 3: 2 individuals with cancer wrongly predicted as being cancer-free (sample 1 and 2), and 1 person without cancer that is wrongly predicted to have cancer (sample 9). Notice, that if we compare the actual classification set to the predicted classification set, there are 4 different outcomes that could result in any particular column: The actual classification is positive and the predicted classification is positive (1,1). This is called a true positive result because the positive sample was correctly identified by the classifier. The actual classification is positive and the predicted classification is negative (1,0). This is called a false negative result because the positive sample is incorrectly identified by the classifier as being negative. The actual classification is negative and the predicted classification is positive (0,1). This is called a false positive result because the negative sample is incorrectly identified by the classifier as being positive. The actual classification is negative and the predicted classification is negative (0,0). This is called a true negative result because the negative sample gets correctly identified by the classifier. We can then perform the comparison between actual and predicted classifications and add this information to the table, making correct results appear in green so they are more easily identifiable. The template for any binary confusion matrix uses the four kinds of results discussed above (true positives, false negatives, false positives, and true negatives) along with the positive and negative classifications. The four outcomes can be formulated in a 2×2 confusion matrix, as follows: The color convention of the three data tables above were picked to match this confusion matrix, in order to easily differentiate the data. Now, we can simply total up each type of result, substitute into the template, and create a confusion matrix that will concisely summarize the results of testing the classifier: In this confusion matrix, of the 8 samples with cancer, the system judged that 2 were cancer-free, and of the 4 samples without cancer, it predicted that 1 did have cancer. All correct predictions are located in the diagonal of the table (highlighted in green), so it is easy to visually inspect the table for prediction errors, as values outside the diagonal will represent them. By summing up the 2 rows of the confusion matrix, one can also deduce the total number of positive (P) and negative (N) samples in the original dataset, i.e. P = T P + F N {\displaystyle P=TP+FN} and N = F P + T N {\displaystyle N=FP+TN} . == Table of confusion == In predictive analytics, a table of confusion (sometimes also called a confusion matrix) is a table with two rows and two columns that reports the number of true positives, false negatives, false positives, and true negatives. This allows more detailed analysis than simply observing the proportion of correct classifications (accuracy). Accuracy will yield misleading results if the data set is unbalanced; that is, when the numbers of observations in different classes vary greatly. For example, if there were 95 cancer samples and only 5 non-cancer samples in the data, a particular classifier might classify all the observations as having cancer. The overall accuracy would be 95%, but in more detail the classifier would have a 100% recognition rate (sensitivity) for the cancer class but a 0% recognition rate for the non-cancer class. F1 score is even more unreliable in such cases, and here would yield over 97.4%, whereas informedness removes such bias and yields 0 as the probability of an informed decision for any form of guessing (here always guessing cancer). According to Davide Chicco and Giuseppe Jurman, the most informative metric to evaluate a confusion matrix is the Matthews correlation coefficient (MCC). Other metrics can be included in a confusion matrix, each of them having their significance and use. Some researchers have argued that the confusion matrix, and the metrics derived from it, do not truly reflect a model's knowledge. In particular, the confusion matrix cannot show whether correct predictions were reached through sound reasoning or merely by chance (a problem known in philosophy as epistemic luck). It also does not capture situations where the facts used to make a prediction later change or turn out to be wrong (defeasibility). This means that while the confusion matrix is a useful tool for measuring classification performance, it may give an incomplete picture of a model’s true reliability. == Confusion matrices with more than two categories == Confusion matrix is not limited to binary classification and can be used in multi-class classifiers as well. The confusion matrices discussed above have only two conditions: positive and negative. For example, the table below summarizes communication of a whistled language between two speakers, with zero values omitted for clarity. == Confusion matrices in multi-label and soft-label classification == Confusion matrices are not limited to single-label classification (where only one class is present) or hard-label settings (where classes are either fully present, 1, or absent, 0). They can also be extended to Multi-label classification (where multiple classes can be predicted at once) and soft-label classification (where classes can be partially present). One such extension is the Transport-based Confusion Matrix (TCM), which builds on the theory of optimal transport and the principle of maximum entropy. TCM applies to single-label, multi-label, and soft-label settings. It retains the familiar structure of the standard confusion matrix: a square matrix sized by the number of classes, with diagonal entries indicating correct predictions and off-diagonal entries indicating confusion. In the single-label case, TCM is identical to the standard confusion matrix. TCM follows the same reasoning as the standard confusion matrix: if class A is overestimated (its predicted value is greater than its label value) and class B is underestimated (its predicted value is less than its label value), A is considered confused with B, and the entry (B, A) is increased. If a class is both predicted and present, it is correctly identified, and the diagonal entry (A, A) increases. Optimal transport and maximum entropy are used to determine the extent to which these entries are updated. TCM enables clearer comparison between predictions and labels in complex classification tasks, while maintaining a consistent matrix format across settings.

Computational intelligence

In computer science, computational intelligence (CI) refers to concepts, paradigms, algorithms and implementations of systems that are designed to show "intelligent" behavior in complex and changing environments. These systems are aimed at mastering complex tasks in a wide variety of technical or commercial areas and offer solutions that recognize and interpret patterns, control processes, support decision-making or autonomously manoeuvre vehicles or robots in unknown environments, among other things. These concepts and paradigms are characterized by the ability to learn or adapt to new situations, to generalize, to abstract, to discover and associate. Nature-analog or nature-inspired methods play a key role in this. CI approaches primarily address those complex real-world problems for which traditional or mathematical modeling is not appropriate for various reasons: the processes cannot be described exactly with complete knowledge, the processes are too complex for mathematical reasoning, they contain some uncertainties during the process, such as unforeseen changes in the environment or in the process itself, or the processes are simply stochastic in nature. Thus, CI techniques are properly aimed at processes that are ill-defined, complex, nonlinear, time-varying and/or stochastic. A recent definition of the IEEE Computational Intelligence Societey describes CI as the theory, design, application and development of biologically and linguistically motivated computational paradigms. Traditionally the three main pillars of CI have been Neural Networks, Fuzzy Systems and Evolutionary Computation. ... CI is an evolving field and at present in addition to the three main constituents, it encompasses computing paradigms like ambient intelligence, artificial life, cultural learning, artificial endocrine networks, social reasoning, and artificial hormone networks. ... Over the last few years there has been an explosion of research on Deep Learning, in particular deep convolutional neural networks. Nowadays, deep learning has become the core method for artificial intelligence. In fact, some of the most successful AI systems are based on CI. However, as CI is an emerging and developing field there is no final definition of CI, especially in terms of the list of concepts and paradigms that belong to it. The general requirements for the development of an “intelligent system” are ultimately always the same, namely the simulation of intelligent thinking and action in a specific area of application. To do this, the knowledge about this area must be represented in a model so that it can be processed. The quality of the resulting system depends largely on how well the model was chosen in the development process. Sometimes data-driven methods are suitable for finding a good model and sometimes logic-based knowledge representations deliver better results. Hybrid models are usually used in real applications. According to actual textbooks, the following methods and paradigms, which largely complement each other, can be regarded as parts of CI: Fuzzy systems Neural networks and, in particular, convolutional neural networks Evolutionary computation and, in particular, multi-objective evolutionary optimization Swarm intelligence Bayesian networks Artificial immune systems Learning theory Probabilistic methods == Relationship between hard and soft computing and artificial and computational intelligence == Artificial intelligence (AI) is used in the media, but also by some of the scientists involved, as a kind of umbrella term for the various techniques associated with it or with CI. Craenen and Eiben state that attempts to define or at least describe CI can usually be assigned to one or more of the following groups: "Relative definition” comparing CI to AI Conceptual treatment of key notions and their roles in CI Listing of the (established) areas that belong to it The relationship between CI and AI has been a frequently discussed topic during the development of CI. While the above list implies that they are synonyms, the vast majority of AI/CI researchers working on the subject consider them to be distinct fields, where either CI is an alternative to AI AI includes CI CI includes AI The view of the first of the above three points goes back to Zadeh, the founder of the fuzzy set theory, who differentiated machine intelligence into hard and soft computing techniques, which are used in artificial intelligence on the one hand and computational intelligence on the other. In hard computing (HC) and traditional AI (e.g. expert systems), inaccuracy and uncertainty are undesirable characteristics of a system, while soft computing (SC) and thus CI focus on dealing with these characteristics. The adjacent figure illustrates this view and lists the most important CI techniques. Another frequently mentioned distinguishing feature is the representation of information in symbolic form in AI and in sub-symbolic form in CI techniques. Hard computing is a conventional computing method based on the principles of certainty and accuracy and it is deterministic. It requires a precisely stated analytical model of the task to be processed and a prewritten program, i.e. a fixed set of instructions. The models used are based on Boolean logic (also called crisp logic), where e.g. an element can be either a member of a set or not and there is nothing in between. When applied to real-world tasks, systems based on HC result in specific control actions defined by a mathematical model or algorithm. If an unforeseen situation occurs that is not included in the model or algorithm used, the action will most likely fail. Soft computing, on the other hand, is based on the fact that the human mind is capable of storing information and processing it in a goal-oriented way, even if it is imprecise and lacks certainty. SC is based on the model of the human brain with probabilistic thinking, fuzzy logic and multi-valued logic. Soft computing can process a wealth of data and perform a large number of computations, which may not be exact, in parallel. For hard problems for which no satisfying exact solutions based on HC are available, SC methods can be applied successfully. SC methods are usually stochastic in nature i.e., they are a randomly defined processes that can be analyzed statistically but not with precision. Up to now, the results of some CI methods, such as deep learning, cannot be verified and it is also not clear what they are based on. This problem represents an important scientific issue for the future. AI and CI are catchy terms, but they are also so similar that they can be confused. The meaning of both terms has developed and changed over a long period of time, with AI being used first. Bezdek describes this impressively and concludes that such buzzwords are frequently used and hyped by the scientific community, science management and (science) journalism. Not least because AI and biological intelligence are emotionally charged terms and it is still difficult to find a generally accepted definition for the basic term intelligence. == History == In 1950, Alan Turing, one of the founding fathers of computer science, developed a test for computer intelligence known as the Turing test. In this test, a person can ask questions via a keyboard and a monitor without knowing whether his counterpart is a human or a computer. A computer is considered intelligent if the interrogator cannot distinguish the computer from a human. This illustrates the discussion about intelligent computers at the beginning of the computer age. The term Computational Intelligence was first used as the title of the journal of the same name in 1985 and later by the IEEE Neural Networks Council (NNC), which was founded 1989 by a group of researchers interested in the development of biological and artificial neural networks. On November 21, 2001, the NNC became the IEEE Neural Networks Society, to become the IEEE Computational Intelligence Society two years later by including new areas of interest such as fuzzy systems and evolutionary computation. The NNC helped organize the first IEEE World Congress on Computational Intelligence in Orlando, Florida in 1994. On this conference the first clear definition of Computational Intelligence was introduced by Bezdek: A system is computationally intelligent when it: deals with only numerical (low-level) data, has pattern-recognition components, does not use knowledge in the AI sense; and additionally when it (begins to) exhibit (1) computational adaptivity; (2) computational fault tolerance; (3) speed approaching human-like turnaround and (4) error rates that approximate human performance. Today, with machine learning and deep learning in particular utilizing a breadth of supervised, unsupervised, and reinforcement learning approaches, the CI landscape has been greatly enhanced, with novell intelligent approaches. == The main algorithmic approaches of CI and their applicati

AI literacy

AI literacy or artificial intelligence literacy is "a set of competencies that enables individuals to critically evaluate AI technologies; communicate and collaborate effectively with AI; and use AI as a tool online, at home, and in the workplace." AI is employed in a variety of applications, including self-driving automobiles, virtual assistants and text generation by generative AI models. Users of these tools should be able to make informed decisions. AI literacy may have an impact on students' future employment prospects. With the rise of generative AI platforms, AI literacy has become a topic of conversation in the field of education. Some think AI literacy is essential for school and college students, while others restrict or prohibit the use of AI in assignments, viewing it as a form of academic dishonesty. However, many researchers and educational institutions promote a more nuanced approach, encouraging critical engagement with AI while developing policies that balance academic integrity with opportunities for learning. == Definitions == Other definitions of AI literacy include the ability to understand, use, monitor, and critically reflect on AI applications. That use of the term usually refers to teaching skills and knowledge to the general public, particularly those who are not adept in AI and the ability to understand, use, evaluate, and ethically navigate AI. As research into AI literacy is still emerging and focused on developing context-specific skills, there is not yet a single, broadly agreed-upon definition. AI literacy is linked to other forms of literacy. AI literacy requires digital literacy, whereas scientific and computational literacy may inform it. Data literacy also significantly overlaps with it. == Categories == AI literacy encompasses multiple categories, including a theoretical understanding of how artificial intelligence works, the usage of artificial intelligence technologies, and the critical appraisal of artificial intelligence, and its ethics. === Know and understand AI === Knowledge and understanding of AI refers to a basic understanding of what artificial intelligence is and how it works. This includes familiarity with machine learning algorithms and the limitations and biases present in AI systems. Users who know and understand AI should be familiar with various technologies that use artificial intelligence, including cognitive systems, robotics and machine learning. This includes recognizing that large language models (LLMs) are machine learning models trained on extensive datasets which generate new text rather than retrieving pre-written responses. === Use and apply AI === Using and applying AI refers to the ability to use AI tools to solve problems and perform tasks such as programming and analyzing big data. Some consider prompt engineering, the practice of designing effective prompts to guide generative AI platforms more effectively, as another competency within AI literacy. === Evaluate and create AI === Evaluation and creation refers to the ability to critically evaluate the quality and reliability of AI systems. It also refers to designing and building fair and ethical AI systems. To evaluate correctly, users should also learn in which areas AI is strong, and in which areas it is weak. === AI ethics === AI ethics refers to understanding the moral implications of AI, and the making informed decisions regarding the use of AI tools. This area includes considerations such as: Accountability: Hold AI actors accountable for the operation of AI systems and adherence to ethical ideals. Accuracy: Identify and report sources of error and uncertainty in algorithms and data. Auditability: Enable other parties to audit and assess algorithm behavior via transparent information sharing. Explainability: Make sure that algorithmic judgments and the underlying data can be presented in simple language. Fairness: Prevent biases and consider varied viewpoints. To do so, increase the diversity of researchers in the field. Human Centricity and Well-being: Prioritize human well-being in AI development and deployment. Human rights Alignment: Ensure that technology do not infringe internationally recognized human rights. Inclusivity: Make AI accessible to everyone. Progress: Choose high value initiatives. Responsibility, accountability, and transparency: Foster trust via responsibility, accountability, and fairness. Robustness and Security: Make AI systems safe, secure, and resistant to manipulation or data breach. Sustainability: Choose implementations that generate long-term, useful benefits. Environmental Implications: How this tool impacts the environment, any restrictions or laws, if this impact is worth the effects or not. === Enabling AI === Support AI by developing associated knowledge and skills such as programming and statistics. == Promoting AI literacy == Several governments have recognized the need to promote AI literacy, including among adults. Such programs have been published in the United States, China, Germany and Finland. Programs intended for the general public usually consist of short and easy to understand online study units. Programs intended for children are usually project-based. Programs for students at colleges and universities often address the specific professional needs of the student, depending on their field of study. Beyond the education system, AI literacy can also be developed in the community, for example in museums. === Schools === Schools use diverse pedagogies to promote AI literacy. These include: Performing a Turing test with an intelligent agent Creating chatbots Building apps using Blockly-based programming Project-based learning Building robots Data visualization Training AI models Artificial intelligence curricula can improve students' understanding of topics such as machine learning, neural networks, and deep learning. === Higher education === Before the second decade of the 21st century, artificial intelligence was studied mainly in STEM courses. Later, projects emerged to increase artificial intelligence education, specifically to promote AI literacy. Most courses start with one or more study units that deal with basic questions such as what artificial intelligence is, where it comes from, what it can do and what it can't do. Most courses also refer to machine learning and deep learning. Some of the courses deal with moral issues in artificial intelligence. In Ireland, the Higher Education Authority published Generative AI in Higher Education Teaching & Learning: Policy Framework in December 2025, which encouraged higher education institutions to embed AI literacy across programmes as a core graduate attribute. ==== Disciplinary policy ==== As a response to the increase of generative AI use in education, several disciplines formed committees or task forces to examine context-specific approaches toward AI literacy. In spring 2025, the Modern Language Association and Conference on College Composition and Communication Joint Task Force finished development of three working papers, a guide on AI literacy for students, and a collection of resources addressing AI use in writing. The task force emphasized the need for "a culture of critical AI literacy" and included guidelines not only for students but also educators and institutions, highlighting the need for modeling ethical AI use in planning processes. Similarly, a committee formed by the American Historical Association Council published "Guiding Principles for Artificial Intelligence in History Education" which encouraged "clear and transparent engagement with generative AI." The guidelines demonstrate the value of criticality when working with generative AI in thinking and research.