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Double descentinstatisticsandmachine learningis the phenomenon where amodelwith a small number ofparametersand a model with an extremely large number of parameters both have a smalltraining error, but a model whose number of parameters is about the same as the number ofdata pointsused to train the model will have a muc... | https://en.wikipedia.org/wiki/Double_descent |
Instatistics, theGauss–Markov theorem(or simplyGauss theoremfor some authors)[1]states that theordinary least squares(OLS) estimator has the lowestsampling variancewithin theclassoflinearunbiasedestimators, if theerrorsin thelinear regression modelareuncorrelated, haveequal variancesand expectation value of zero.[2]The... | https://en.wikipedia.org/wiki/Gauss%E2%80%93Markov_theorem |
Inmachine learning,hyperparameter optimization[1]or tuning is the problem of choosing a set of optimalhyperparametersfor a learning algorithm. A hyperparameter is aparameterwhose value is used to control the learning process, which must be configured before the process starts.[2][3]
Hyperparameter optimization determi... | https://en.wikipedia.org/wiki/Hyperparameter_optimization |
The law of total varianceis a fundamental result inprobability theorythat expresses the variance of a random variableYin terms of its conditional variances and conditional means given another random variableX. Informally, it states that the overall variability ofYcan be split into an “unexplained” component (the averag... | https://en.wikipedia.org/wiki/Law_of_total_variance |
Instatisticsaminimum-variance unbiased estimator (MVUE)oruniformly minimum-variance unbiased estimator (UMVUE)is anunbiased estimatorthat has lower variance than any other unbiased estimator for all possible values of the parameter.
For practical statistics problems, it is important to determine the MVUE if one exists... | https://en.wikipedia.org/wiki/Minimum-variance_unbiased_estimator |
Model selectionis the task of selecting amodelfrom among various candidates on the basis of performance criterion to choose the best one.[1]In the context ofmachine learningand more generallystatistical analysis, this may be the selection of astatistical modelfrom a set of candidate models, given data. In the simplest ... | https://en.wikipedia.org/wiki/Model_selection |
Instatistics,regression validationis the process of deciding whether the numerical results quantifying hypothesized relationships between variables, obtained fromregression analysis, are acceptable as descriptions of the data. The validation process can involve analyzing thegoodness of fitof the regression, analyzing w... | https://en.wikipedia.org/wiki/Regression_model_validation |
Inestimation theoryandstatistics, theCramér–Rao bound(CRB) relates toestimationof a deterministic (fixed, though unknown) parameter. The result is named in honor ofHarald CramérandCalyampudi Radhakrishna Rao,[1][2][3]but has also been derived independently byMaurice Fréchet,[4]Georges Darmois,[5]and byAlexander Aitken... | https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Rao_bound |
Instatistical inference, specificallypredictive inference, aprediction intervalis an estimate of anintervalin which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used inregression analysis.
A simple example is given by a six-sided die w... | https://en.wikipedia.org/wiki/Prediction_interval |
Instochastic game theory,Bayesian regretis the expected difference ("regret") between theutilityof a given strategy and the utility of the best possible strategy in hindsight—i.e., the strategy that would have maximized expected payoff if the true underlying model or distribution were known. This notion of regret measu... | https://en.wikipedia.org/wiki/Bayesian_regret |
Inmachine learningandmathematical optimization,loss functions for classificationare computationally feasibleloss functionsrepresenting the price paid for inaccuracy of predictions inclassification problems(problems of identifying which category a particular observation belongs to).[1]GivenX{\displaystyle {\mathcal {X}}... | https://en.wikipedia.org/wiki/Loss_functions_for_classification |
Discounted maximum loss, also known asworst-caserisk measure, is thepresent valueof the worst-case scenario for a financialportfolio.
In investment, in order to protect the value of an investment, one must consider all possible alternatives to the initial investment. How one does this comes down to personal preference... | https://en.wikipedia.org/wiki/Discounted_maximum_loss |
Statistical riskis aquantificationof a situation'sriskusingstatistical methods. These methods can be used to estimate aprobability distributionfor the outcome of a specificvariable, or at least one or more keyparametersof that distribution, and from that estimated distribution arisk functioncan be used to obtain a sing... | https://en.wikipedia.org/wiki/Statistical_risk |
Crossoverinevolutionary algorithmsandevolutionary computation, also calledrecombination, is agenetic operatorused to combine thegenetic informationof two parents to generate new offspring. It is one way tostochasticallygenerate newsolutionsfrom an existing population, and is analogous to thecrossoverthat happens during... | https://en.wikipedia.org/wiki/Crossover_(genetic_algorithm) |
Domain adaptationis a field associated withmachine learningandtransfer learning. It addresses the challenge of training a model on one data distribution (thesource domain) and applying it to a related but different data distribution (thetarget domain).
A common example isspam filtering, where a model trained on emails... | https://en.wikipedia.org/wiki/Domain_adaptation |
General game playing(GGP) is the design ofartificial intelligenceprograms to be able to play more than one game successfully.[1][2][3]For many games like chess, computers are programmed to play these games using a specially designed algorithm, which cannot be transferred to another context. For instance, achess-playing... | https://en.wikipedia.org/wiki/General_game_playing |
Multi-task learning(MTL) is a subfield ofmachine learningin which multiple learning tasks are solved at the same time, while exploiting commonalities and differences across tasks. This can result in improved learning efficiency and prediction accuracy for the task-specific models, when compared to training the models s... | https://en.wikipedia.org/wiki/Multi-task_learning |
Multi-task learning(MTL) is a subfield ofmachine learningin which multiple learning tasks are solved at the same time, while exploiting commonalities and differences across tasks. This can result in improved learning efficiency and prediction accuracy for the task-specific models, when compared to training the models s... | https://en.wikipedia.org/wiki/Multitask_optimization |
Transfer of learningoccurs when people apply information, strategies, and skills they have learned to a new situation or context. Transfer is not a discrete activity, but is rather an integral part of the learning process. Researchers attempt to identify when and how transfer occurs and to offer strategies to improve t... | https://en.wikipedia.org/wiki/Transfer_of_learning |
Educational psychologyis the branch ofpsychologyconcerned with the scientific study of humanlearning. The study of learning processes, from bothcognitiveandbehavioralperspectives, allows researchers to understand individual differences inintelligence,cognitivedevelopment,affect,motivation, self-regulation, and self-con... | https://en.wikipedia.org/wiki/Educational_psychology |
Zero-shot learning(ZSL) is a problem setup indeep learningwhere, at test time, a learner observes samples from classes which werenotobserved duringtraining, and needs to predict the class that they belong to. The name is a play on words based on the earlier concept ofone-shot learning, in which classification can be le... | https://en.wikipedia.org/wiki/Zero-shot_learning |
External validityis the validity of applying the conclusions of a scientific study outside the context of that study.[1]In other words, it is the extent to which the results of a study can generalize or transport to other situations, people, stimuli, and times.[2][3]Generalizability refers to the applicability of a pre... | https://en.wikipedia.org/wiki/External_validity |
Attentionis amachine learningmethod that determines the importance of each component in a sequence relative to the other components in that sequence. Innatural language processing, importance is represented by"soft"weights assigned to each word in a sentence. More generally, attention encodes vectors calledtokenembeddi... | https://en.wikipedia.org/wiki/Attention_(machine_learning) |
Inmathematics(in particular,functional analysis),convolutionis amathematical operationon twofunctionsf{\displaystyle f}andg{\displaystyle g}that produces a third functionf∗g{\displaystyle f*g}, as theintegralof the product of the two functions after one is reflected about the y-axis and shifted. The termconvolutionref... | https://en.wikipedia.org/wiki/Convolution |
Natural language processing(NLP) is a subfield ofcomputer scienceand especiallyartificial intelligence. It is primarily concerned with providing computers with the ability to process data encoded innatural languageand is thus closely related toinformation retrieval,knowledge representationandcomputational linguistics, ... | https://en.wikipedia.org/wiki/Natural-language_processing |
Theneocognitronis a hierarchical, multilayeredartificial neural networkproposed byKunihiko Fukushimain 1979.[1][2]It has been used for Japanesehandwritten character recognitionand otherpattern recognitiontasks, and served as the inspiration forconvolutional neural networks.[3]
Previously in 1969, he published a simila... | https://en.wikipedia.org/wiki/Neocognitron |
Thescale-invariant feature transform(SIFT) is acomputer visionalgorithm to detect, describe, and match localfeaturesin images, invented byDavid Lowein 1999.[1]Applications includeobject recognition,robotic mappingand navigation,image stitching,3D modeling,gesture recognition,video tracking, individual identification of... | https://en.wikipedia.org/wiki/Scale-invariant_feature_transform |
Time delay neural network(TDNN)[1]is a multilayerartificial neural networkarchitecture whose purpose is to 1) classify patterns with shift-invariance, and 2) model context at each layer of the network.
Shift-invariant classification means that the classifier does not require explicit segmentation prior to classificati... | https://en.wikipedia.org/wiki/Time_delay_neural_network |
Avision processing unit(VPU) is (as of 2023) an emerging class ofmicroprocessor; it is a specific type ofAI accelerator, designed toacceleratemachine visiontasks.[1][2]
Vision processing units are distinct fromgraphics processing units(which are specialised forvideo encoding and decoding) in their suitability for runn... | https://en.wikipedia.org/wiki/Vision_processing_unit |
Inprobability theoryandstatistics, thecoefficient of variation(CV), also known as normalizedroot-mean-square deviation(NRMSD),percent RMS, andrelative standard deviation(RSD), is astandardizedmeasure ofdispersionof aprobability distributionorfrequency distribution. It is defined as the ratio of thestandard deviationσ{\... | https://en.wikipedia.org/wiki/Coefficient_of_variation |
In mathematics, theerror function(also called theGauss error function), often denoted byerf, is a functionerf:C→C{\displaystyle \mathrm {erf} :\mathbb {C} \to \mathbb {C} }defined as:[1]erfz=2π∫0ze−t2dt.{\displaystyle \operatorname {erf} z={\frac {2}{\sqrt {\pi }}}\int _{0}^{z}e^{-t^{2}}\,\mathrm {d} t.}
The integral... | https://en.wikipedia.org/wiki/Error_function |
TheMahalanobis distanceis ameasure of the distancebetween a pointP{\displaystyle P}and aprobability distributionD{\displaystyle D}, introduced byP. C. Mahalanobisin 1936.[1]The mathematical details of Mahalanobis distance first appeared in theJournal of The Asiatic Society of Bengalin 1936.[2]Mahalanobis's definition w... | https://en.wikipedia.org/wiki/Mahalanobis_distance |
TheOmega ratiois a risk-return performance measure of an investment asset, portfolio, or strategy. It was devised by Con Keating and William F. Shadwick in 2002 and is defined as the probability weighted ratio of gains versus losses for some threshold return target.[1]The ratio is an alternative for the widely usedShar... | https://en.wikipedia.org/wiki/Omega_ratio |
Astandard normal deviateis anormally distributeddeviate. It is arealizationof astandard normal random variable, defined as arandom variablewithexpected value0 andvariance1.[1]Where collections of such random variables are used, there is often an associated (possibly unstated) assumption that members of such collections... | https://en.wikipedia.org/wiki/Standard_normal_deviate |
Instatistics, astudentized residualis thedimensionless ratioresulting from the division of aresidualby anestimateof itsstandard deviation, both expressed in the sameunits. It is a form of aStudent'st-statistic, with the estimate of error varying between points.
This is an important technique in the detection ofoutlier... | https://en.wikipedia.org/wiki/Studentized_residual |
The termnormal scoreis used with two different meanings instatistics. One of them relates to creating a single value which can be treated as if it had arisen from astandard normal distribution(zero mean, unit variance). The second one relates to assigning alternative values to data points within a dataset, with the bro... | https://en.wikipedia.org/wiki/Normal_score |
Aratio distribution(also known as aquotient distribution) is aprobability distributionconstructed as the distribution of theratioofrandom variableshaving two other known distributions.
Given two (usuallyindependent) random variablesXandY, the distribution of the random variableZthat is formed as the ratioZ=X/Yis aratio... | https://en.wikipedia.org/wiki/Ratio_distribution |
Feature scalingis a method used to normalize the range of independent variables or features of data. Indata processing, it is also known asdata normalizationand is generally performed during thedata preprocessingstep.
Since the range of values of raw data varies widely, in somemachine learningalgorithms, objective fun... | https://en.wikipedia.org/wiki/Feature_scaling |
Inmachine learning, ahyperparameteris aparameterthat can be set in order to define any configurable part of amodel's learning process. Hyperparameters can be classified as either model hyperparameters (such as the topology and size of aneural network) or algorithm hyperparameters (such as thelearning rateand the batch ... | https://en.wikipedia.org/wiki/Hyperparameter_(machine_learning) |
Innumerical analysis, aquasi-Newton methodis aniterative numerical methodused either tofind zeroesor tofind local maxima and minimaof functions via an iterativerecurrence formulamuch like the one forNewton's method, except using approximations of thederivativesof the functions in place of exact derivatives. Newton's me... | https://en.wikipedia.org/wiki/Variable_metric_methods |
Automated machine learning(AutoML) is the process ofautomatingthe tasks of applyingmachine learningto real-world problems. It is the combination of automation and ML.[1]
AutoML potentially includes every stage from beginning with a raw dataset to building a machine learning model ready for deployment. AutoML was propo... | https://en.wikipedia.org/wiki/AutoML |
Incontrol theoryaself-tuningsystem is capable of optimizing its own internal running parameters in order to maximize or minimize the fulfilment of anobjective function; typically the maximization ofefficiencyorerrorminimization.
Self-tuning and auto-tuning often refer to the same concept. Many software research group... | https://en.wikipedia.org/wiki/Self-tuning |
Inmachine learning, thevanishing gradient problemis the problem of greatly diverginggradientmagnitudes between earlier and later layers encountered when trainingneural networkswithbackpropagation. In such methods, neural network weights are updated proportional to theirpartial derivativeof theloss function.[1]As the nu... | https://en.wikipedia.org/wiki/Vanishing_gradient_problem |
Artificial intelligence(AI) has been used in applications throughout industry and academia. In a manner analogous to electricity or computers, AI serves as ageneral-purpose technology. AI programs are designed to simulate human perception and understanding. These systems are capable of adapting to new information and r... | https://en.wikipedia.org/wiki/Applications_of_artificial_intelligence |
The following tables compare notablesoftware frameworks,libraries, andcomputer programsfordeep learningapplications.
[further explanation needed] | https://en.wikipedia.org/wiki/Comparison_of_deep_learning_software |
Compressed sensing(also known ascompressive sensing,compressive sampling, orsparse sampling) is asignal processingtechnique for efficiently acquiring and reconstructing asignalby finding solutions tounderdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can b... | https://en.wikipedia.org/wiki/Compressed_sensing |
Anecho state network(ESN)[1][2]is a type ofreservoir computerthat uses arecurrent neural networkwith a sparsely connected hidden layer (with typically 1% connectivity). The connectivity and weights of hiddenneuronsare fixed and randomly assigned. The weights of output neurons can be learned so that the network can prod... | https://en.wikipedia.org/wiki/Echo_state_network |
The following is a list of current and past, non-classified notableartificial intelligenceprojects. | https://en.wikipedia.org/wiki/List_of_artificial_intelligence_projects |
Aliquid state machine(LSM) is a type ofreservoir computerthat uses aspiking neural network. An LSM consists of a large collection of units (callednodes, orneurons). Each node receives time varying input from external sources (theinputs) as well as from other nodes. Nodes arerandomly connectedto each other. Therecurrent... | https://en.wikipedia.org/wiki/Liquid_state_machine |
Reservoir computingis a framework for computation derived fromrecurrent neural networktheory that maps input signals into higher dimensional computational spaces through the dynamics of a fixed, non-linear system called a reservoir.[1]After the input signal is fed into the reservoir, which is treated as a "black box," ... | https://en.wikipedia.org/wiki/Reservoir_computing |
Scale-spacetheory is a framework formulti-scalesignalrepresentationdeveloped by thecomputer vision,image processingandsignal processingcommunities with complementary motivations fromphysicsandbiological vision. It is a formal theory for handling image structures at differentscales, by representing an image as a one-par... | https://en.wikipedia.org/wiki/Scale_space#Deep_learning_and_scale_space |
Neural coding(orneural representation) is aneurosciencefield concerned with characterising the hypothetical relationship between thestimulusand the neuronal responses, and the relationship among theelectrical activitiesof the neurons in theensemble.[1][2]Based on the theory that
sensory and other information is represe... | https://en.wikipedia.org/wiki/Sparse_coding |
Inmachine learning, the termstochastic parrotis a metaphor to describe the claim thatlarge language models, though able to generate plausible language, do not understand the meaning of the language they process.[1][2]The term was coined byEmily M. Bender[2][3]in the 2021artificial intelligenceresearch paper "On the Dan... | https://en.wikipedia.org/wiki/Stochastic_parrot |
Topological deep learning (TDL)[1][2][3][4][5][6]is a research field that extendsdeep learningto handle complex,non-Euclideandata structures. Traditional deep learning models, such asconvolutional neural networks(CNNs) andrecurrent neural networks(RNNs), excel in processing data on regular grids and sequences. However,... | https://en.wikipedia.org/wiki/Topological_deep_learning |
Instatistics,Hodges' estimator[1](or theHodges–Le Cam estimator[2]), named forJoseph Hodges, is a famouscounterexampleof anestimatorwhich is "superefficient",[3]i.e. it attains smaller asymptotic variance than regularefficient estimators. The existence of such a counterexample is the reason for the introduction of the ... | https://en.wikipedia.org/wiki/Hodges%27_estimator |
TheJames–Stein estimatoris anestimatorof themeanθ:=(θ1,θ2,…θm){\displaystyle {\boldsymbol {\theta }}:=(\theta _{1},\theta _{2},\dots \theta _{m})}for a multivariaterandom variableY:=(Y1,Y2,…Ym){\displaystyle {\boldsymbol {Y}}:=(Y_{1},Y_{2},\dots Y_{m})}.
It arose sequentially in two main published papers. The earlier ... | https://en.wikipedia.org/wiki/James%E2%80%93Stein_estimator |
Instatistics, themean percentage error (MPE)is the computed average of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast.
The formula for the mean percentage error is:
whereat{\textstyle a_{t}}is the actual value of the quantity being forecast,ft{\textstyle f_{t}... | https://en.wikipedia.org/wiki/Mean_percentage_error |
Mean square quantization error(MSQE) is afigure of meritfor the process ofanalog to digital conversion.
In this conversion process, analog signals in acontinuous rangeof values are converted to a discrete set of values by comparing them with a sequence of thresholds.
The quantization error of a signal is the differenc... | https://en.wikipedia.org/wiki/Mean_square_quantization_error |
Instatistics, thereduced chi-square statisticis used extensively ingoodness of fittesting. It is also known asmean squared weighted deviation(MSWD) inisotopic dating[1]andvariance of unit weightin the context ofweighted least squares.[2][3]
Its square root is calledregression standard error,[4]standard error of the re... | https://en.wikipedia.org/wiki/Reduced_chi-squared_statistic |
Instatistical mechanics, themean squared displacement(MSD), also calledmean square displacement,average squared displacement, ormean square fluctuation, is a measure of thedeviationof thepositionof aparticlewith respect to a reference position over time. It is the most common measure of the spatial extent of randommoti... | https://en.wikipedia.org/wiki/Mean_squared_displacement |
Instatisticsthemean squared prediction error(MSPE), also known asmean squared error of the predictions, of asmoothing,curve fitting, orregressionprocedure is theexpected valueof thesquaredprediction errors(PE), thesquare differencebetween the fitted values implied by the predictive functiong^{\displaystyle {\widehat {g... | https://en.wikipedia.org/wiki/Mean_squared_prediction_error |
Instatisticsandsignal processing, aminimum mean square error(MMSE) estimator is an estimation method which minimizes themean square error(MSE), which is a common measure of estimator quality, of the fitted values of adependent variable. In theBayesiansetting, the term MMSE more specifically refers to estimation with qu... | https://en.wikipedia.org/wiki/Minimum_mean_square_error |
Peak signal-to-noise ratio(PSNR) is an engineering term for the ratio between the maximum possible power of asignaland the power of corruptingnoisethat affects the fidelity of its representation. Because many signals have a very widedynamic range, PSNR is usually expressed as alogarithmicquantity using thedecibelscale.... | https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio |
Bayesian interpretation of kernel regularizationexamines howkernel methodsinmachine learningcan be understood through the lens ofBayesian statistics, a framework that uses probability to model uncertainty. Kernel methods are founded on the concept of similarity between inputs within a structured space. While techniques... | https://en.wikipedia.org/wiki/Bayesian_interpretation_of_regularization |
In the field ofstatistical learning theory,matrix regularizationgeneralizes notions of vector regularization to cases where the object to be learned is a matrix. The purpose of regularization is to enforce conditions, for example sparsity or smoothness, that can produce stable predictive functions. For example, in the ... | https://en.wikipedia.org/wiki/Matrix_regularization |
Spectral regularizationis any of a class ofregularizationtechniques used inmachine learningto control the impact of noise and preventoverfitting. Spectral regularization can be used in a broad range of applications, from deblurring images to classifying emails into a spam folder and a non-spam folder. For instance, in ... | https://en.wikipedia.org/wiki/Regularization_by_spectral_filtering |
Regularized least squares(RLS) is a family of methods for solving theleast-squaresproblem while usingregularizationto further constrain the resulting solution.
RLS is used for two main reasons. The first comes up when the number of variables in the linear system exceeds the number of observations. In such settings, th... | https://en.wikipedia.org/wiki/Regularized_least_squares |
Inmathematical optimization, themethod of Lagrange multipliersis a strategy for finding the localmaxima and minimaof afunctionsubject toequation constraints(i.e., subject to the condition that one or moreequationshave to be satisfied exactly by the chosen values of thevariables).[1]It is named after the mathematicianJo... | https://en.wikipedia.org/wiki/Lagrange_multiplier |
Inmathematics, more specifically in the theory ofMonte Carlo methods,variance reductionis a procedure used to increase theprecisionof theestimatesobtained for a given simulation or computational effort.[1]Every output random variable from the simulation is associated with avariancewhich limits the precision of the simu... | https://en.wikipedia.org/wiki/Variance_reduction |
Innumerical analysis, thecondition numberof afunctionmeasures how much the output value of the function can change for a small change in the input argument. This is used to measure howsensitivea function is to changes or errors in the input, and how much error in the output results from an error in the input. Very freq... | https://en.wikipedia.org/wiki/Ill-conditioned_matrix |
In the theory ofvector spaces, asetofvectorsis said to belinearly independentif there exists no nontriviallinear combinationof the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to belinearly dependent. These concepts are central to the definition ofdimension.[1]
A... | https://en.wikipedia.org/wiki/Linear_independence |
Thecross-entropy(CE)methodis aMonte Carlomethod forimportance samplingandoptimization. It is applicable to bothcombinatorialandcontinuousproblems, with either a static or noisy objective.
The method approximates the optimal importance sampling estimator by repeating two phases:[1]
Reuven Rubinsteindeveloped the metho... | https://en.wikipedia.org/wiki/Cross-entropy_method |
Inmathematical statistics, theKullback–Leibler(KL)divergence(also calledrelative entropyandI-divergence[1]), denotedDKL(P∥Q){\displaystyle D_{\text{KL}}(P\parallel Q)}, is a type ofstatistical distance: a measure of how much a modelprobability distributionQis different from a true probability distributionP.[2][3]Mathem... | https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_distance |
Instatistics,maximum likelihood estimation(MLE) is a method ofestimatingtheparametersof an assumedprobability distribution, given some observed data. This is achieved bymaximizingalikelihood functionso that, under the assumedstatistical model, theobserved datais most probable. Thepointin theparameter spacethat maximize... | https://en.wikipedia.org/wiki/Maximum-likelihood_estimation |
Ininformation theory,perplexityis a measure of uncertainty in the value of a sample from a discrete probability distribution. The larger the perplexity, the less likely it is that an observer can guess the value which will be drawn from the distribution. Perplexity was originally introduced in 1977 in the context ofspe... | https://en.wikipedia.org/wiki/Perplexity |
Instatistics,multivariate adaptive regression splines(MARS) is a form ofregression analysisintroduced byJerome H. Friedmanin 1991.[1]It is anon-parametric regressiontechnique and can be seen as an extension oflinear modelsthat automatically models nonlinearities and interactions between variables.
The term "MARS" is t... | https://en.wikipedia.org/wiki/Multivariate_adaptive_regression_spline#Hinge_functions |
Incomputer science,array programmingrefers to solutions that allow the application of operations to an entire set of values at once. Such solutions are commonly used inscientificand engineering settings.
Modern programming languages that support array programming (also known asvectorormultidimensionallanguages) have b... | https://en.wikipedia.org/wiki/Array_programming |
Listed here are notable end-user computer applications intended for use withnumericalordata analysis: | https://en.wikipedia.org/wiki/List_of_numerical-analysis_software |
Theanois aPythonlibrary and optimizing compiler for manipulating and evaluating mathematical expressions, especially matrix-valued ones.[2]In Theano, computations are expressed using aNumPy-esque syntax andcompiledto run efficiently on either CPU orGPUarchitectures.
Theano is anopen sourceproject[3]primarily developed... | https://en.wikipedia.org/wiki/Theano_(software) |
Matplotlib(portmanteau ofMATLAB, plot, and library[3]) is aplottinglibraryfor thePythonprogramming languageand itsnumerical mathematicsextensionNumPy. It provides anobject-orientedAPIfor embedding plots into applications using general-purposeGUI toolkitslikeTkinter,wxPython,Qt, orGTK. There is also aprocedural"pylab" i... | https://en.wikipedia.org/wiki/Matplotlib |
Fortran(/ˈfɔːrtræn/; formerlyFORTRAN) is athird-generation,compiled,imperativeprogramming languagethat is especially suited tonumeric computationandscientific computing.
Fortran was originally developed byIBMwith a reference manual being released in 1956;[3]however, the first compilers only began to produce accurate c... | https://en.wikipedia.org/wiki/Fortran |
In computing,row-major orderandcolumn-major orderare methods for storingmultidimensional arraysin linear storage such asrandom access memory.
The difference between the orders lies in which elements of an array are contiguous in memory. In row-major order, the consecutive elements of a row reside next to each other, w... | https://en.wikipedia.org/wiki/Row-_and_column-major_order |
f2cis a program toconvertFortran 77toCcode, developed atBell Laboratories. The standalone f2c program was based on the core of the first complete Fortran 77compilerto be implemented, the "f77" program byFeldmanandWeinberger. Because the f77 compiler was itself written in C and relied on a C compiler back end to comp... | https://en.wikipedia.org/wiki/F2c |
Correspondence analysis(CA) is a multivariatestatistical techniqueproposed[1]byHerman Otto Hartley(Hirschfeld)[2]and later developed byJean-Paul Benzécri.[3]It is conceptually similar toprincipal component analysis, but applies to categorical rather than continuous data. In a similar manner to principal component analy... | https://en.wikipedia.org/wiki/Correspondence_analysis |
Instatistics,multiple correspondence analysis(MCA) is adata analysistechnique for nominal categorical data, used to detect and represent underlying structures in a data set. It does this by representing data as points in a low-dimensionalEuclidean space. The procedure thus appears to be the counterpart ofprincipal comp... | https://en.wikipedia.org/wiki/Multiple_correspondence_analysis |
Instatistics,factor analysis of mixed dataorfactorial analysis of mixed data(FAMD, in the French original:AFDMorAnalyse Factorielle de Données Mixtes), is thefactorial methoddevoted to data tables in which a group of individuals is described both by quantitative and qualitative variables. It belongs to the exploratory ... | https://en.wikipedia.org/wiki/Factor_analysis_of_mixed_data |
Instatistics,canonical-correlation analysis(CCA), also calledcanonical variates analysis, is a way of inferring information fromcross-covariance matrices. If we have two vectorsX= (X1, ...,Xn) andY= (Y1, ...,Ym) ofrandom variables, and there arecorrelationsamong the variables, then canonical-correlation analysis will ... | https://en.wikipedia.org/wiki/Canonical_correlation |
ACUR matrix approximationis a set of threematricesthat, when multiplied together, closely approximate a given matrix.[1][2][3]A CUR approximation can be used in the same way as thelow-rank approximationof thesingular value decomposition(SVD). CUR approximations are less accurate than the SVD, but they offer two key ad... | https://en.wikipedia.org/wiki/CUR_matrix_approximation |
Detrended correspondence analysis (DCA)is a multivariatestatisticaltechnique widely used byecologiststo find the main factors or gradients in large, species-rich but usually sparse data matrices that typifyecological communitydata. DCA is frequently used to suppress artifacts inherent in most othermultivariate analyses... | https://en.wikipedia.org/wiki/Detrended_correspondence_analysis |
Directional component analysis(DCA)[1][2][3]is a statistical method used in climate science for identifying representative patterns of variability in space-time data-sets such as historical climate observations,[1]weather prediction ensembles[2]orclimate ensembles.[3]
The first DCA pattern is a pattern of weather or c... | https://en.wikipedia.org/wiki/Directional_component_analysis |
Indata science,dynamic mode decomposition(DMD) is adimensionality reductionalgorithm developed by Peter J. Schmid and Joern Sesterhenn in 2008.[1][2]Given a time series of data, DMD computes a set of modes, each of which is associated with a fixed oscillationfrequencyand decay/growth rate. Forlinear systemsin particul... | https://en.wikipedia.org/wiki/Dynamic_mode_decomposition |
Aneigenface(/ˈaɪɡən-/EYE-gən-) is the name given to a set ofeigenvectorswhen used in thecomputer visionproblem of humanface recognition.[1]The approach of using eigenfaces forrecognitionwas developed by Sirovich and Kirby and used byMatthew TurkandAlex Pentlandin face classification.[2][3]The eigenvectors are derived f... | https://en.wikipedia.org/wiki/Eigenface |
Most real world data sets consist of data vectors whose individual components are notstatistically independent. In other words, knowing the value of an element will provide information about the value of elements in the data vector. When this occurs, it can be desirable to create afactorial codeof the data, i.e., a new... | https://en.wikipedia.org/wiki/Factorial_code |
Functional principal component analysis(FPCA) is astatistical methodfor investigating the dominantmodes of variationoffunctional data. Using this method, arandom functionis represented in the eigenbasis, which is anorthonormalbasis of theHilbert spaceL2that consists of the eigenfunctions of theautocovariance operator... | https://en.wikipedia.org/wiki/Functional_principal_component_analysis |
Geometric data analysiscomprisesgeometricaspects ofimage analysis,pattern analysis, andshape analysis, and the approach ofmultivariate statistics, which treat arbitrary data sets asclouds of pointsin a space that isn-dimensional. This includestopological data analysis,cluster analysis, inductive data analysis,correspon... | https://en.wikipedia.org/wiki/Geometric_data_analysis |
Insignal processing,independent component analysis(ICA) is a computational method for separating amultivariatesignal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents arestatistically independentfrom each other.[1]ICA was invented by Jeanny Héraul... | https://en.wikipedia.org/wiki/Independent_component_analysis |
In the field ofmultivariate statistics,kernel principal component analysis (kernel PCA)[1]is an extension ofprincipal component analysis(PCA) using techniques ofkernel methods. Using a kernel, the originally linear operations of PCA are performed in areproducing kernel Hilbert space.
Recall that conventional PCA opera... | https://en.wikipedia.org/wiki/Kernel_PCA |
L1-norm principal component analysis (L1-PCA)is a general method for multivariate data analysis.[1]L1-PCA is often preferred over standard L2-normprincipal component analysis(PCA) when the analyzed data may containoutliers(faulty values or corruptions), as it is believed to berobust.[2][3][4]
Both L1-PCA and standard ... | https://en.wikipedia.org/wiki/L1-norm_principal_component_analysis |
In mathematics,low-rank approximationrefers to the process of approximating a given matrix by a matrix of lower rank. More precisely, it is aminimizationproblem, in which thecost functionmeasures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint t... | https://en.wikipedia.org/wiki/Low-rank_approximation |
In themathematicaldiscipline oflinear algebra, amatrix decompositionormatrix factorizationis afactorizationof amatrixinto a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.
Innumerical analysis, different decompositions are used to implement effi... | https://en.wikipedia.org/wiki/Matrix_decomposition |
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