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Perceptual Evaluation of Video Quality(PEVQ)is an end-to-end (E2E) measurement algorithm to score thepicture quality of a video presentationby means of a 5-pointmean opinion score(MOS). It is, therefore, a video quality model. PEVQ was benchmarked by theVideo Quality Experts Group(VQEG) in the course of the Multimedia ... | https://en.wikipedia.org/wiki/Perceptual_Evaluation_of_Video_Quality |
Thestructural similarityindex measure(SSIM) is a method for predicting the perceived quality of digital television and cinematic pictures, as well as other kinds of digital images and videos. It is also used for measuring the similarity between two images. The SSIM index is afull reference metric; in other words, the ... | https://en.wikipedia.org/wiki/Structural_similarity_index_measure |
Subjective video qualityisvideo qualityas experienced by humans. It is concerned with how video is perceived by a viewer (also called "observer" or "subject") and designates their opinion on a particularvideosequence. It is related to the field ofQuality of Experience. Measuring subjective video quality is necessary be... | https://en.wikipedia.org/wiki/Subjective_video_quality |
Video Multimethod Assessment Fusion(VMAF) is an objective full-referencevideo qualitymetric developed byNetflixin cooperation with theUniversity of Southern California, the IPI/LS2N labNantes Université, and the Laboratory for Image and Video Engineering (LIVE) atThe University of Texas at Austin. It predicts subjecti... | https://en.wikipedia.org/wiki/Video_Multimethod_Assessment_Fusion |
Video qualityis a characteristic of avideopassed through a video transmission or processing system that describes perceived video degradation (typically compared to the original video). Video processing systems may introduce some amount of distortion or artifacts in the video signal that negatively impact the user's pe... | https://en.wikipedia.org/wiki/Video_quality |
Bayesian linear regressionis a type ofconditional modelingin which the mean of one variable is described by alinear combinationof other variables, with the goal of obtaining theposterior probabilityof the regression coefficients (as well as other parameters describing thedistributionof the regressand) and ultimately al... | https://en.wikipedia.org/wiki/Bayesian_linear_regression |
Ridge regression(also known asTikhonov regularization, named forAndrey Tikhonov) is a method of estimating thecoefficientsof multiple-regression modelsin scenarios where the independent variables are highly correlated.[1]It has been used in many fields including econometrics, chemistry, and engineering.[2]It is a metho... | https://en.wikipedia.org/wiki/Tikhonov_regularization#Bayesian_interpretation |
Instatisticsandmachine learning,lasso(least absolute shrinkage and selection operator; alsoLasso,LASSOorL1 regularization)[1]is aregression analysismethod that performs bothvariable selectionandregularizationin order to enhance the prediction accuracy and interpretability of the resultingstatistical model. The lasso me... | https://en.wikipedia.org/wiki/Lasso_regression |
Instatistics,least-angle regression (LARS)is an algorithm for fittinglinear regressionmodels to high-dimensional data, developed byBradley Efron,Trevor Hastie,Iain JohnstoneandRobert Tibshirani.[1]
Suppose we expect a response variable to be determined by a linear combination of a subset of potential covariates. Then... | https://en.wikipedia.org/wiki/Least-angle_regression |
Least-squares adjustmentis a model for the solution of anoverdetermined systemof equations based on the principle ofleast squaresofobservation residuals. It is used extensively in the disciplines ofsurveying,geodesy, andphotogrammetry—the field ofgeomatics, collectively.
There are three forms of least squares adjustme... | https://en.wikipedia.org/wiki/Adjustment_of_observations |
TheGittins indexis a measure of the reward that can be achieved through a givenstochastic processwith certain properties, namely: the process has an ultimate termination state and evolves with an option, at each intermediate state, of terminating. Upon terminating at a given state, the reward achieved is the sum of the... | https://en.wikipedia.org/wiki/Gittins_index |
In the field ofcalculus of variationsinmathematics, the method ofLagrange multipliers on Banach spacescan be used to solve certain infinite-dimensionalconstrainedoptimization problems. The method is a generalization of the classical method ofLagrange multipliersas used to findextremaof afunctionof finitely many variabl... | https://en.wikipedia.org/wiki/Lagrange_multipliers_on_Banach_spaces |
Instatistics, thescore testassessesconstraintsonstatistical parametersbased on thegradientof thelikelihood function—known as thescore—evaluated at the hypothesized parameter value under thenull hypothesis. Intuitively, if the restricted estimator is near themaximumof the likelihood function, the score should not differ... | https://en.wikipedia.org/wiki/Lagrange_multiplier_test |
In the field ofmathematical optimization,Lagrangian relaxationis arelaxation methodwhichapproximatesa difficult problem ofconstrained optimizationby a simpler problem. A solution to the relaxed problem is an approximate solution to the original problem, and provides useful information.
The method penalizes violations ... | https://en.wikipedia.org/wiki/Lagrangian_relaxation |
Instatistics,explained variationmeasures the proportion to which a mathematical model accounts for the variation (dispersion) of a given data set. Often, variation is quantified asvariance; then, the more specific termexplained variancecan be used.
The complementary part of the total variation is calledunexplainedorre... | https://en.wikipedia.org/wiki/Explained_variance |
In themathematicalsubfield ofnumerical analysis,numerical stabilityis a generally desirable property ofnumerical algorithms. The precise definition of stability depends on the context: one important context isnumerical linear algebra, and another is algorithms for solving ordinary and partial differential equations by ... | https://en.wikipedia.org/wiki/Numerical_stability |
Inlinear algebra, aHilbert matrix, introduced byHilbert(1894), is asquare matrixwith entries being theunit fractions
For example, this is the 5 × 5 Hilbert matrix:
The entries can also be defined by the integral
that is, as aGramian matrixfor powers ofx. It arises in theleast squaresapproximation of arbitrary funct... | https://en.wikipedia.org/wiki/Hilbert_matrix |
Inmathematics, awell-posed problemis one for which the following properties hold:[a]
Examples ofarchetypalwell-posed problems include theDirichlet problem for Laplace's equation, and theheat equationwith specified initial conditions. These might be regarded as 'natural' problems in that there are physical processes mo... | https://en.wikipedia.org/wiki/Ill-posed_problem |
Wilson matrixis the following4×4{\displaystyle 4\times 4}matrix having integers as elements:[1][2][3][4][5]
This is thecoefficient matrixof the followingsystem of linear equationsconsidered in a paper by J. Morris published in 1946:[6]
Morris ascribes the source of the set of equations to one T. S. Wilson but no deta... | https://en.wikipedia.org/wiki/Wilson_matrix |
Importance samplingis aMonte Carlo methodfor evaluating properties of a particulardistribution, while only having samples generated from a different distribution than the distribution of interest. Its introduction in statistics is generally attributed to a paper byTeun KloekandHerman K. van Dijkin 1978,[1]but its precu... | https://en.wikipedia.org/wiki/Importance_sampling |
Local regressionorlocal polynomial regression,[1]also known asmoving regression,[2]is a generalization of themoving averageandpolynomial regression.[3]Its most common methods, initially developed forscatterplot smoothing, areLOESS(locally estimated scatterplot smoothing) andLOWESS(locally weighted scatterplot smoothing... | https://en.wikipedia.org/wiki/Local_regression |
Instatistical modeling(especiallyprocess modeling), polynomial functions and rational functions are sometimes used as an empirical technique forcurve fitting.
Apolynomial functionis one that has the form
wherenis a non-negativeintegerthat defines the degree of the polynomial. A polynomial with a degree of 0 is simply... | https://en.wikipedia.org/wiki/Rational_function_modeling |
Smoothing splinesare function estimates,f^(x){\displaystyle {\hat {f}}(x)}, obtained from a set of noisy observationsyi{\displaystyle y_{i}}of the targetf(xi){\displaystyle f(x_{i})}, in order to balance a measure ofgoodness of fitoff^(xi){\displaystyle {\hat {f}}(x_{i})}toyi{\displaystyle y_{i}}with a derivative based... | https://en.wikipedia.org/wiki/Spline_regression |
Incomputer programming,array slicingis an operation that extracts a subset of elements from anarrayand packages them as another array, possibly in a differentdimensionfrom the original.
Common examples of array slicing are extracting a substring from astringof characters, the "ell" in "hello", extracting a row or colu... | https://en.wikipedia.org/wiki/Array_slicing |
This is a list of notableprogramming languages, grouped by type.
The groupings are overlapping; not mutually exclusive. A language can be listed in multiple groupings.
Agent-oriented programming allows the developer to build, extend and usesoftware agents, which are abstractions of objects that can message other agen... | https://en.wikipedia.org/wiki/List_of_programming_languages_by_type#Array_languages |
This is a list of notableprogramming languages, grouped by type.
The groupings are overlapping; not mutually exclusive. A language can be listed in multiple groupings.
Agent-oriented programming allows the developer to build, extend and usesoftware agents, which are abstractions of objects that can message other agen... | https://en.wikipedia.org/wiki/List_of_programming_languages_by_type#Numerical_analysis |
The followingoutlineis provided as an overview of and topical guide to software:
Software– collection ofcomputer programsand relateddatathat provides the information for the functioning of acomputer. It is held in various forms ofmemoryof the computer. It comprises procedures, algorithms, and documentation concerned w... | https://en.wikipedia.org/wiki/Outline_of_software |
Incomputer science, anarrayis adata structureconsisting of a collection ofelements(valuesorvariables), of same memory size, each identified by at least onearray indexorkey, a collection of which may be a tuple, known as an index tuple. An array is stored such that the position (memory address) of each element can be co... | https://en.wikipedia.org/wiki/Array_(data_structure) |
Thiscomparison of programming languages (array)compares the features ofarray data structuresormatrixprocessing for various computerprogramming languages.
The following list containssyntaxexamples of how to determine the dimensions (index of the first element, the last element or the size in elements).
Some languages ... | https://en.wikipedia.org/wiki/Comparison_of_programming_languages_(array) |
Incomputer science,arrayis adata typethat represents a collection ofelements(valuesorvariables), each selected by one or more indices (identifying keys) that can be computed atrun timeduring program execution. Such a collection is usually called anarray variableorarray value.[1]By analogy with the mathematical concepts... | https://en.wikipedia.org/wiki/Index_origin |
Matrix representationis a method used by acomputer languageto store column-vectormatricesof more than one dimension inmemory.FortranandCuse different schemes for their native arrays.Fortranuses "Column Major" (AoS), in which all the elements for a given column are stored contiguously in memory.Cuses "Row Major" (SoA), ... | https://en.wikipedia.org/wiki/Matrix_representation |
Inmathematical analysisandcomputer science,functionswhich areZ-order,Lebesgue curve,Mortonspace-filling curve,[1]Morton orderorMorton codemapmultidimensional data to one dimensionwhile preserving locality of the data points (two points close together in multidimensions with high probability lie also close together in M... | https://en.wikipedia.org/wiki/Morton_order |
Innumerical analysisandscientific computing, asparse matrixorsparse arrayis amatrixin which most of the elements are zero.[1]There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify assparsebut a common criterion is that the number of non-zero elements is roughly equal to th... | https://en.wikipedia.org/wiki/Sparse_matrix#Storing_a_sparse_matrix |
Inmathematics, especially inlinear algebraandmatrix theory, thevectorizationof amatrixis alinear transformationwhich converts the matrix into avector. Specifically, the vectorization of am×nmatrixA, denoted vec(A), is themn× 1column vector obtained by stacking the columns of the matrixAon top of one another:vec(A)=[a1... | https://en.wikipedia.org/wiki/Vectorization_(mathematics) |
Instatistics, thegeneralizedcanonical correlationanalysis(gCCA), is a way of making sense ofcross-correlationmatrices between the sets of random variables when there are more than two sets. While a conventional CCA generalizesprincipal component analysis(PCA) to two sets of random variables, a gCCA generalizes PCA to ... | https://en.wikipedia.org/wiki/Generalized_canonical_correlation |
The concept ofanglesbetweenlines(in theplaneor inspace), between two planes (dihedral angle) or between a line and a plane can be generalized to arbitrarydimensions. This generalization was first discussed byCamille Jordan.[1]For any pair offlatsin aEuclidean spaceof arbitrary dimension one can define a set of mutual a... | https://en.wikipedia.org/wiki/Angles_between_flats |
Regularized canonical correlation analysisis a way of usingridge regressionto solve thesingularityproblem in thecross-covariance matricesofcanonical correlation analysis. By convertingcov(X,X){\displaystyle \operatorname {cov} (X,X)}andcov(Y,Y){\displaystyle \operatorname {cov} (Y,Y)}intocov(X,X)+λIX{\displaystyle \... | https://en.wikipedia.org/wiki/Regularized_canonical_correlation_analysis |
Inlinear algebra, aneigenvector(/ˈaɪɡən-/EYE-gən-) orcharacteristic vectoris avectorthat has itsdirectionunchanged (or reversed) by a givenlinear transformation. More precisely, an eigenvectorv{\displaystyle \mathbf {v} }of a linear transformationT{\displaystyle T}isscaled by a constant factorλ{\displaystyle \lambda }w... | https://en.wikipedia.org/wiki/Eigenvalue,_eigenvector_and_eigenspace |
Ordinationorgradient analysis, inmultivariate analysis, is a method complementary todata clustering, and used mainly inexploratory data analysis(rather than inhypothesis testing). In contrast to cluster analysis, ordinationordersquantities in a (usually lower-dimensional) latent space. In the ordination space, quantit... | https://en.wikipedia.org/wiki/Ordination_(statistics) |
Inarchaeology, seriation is arelative datingmethod in whichassemblagesorartifactsfrom numerous sites in the same culture are placed in chronological order. Whereabsolute datingmethods, such as radio carbon, cannot be applied, archaeologists have to userelative datingmethods to date archaeological finds and features. S... | https://en.wikipedia.org/wiki/Seriation_(archaeology) |
Principal component analysis(PCA) is alineardimensionality reductiontechnique with applications inexploratory data analysis, visualization anddata preprocessing.
The data islinearly transformedonto a newcoordinate systemsuch that the directions (principal components) capturing the largest variation in the data can be ... | https://en.wikipedia.org/wiki/Principal_Component_Analysis |
Inlinear algebra,eigendecompositionis thefactorizationof amatrixinto acanonical form, whereby the matrix is represented in terms of itseigenvalues and eigenvectors. Onlydiagonalizable matricescan be factorized in this way. When the matrix being factorized is anormalor realsymmetric matrix, the decomposition is called "... | https://en.wikipedia.org/wiki/Eigenvalue_decomposition |
TheHilbert–Huang transform(HHT) is a way to decompose asignalinto so-called intrinsic mode functions (IMF) along with a trend, and obtaininstantaneous frequencydata. It is designed to work well for data that isnonstationaryandnonlinear.
The Hilbert–Huang transform (HHT), aNASAdesignated name,[1]was proposed byNorden ... | https://en.wikipedia.org/wiki/Empirical_mode_decomposition |
In the physics ofhydrodynamics, aglobal modeof a system is one in which the system executes coherentoscillationsin time. Suppose a quantityy(x,t){\displaystyle y(x,t)}which depends on spacex{\displaystyle x}and timet{\displaystyle t}is governed by somepartial differential equationwhich does not have an explicit depende... | https://en.wikipedia.org/wiki/Global_mode |
Anormal modeof adynamical systemis a pattern of motion in which all parts of the system movesinusoidallywith the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as itsnatur... | https://en.wikipedia.org/wiki/Normal_mode |
Theproper orthogonal decompositionis anumerical methodthat enables a reduction in the complexity of computer intensive simulations such ascomputational fluid dynamicsandstructural analysis(likecrash simulations). Typically influid dynamicsandturbulences analysis, it is used to replace theNavier–Stokes equationsby simpl... | https://en.wikipedia.org/wiki/Proper_orthogonal_decomposition |
Inlinear algebra, thesingular value decomposition(SVD) is afactorizationof arealorcomplexmatrixinto a rotation, followed by a rescaling followed by another rotation. It generalizes theeigendecompositionof a squarenormal matrixwith an orthonormal eigenbasis to anym×n{\displaystyle m\times n}matrix. It is related to th... | https://en.wikipedia.org/wiki/Singular-value_decomposition |
Thehistory ofanthropometryincludes its use as an early tool ofanthropology, use for identification, use for the purposes of understanding human physical variation inpaleoanthropologyand in various attempts to correlate physical with racial and psychological traits. At various points in history, certain anthropometrics ... | https://en.wikipedia.org/wiki/Craniofacial_anthropometry |
Human physical appearanceis the outwardphenotypeor look of human beings.
There are functionally infinite variations in human phenotypes, though society reduces the variability to distinct categories. The physical appearance of humans, in particular those attributes which are regarded as important forphysical attractiv... | https://en.wikipedia.org/wiki/Human_appearance |
Source separation,blind signal separation(BSS) orblind source separation, is the separation of a set of sourcesignalsfrom a set of mixed signals, without the aid of information (or with very little information) about the source signals or the mixing process. It is most commonly applied indigital signal processingand in... | https://en.wikipedia.org/wiki/Blind_signal_separation |
Digital image processingis the use of adigital computerto processdigital imagesthrough analgorithm.[1][2]As a subcategory or field ofdigital signal processing, digital image processing has many advantages overanalog image processing. It allows a much wider range of algorithms to be applied to the input data and can avo... | https://en.wikipedia.org/wiki/Image_processing |
Algebraic statisticsis the use ofalgebrato advancestatistics. Algebra has been useful forexperimental design,parameter estimation, andhypothesis testing.
Traditionally, algebraic statistics has been associated with the design of experiments andmultivariate analysis(especiallytime series). In recent years, the term "al... | https://en.wikipedia.org/wiki/Algebraic_statistics |
In statistics,combinatorial data analysis(CDA) is the study of data sets where the order in which objects are arranged is important. CDA can be used either to determine how well a givencombinatorialconstruct reflects the observed data, or to search for a suitable combinatorial construct that does fit the data.[1][2][3]... | https://en.wikipedia.org/wiki/Combinatorial_data_analysis |
Computational anatomyis an interdisciplinary field ofbiologyfocused on quantitative investigation and modelling of anatomical shapes variability.[1][2]It involves the development and application of mathematical, statistical and data-analytical methods for modelling and simulation of biological structures.
The field is... | https://en.wikipedia.org/wiki/Computational_anatomy |
Themanifold hypothesisposits that manyhigh-dimensionaldata sets that occur in the real world actually lie along low-dimensionallatent manifoldsinside that high-dimensional space.[1][2][3][4]As a consequence of the manifold hypothesis, many data sets that appear to initially require many variables to describe, can actua... | https://en.wikipedia.org/wiki/Manifold_hypothesis |
Indynamical systems, aspectral submanifold(SSM) is the uniquesmoothestinvariant manifoldserving as the nonlinear extension of a spectral subspace of a linear dynamical system under the addition of nonlinearities.[2]SSM theory provides conditions for when invariant properties of eigenspaces of a linear dynamical system ... | https://en.wikipedia.org/wiki/Spectral_submanifold |
In the study ofdynamical systems, adelay embedding theoremgives the conditions under which achaoticdynamical system can be reconstructed from a sequence of observations of the state of that system. The reconstruction preserves the properties of the dynamical system that do not change under smoothcoordinate changes(i.e.... | https://en.wikipedia.org/wiki/Takens%27s_theorem |
Inmathematics, particularly indifferential topology, there are two Whitney embedding theorems, named afterHassler Whitney:
The weak Whitney embedding is proved through a projection argument.
When the manifold iscompact, one can first use a covering by finitely many local charts and then reduce the dimension with suit... | https://en.wikipedia.org/wiki/Whitney_embedding_theorem |
Linear discriminant analysis(LDA),normal discriminant analysis(NDA),canonical variates analysis(CVA), ordiscriminant function analysisis a generalization ofFisher's linear discriminant, a method used instatisticsand other fields, to find alinear combinationof features that characterizes or separates two or more classes... | https://en.wikipedia.org/wiki/Discriminant_analysis |
Elastic mapsprovide a tool fornonlinear dimensionality reduction. By their construction, they are a system of elasticspringsembedded in the data
space.[1]This system approximates a low-dimensional manifold. The elastic coefficients of this system allow the switch from completely unstructuredk-means clustering(zero elas... | https://en.wikipedia.org/wiki/Elastic_map |
Agrowing self-organizing map (GSOM)is a growing variant of aself-organizing map(SOM). The GSOM was developed to address the issue of identifying a suitable map size in theSOM. It starts with a minimal number of nodes (usually 4) and grows new nodes on the boundary based on a heuristic. By using the value called Spread ... | https://en.wikipedia.org/wiki/Growing_self-organizing_map |
Bienenstock–Cooper–Munro(BCM)theory,BCM synaptic modification, or theBCM rule, named afterElie Bienenstock,Leon Cooper, and Paul Munro, is a physical theory of learning in thevisual cortexdeveloped in 1981.
The BCM model proposes a sliding threshold forlong-term potentiation(LTP) orlong-term depression(LTD) induction,... | https://en.wikipedia.org/wiki/BCM_theory |
Contrastive Hebbian learningis a biologically plausible form ofHebbian learning.
It is based on the contrastive divergence algorithm, which has been used to train a variety of energy-based latent variable models.[1]
In 2003, contrastive Hebbian learning was shown to be equivalent in power to thebackpropagationalgorit... | https://en.wikipedia.org/wiki/Contrastive_Hebbian_learning |
Thegeneralized Hebbian algorithm, also known in the literature asSanger's rule, is a linearfeedforward neural networkforunsupervised learningwith applications primarily inprincipal components analysis. First defined in 1989,[1]it is similar toOja's rulein its formulation and stability, except it can be applied to netwo... | https://en.wikipedia.org/wiki/Generalized_Hebbian_algorithm |
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_components_analysis |
Inneuroscience,synaptic plasticityis the ability ofsynapsestostrengthen or weakenover time, in response to increases or decreases in their activity.[1]Sincememoriesare postulated to be represented by vastly interconnectedneural circuitsin thebrain, synaptic plasticity is one of the important neurochemical foundations o... | https://en.wikipedia.org/wiki/Synaptic_plasticity |
Instatistics,Procrustes analysisis a form ofstatistical shape analysisused to analyse the distribution of a set ofshapes. The nameProcrustes(Greek:Προκρούστης) refers to a bandit from Greek mythology who made his victims fit his bed either by stretching their limbs or cutting them off.
In mathematics:
When a shape is... | https://en.wikipedia.org/wiki/Procrustes_analysis |
Instatistics,Deming regression, named afterW. Edwards Deming, is anerrors-in-variables modelthat tries to find theline of best fitfor a two-dimensional data set. It differs from thesimple linear regressionin that it accounts forerrorsin observations on both thex- and they- axis. It is a special case oftotal least squar... | https://en.wikipedia.org/wiki/Deming_regression |
Instatistical data analysisthetotal sum of squares(TSSorSST) is a quantity that appears as part of a standard way of presenting results of such analyses. For a set of observations,yi,i≤n{\displaystyle y_{i},i\leq n}, it is defined as the sum over all squared differences between the observations and their overallmeany¯{... | https://en.wikipedia.org/wiki/Total_sum_of_squares |
Insignal processing,multitaperanalysis is aspectral density estimationtechnique developed byDavid J. Thomson.[1][2]It canestimatethepower spectrumSXof astationaryergodicfinite-variancerandom processX, given a finite contiguousrealizationofXas data.
The multitaper method overcomes some of the limitations of non-paramet... | https://en.wikipedia.org/wiki/Multitaper |
Theshort-time Fourier transform(STFT) is aFourier-related transformused to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time.[1]In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute... | https://en.wikipedia.org/wiki/Short-time_Fourier_transform |
Instatistical signal processing, the goal ofspectral density estimation(SDE) or simplyspectral estimationis toestimatethespectral density(also known as thepower spectral density) of a signal from a sequence of time samples of the signal.[1]Intuitively speaking, the spectral density characterizes thefrequencycontent of ... | https://en.wikipedia.org/wiki/Spectral_density_estimation |
In the theory ofstochastic processes, theKarhunen–Loève theorem(named afterKari KarhunenandMichel Loève), also known as theKosambi–Karhunen–Loève theorem[1][2]states that astochastic processcan be represented as an infinite linear combination oforthogonal functions, analogous to aFourier seriesrepresentation of a funct... | https://en.wikipedia.org/wiki/Karhunen%E2%80%93Lo%C3%A8ve_theorem |
Inmathematics, atransformation,transform, orself-map[1]is afunctionf, usually with somegeometricalunderpinning, that maps asetXto itself, i.e.f:X→X.[2][3][4]Examples includelinear transformationsofvector spacesandgeometric transformations, which includeprojective transformations,affine transformations, and specific aff... | https://en.wikipedia.org/wiki/Transformation_(function) |
The method ofiteratively reweighted least squares(IRLS) is used to solve certain optimization problems withobjective functionsof the form of ap-norm:
argminβ∑i=1n|yi−fi(β)|p,{\displaystyle \mathop {\operatorname {arg\,min} } _{\boldsymbol {\beta }}\sum _{i=1}^{n}{\big |}y_{i}-f_{i}({\boldsymbol {\beta }}){\big |}^{p}... | https://en.wikipedia.org/wiki/Iteratively_reweighted_least_squares |
The topic ofheteroskedasticity-consistent(HC)standard errorsarises instatisticsandeconometricsin the context oflinear regressionandtime series analysis. These are also known asheteroskedasticity-robust standard errors(or simplyrobust standard errors),Eicker–Huber–White standard errors(alsoHuber–White standard errorsorW... | https://en.wikipedia.org/wiki/Heteroscedasticity-consistent_standard_errors |
Theweighted arithmetic meanis similar to an ordinaryarithmetic mean(the most common type ofaverage), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role indescriptive statisticsand also occurs in... | https://en.wikipedia.org/wiki/Weighted_mean |
In mathematics, afunctionon thereal numbersis called astep functionif it can be written as afinitelinear combinationofindicator functionsofintervals. Informally speaking, a step function is apiecewiseconstant functionhaving only finitely many pieces.
A functionf:R→R{\displaystyle f\colon \mathbb {R} \rightarrow \mathb... | https://en.wikipedia.org/wiki/Step_function |
TheHeaviside step function, or theunit step function, usually denoted byHorθ(but sometimesu,1or𝟙), is astep functionnamed afterOliver Heaviside, the value of which iszerofor negative arguments andonefor positive arguments. Different conventions concerning the valueH(0)are in use. It is an example of the general class... | https://en.wikipedia.org/wiki/Heaviside_step_function |
In the context ofartificial neural networks, therectifierorReLU (rectified linear unit) activation function[1][2]is anactivation functiondefined as the non-negative part of its argument, i.e., theramp function:
wherex{\displaystyle x}is the input to aneuron. This is analogous tohalf-wave rectificationinelectrical engi... | https://en.wikipedia.org/wiki/Softplus_function |
TheSoboleva modified hyperbolic tangent, also known as(parametric) Soboleva modified hyperbolic tangent activation function([P]SMHTAF),[nb 1]is a specialS-shapedfunctionbased on thehyperbolic tangent, given by
This function was originally proposed as "modified hyperbolic tangent"[nb 1]byUkrainianscientist Elena V. Sob... | https://en.wikipedia.org/wiki/Soboleva_modified_hyperbolic_tangent |
Theswish functionis a family ofmathematical functiondefined as follows:
whereβ{\displaystyle \beta }can be constant (usually set to 1) ortrainable.
The swish family was designed to smoothlyinterpolatebetween a linear function and the ReLU function.
When considering positive values, Swish is a particular case of doub... | https://en.wikipedia.org/wiki/Swish_function |
Inprobability theoryandstatistics, theWeibull distribution/ˈwaɪbʊl/is a continuousprobability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
The distribution... | https://en.wikipedia.org/wiki/Weibull_distribution |
Ineconometrics, thetruncated normal hurdle modelis a variant of theTobit modeland was first proposed by Cragg in 1971.[1]
In a standard Tobit model, represented asy=(xβ+u)1[xβ+u>0]{\displaystyle y=(x\beta +u)1[x\beta +u>0]}, whereu|x∼N(0,σ2){\displaystyle u|x\sim N(0,\sigma ^{2})}This model construction implicitly imp... | https://en.wikipedia.org/wiki/Truncated_normal_hurdle_model |
Empiricalmethods
Prescriptiveand policy
Alimited dependent variableis a variable whose range of
possible values is "restricted in some important way."[1]Ineconometrics, the term is often used when
estimation of the relationship between thelimiteddependent variableof interest and other variables requires methods that ... | https://en.wikipedia.org/wiki/Limited_dependent_variable |
Truncated regression modelsare a class ofmodelsin which thesamplehas beentruncatedfor certain ranges of thedependent variable. That means observations with values in the dependent variable below or above certain thresholds are systematically excluded from the sample. Therefore, whole observations are missing, so that n... | https://en.wikipedia.org/wiki/Truncated_regression_model |
Adynamic unobserved effects modelis astatistical modelused ineconometricsforpanel analysis. It is characterized by the influence of previous values of thedependent variableon its present value, and by the presence of unobservableexplanatory variables.
The term “dynamic” here means the dependence of the dependent varia... | https://en.wikipedia.org/wiki/Dynamic_unobserved_effects_model#Censored_dependent_variable |
Instatistics, aprobit modelis a type ofregressionwhere thedependent variablecan take only two values, for example married or not married. The word is aportmanteau, coming fromprobability+unit.[1]The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a ... | https://en.wikipedia.org/wiki/Probit_model |
Deep learningis a subset ofmachine learningthat focuses on utilizing multilayeredneural networksto perform tasks such asclassification,regression, andrepresentation learning. The field takes inspiration frombiological neuroscienceand is centered around stackingartificial neuronsinto layers and "training" them to proces... | https://en.wikipedia.org/wiki/Deep_Learning |
Theneocortex, also called theneopallium,isocortex, or thesix-layered cortex, is a set of layers of themammaliancerebral cortexinvolved in higher-order brain functions such assensory perception, cognition, generation ofmotor commands,[1]spatial reasoning, andlanguage.[2]The neocortex is further subdivided into thetrue i... | https://en.wikipedia.org/wiki/Neocortex#Layers |
Inbiochemistryandpharmacology, theHill equationrefers to two closely related equations that reflect the binding ofligandsto macromolecules, as a function of the ligandconcentration. Aligandis "a substance that forms a complex with a biomolecule to serve a biological purpose", and amacromoleculeis a very large molecule,... | https://en.wikipedia.org/wiki/Hill_equation_(biochemistry) |
TheHubbert curveis an approximation of the production rate of a resource over time. It is a symmetriclogistic distributioncurve,[1]often confused with the "normal"gaussian function. It first appeared in "Nuclear Energy and the Fossil Fuels," geologistM. King Hubbert's 1956 presentation to theAmerican Petroleum Insti... | https://en.wikipedia.org/wiki/Hubbert_curve |
Instatistics,Smooth Transition Autoregressive(STAR)modelsare typically applied totime seriesdata as an extension ofautoregressive models, in order to allow for higher degree of flexibility in model parameters through asmooth transition.
Given a time series of dataxt, the STAR model is a tool for understanding and, per... | https://en.wikipedia.org/wiki/STAR_model |
Inbiochemistry,Michaelis–Menten kinetics, named afterLeonor MichaelisandMaud Menten, is the simplest case ofenzyme kinetics, applied to enzyme-catalysed reactions involving the transformation of one substrate into one product. It takes the form of adifferential equationdescribing thereaction ratev{\displaystyle v}(rate... | https://en.wikipedia.org/wiki/Michaelis%E2%80%93Menten_kinetics |
Inecology,r/Kselection theoryrelates to theselectionof combinations oftraitsin an organism that trade off between quantity and quality of offspring. The focus on either an increased quantity of offspring at the expense of reduced individualparental investmentofr-strategists, or on a reduced quantity of offspring with a... | https://en.wikipedia.org/wiki/R/K_selection_theory |
(−1/b){E[ln(X)]−ln(η)}{\displaystyle (-1/b)\{\mathrm {E} [\ln(X)]-\ln(\eta )\}\,}whereX=ηe−bx{\displaystyle X=\eta e^{-bx}\,}and
(1/b2)(E{[ln(X)]2}−(E[ln(X)])2){\displaystyle (1/b^{2})(\mathrm {E} \{[\ln(X)]^{2}\}-(\mathrm {E} [\ln(X)])^{2})\,}
Theshifted Gompertz distributionis the distribution of the larger of ... | https://en.wikipedia.org/wiki/Shifted_Gompertz_distribution |
1800s:Martineau·Tocqueville·Marx·Spencer·Le Bon·Ward·Pareto·Tönnies·Veblen·Simmel·Durkheim·Addams·Mead·Weber·Du Bois·Mannheim·Elias
Insociology, atipping pointis a point in time when a group—or many group members—rapidly and dramatically changes its behavior by widely adopting a previously rare practice.[1]
The phras... | https://en.wikipedia.org/wiki/Tipping_point_(sociology) |
Ingeometry, thegeometric medianof adiscrete point setin aEuclidean spaceis the point minimizing the sum of distances to the sample points. This generalizes themedian, which has the property of minimizing the sum of distances or absolute differences for one-dimensional data. It is also known as thespatial median,[1]Eucl... | https://en.wikipedia.org/wiki/Geometric_median |
Quantile regressionis a type ofregression analysisused in statistics and econometrics. Whereas themethod of least squaresestimates the conditionalmeanof the response variable across values of the predictor variables, quantile regression estimates the conditionalmedian(or otherquantiles) of the response variable. [Ther... | https://en.wikipedia.org/wiki/Quantile_regression |
Instatistics,linear regressionis amodelthat estimates the relationship between ascalarresponse (dependent variable) and one or more explanatory variables (regressororindependent variable). A model with exactly one explanatory variable is asimple linear regression; a model with two or more explanatory variables is amult... | https://en.wikipedia.org/wiki/Linear_regression_model |
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