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Instatistics, theBonferroni correctionis a method to counteract themultiple comparisons problem.
The method is named for its use of theBonferroni inequalities.[1]Application of the method toconfidence intervalswas described byOlive Jean Dunn.[2]
Statistical hypothesis testingis based on rejecting thenull hypothesiswh... | https://en.wikipedia.org/wiki/Bonferroni_correction |
Inprobability theoryandstatistics, theχ2{\displaystyle \chi ^{2}}-distributionwithk{\displaystyle k}degrees of freedomis the distribution of a sum of the squares ofk{\displaystyle k}independentstandard normalrandom variables.[2]
The chi-squared distributionχk2{\displaystyle \chi _{k}^{2}}is a special case of thegamma ... | https://en.wikipedia.org/wiki/Chi-squared_distribution |
Instatistics, alatent class model(LCM) is a model for clustering multivariate discrete data. It assumes that the data arise from a mixture of discrete distributions, within each of which the variables are independent. It is called a latent class model because the class to which each data point belongs is unobserved, or... | https://en.wikipedia.org/wiki/Latent_class_model |
Inmarketing,market segmentationorcustomer segmentationis the process of dividing a consumer or businessmarketinto meaningful sub-groups of current or potentialcustomers(orconsumers) known assegments.[1]Its purpose is to identify profitable and growing segments that a company can target with distinct marketing strategie... | https://en.wikipedia.org/wiki/Market_segment |
Instatistics, themultiple comparisons,multiplicityormultiple testing problemoccurs when one considers a set ofstatistical inferencessimultaneously[1]orestimatesa subset of parameters selected based on the observed values.[2]
The larger the number of inferences made, the more likely erroneous inferences become. Severa... | https://en.wikipedia.org/wiki/Multiple_comparisons |
Decision tree learningis asupervised learningapproach used instatistics,data miningandmachine learning. In this formalism, a classification or regressiondecision treeis used as apredictive modelto draw conclusions about a set of observations.
Tree models where the target variable can take a discrete set of values are ... | https://en.wikipedia.org/wiki/Classification_and_regression_tree |
BrownBoostis aboostingalgorithm that may be robust tonoisy datasets. BrownBoost is an adaptive version of theboost by majorityalgorithm. As is the case for all boosting algorithms, BrownBoost is used in conjunction with othermachine learningmethods. BrownBoost was introduced byYoav Freundin 2001.[1]
AdaBoostperforms ... | https://en.wikipedia.org/wiki/BrownBoost |
Themultiplicative weights update methodis analgorithmic techniquemost commonly used for decision making and prediction, and also widely deployed in game theory and algorithm design. The simplest use case is the problem of prediction from expert advice, in which a decision maker needs to iteratively decide on an expert ... | https://en.wikipedia.org/wiki/Multiplicative_weight_update_method#AdaBoost_algorithm |
Machine learning(ML) is afield of studyinartificial intelligenceconcerned with the development and study ofstatistical algorithmsthat can learn fromdataandgeneraliseto unseen data, and thus performtaskswithout explicitinstructions.[1]Within a subdiscipline in machine learning, advances in the field ofdeep learninghave ... | https://en.wikipedia.org/wiki/Machine_Learning |
Incomputer science,binary space partitioning(BSP) is a method forspace partitioningwhichrecursivelysubdivides aEuclidean spaceinto twoconvex setsby usinghyperplanesas partitions. This process of subdividing gives rise to a representation of objects within the space in the form of atree data structureknown as aBSP tree.... | https://en.wikipedia.org/wiki/Binary_space_partitioning |
Abounding volume hierarchy(BVH) is atree structureon a set ofgeometricobjects. All geometric objects, which form the leaf nodes of the tree, are wrapped inbounding volumes. These nodes are then grouped as small sets and enclosed within larger bounding volumes. These, in turn, are also grouped and enclosed within other ... | https://en.wikipedia.org/wiki/Bounding_volume_hierarchy |
Cladistics(/kləˈdɪstɪks/klə-DIST-iks; fromAncient Greekκλάδοςkládos'branch')[1]is an approach tobiological classificationin whichorganismsare categorized in groups ("clades") based on hypotheses of most recentcommon ancestry. The evidence for hypothesized relationships is typically sharedderivedcharacteristics (synapom... | https://en.wikipedia.org/wiki/Cladistics |
Computational phylogenetics,phylogeny inference,orphylogenetic inferencefocuses on computational and optimizationalgorithms,heuristics, and approaches involved inphylogeneticanalyses. The goal is to find aphylogenetic treerepresenting optimal evolutionary ancestry between a set ofgenes,species, ortaxa.Maximum likelihoo... | https://en.wikipedia.org/wiki/Computational_phylogenetics |
CURE(Clustering Using REpresentatives) is an efficientdata clusteringalgorithm for largedatabases[citation needed]. Compared withK-means clusteringit is morerobusttooutliersand able to identify clusters having non-spherical shapes and size variances.
The popularK-means clusteringalgorithm minimizes thesum of squared e... | https://en.wikipedia.org/wiki/CURE_data_clustering_algorithm |
In the study ofhierarchical clustering,Dasgupta's objectiveis a measure of the quality of a clustering, defined from asimilarity measureon the elements to be clustered. It is named after Sanjoy Dasgupta, who formulated it in 2016.[1]Its key property is that, when the similarity comes from anultrametric space, the optim... | https://en.wikipedia.org/wiki/Dasgupta%27s_objective |
Adendrogramis adiagramrepresenting atree graph. This diagrammatic representation is frequently used in different contexts:
The namedendrogramderives from the twoancient greekwordsδένδρον(déndron), meaning "tree", andγράμμα(grámma), meaning "drawing, mathematical figure".[7][8]
For a clustering example, suppose that f... | https://en.wikipedia.org/wiki/Dendrogram |
Determining the number of clusters in adata set, a quantity often labelledkas in thek-means algorithm, is a frequent problem indata clustering, and is a distinct issue from the process of actually solving the clustering problem.
For a certain class ofclustering algorithms(in particulark-means,k-medoidsandexpectation–m... | https://en.wikipedia.org/wiki/Determining_the_number_of_clusters_in_a_data_set |
Hierarchical clusteringis one method for findingcommunity structuresin anetwork. The technique arranges the network into a hierarchy of groups according to a specified weight function. The data can then be represented in a tree structure known as adendrogram. Hierarchical clustering can either beagglomerativeordivisiv... | https://en.wikipedia.org/wiki/Hierarchical_clustering_of_networks |
In the theory ofcluster analysis, thenearest-neighbor chain algorithmis analgorithmthat can speed up several methods foragglomerative hierarchical clustering. These are methods that take a collection of points as input, and create a hierarchy of clusters of points by repeatedly merging pairs of smaller clusters to form... | https://en.wikipedia.org/wiki/Nearest-neighbor_chain_algorithm |
Numerical taxonomyis aclassification systemin biologicalsystematicswhich deals with the grouping bynumerical methodsoftaxonomic unitsbased on their character states.[1]It aims to create ataxonomyusing numeric algorithms likecluster analysisrather than using subjective evaluation of their properties. The concept was fir... | https://en.wikipedia.org/wiki/Numerical_taxonomy |
Ordering points to identify the clustering structure(OPTICS) is an algorithm for finding density-based[1]clustersin spatial data. It was presented in 1999 by Mihael Ankerst, Markus M. Breunig,Hans-Peter Kriegeland Jörg Sander.[2]Its basic idea is similar toDBSCAN,[3]but it addresses one of DBSCAN's major weaknesses: th... | https://en.wikipedia.org/wiki/OPTICS_algorithm |
Intopological data analysis,persistent homologyis a method for computing topological features of a space at different spatial resolutions. More persistent features are detected over a wide range of spatial scales and are deemed more likely to represent true features of the underlying space rather than artifacts of sam... | https://en.wikipedia.org/wiki/Persistent_homology |
In social sciences,sequence analysis (SA)is concerned with the analysis of sets of categorical sequences that typically describelongitudinal data. Analyzed sequences are encoded representations of, for example, individual life trajectories such as family formation, school to work transitions, working careers, but they ... | https://en.wikipedia.org/wiki/Social_sequence_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_principal_component_analysis |
Inmathematics,spectralgraph theoryis the study of the properties of agraphin relationship to thecharacteristic polynomial,eigenvalues, andeigenvectorsof matrices associated with the graph, such as itsadjacency matrixorLaplacian matrix.
The adjacency matrix of a simple undirected graph is arealsymmetric matrixand is th... | https://en.wikipedia.org/wiki/Spectral_graph_theory |
Anarchyis a form ofsocietywithoutrulers. As a type ofstateless society, it is commonly contrasted withstates, which are centralized polities that claim amonopoly on violenceover a permanentterritory. Beyond a lack ofgovernment, it can more precisely refer to societies that lack any form ofauthorityorhierarchy. While vi... | https://en.wikipedia.org/wiki/Anarchy |
Aclass browseris a feature of anintegrated development environment(IDE) that allows the programmer to browse, navigate, or visualize the structure ofobject-oriented programmingcode.
Most modern class browsers owe their origins toSmalltalk, one of the earliest object-oriented languages and development environments. The... | https://en.wikipedia.org/wiki/Class_browser |
Agovernmentis the system or group of people governing an organized community, generally astate.
In the case of its broad associative definition, government normally consists oflegislature,executive, andjudiciary. Government is a means by which organizationalpoliciesare enforced, as well as a mechanism for determining ... | https://en.wikipedia.org/wiki/Forms_of_government |
Aheterarchyis a system of organization where the elements of the organization are unranked (non-hierarchical) or where they possess the potential to be ranked a number of different ways.[1]Definitions of the term vary among the disciplines: in social and information sciences, heterarchies arenetworksof elements in whic... | https://en.wikipedia.org/wiki/Heterarchy |
Hierarchicalclassificationis a system of grouping things according to a hierarchy.[1]
In the field ofmachine learning, hierarchical classification is sometimes referred to asinstance space decomposition,[2]which splits a completemulti-classproblem into a set of smaller classification problems.
Thisartificial intellig... | https://en.wikipedia.org/wiki/Hierarchical_classifier |
Hierarchical epistemologyis atheory of knowledgewhich posits that beings have different access torealitydepending on theirontologicalrank.[1]
This article aboutepistemologyis astub. You can help Wikipedia byexpanding it. | https://en.wikipedia.org/wiki/Hierarchical_epistemology |
Hierarchical INTegration, orHINTfor short, is a computerbenchmarkthat ranks a computer system as a whole (i.e. the entire computer instead of individual components). It measures the full range of performance, mostly based on the amount of work a computer can perform over time. A system with a very fast processor would ... | https://en.wikipedia.org/wiki/Hierarchical_INTegration |
Ahierarchical organizationorhierarchical organisation(seespelling differences) is anorganizational structurewhere every entity in theorganization, except one, issubordinateto a single other entity.[1]This arrangement is a form ofhierarchy. In an organization, this hierarchy usually consists of a singular/group ofpowera... | https://en.wikipedia.org/wiki/Hierarchical_organization |
TheHierarchical Music Specification Language(HMSL) is amusicprogramming languagewritten in the 1980s byLarry Polansky,Phil Burk, andDavid RosenboomatMills College.[1]Written on top ofForth, it allowed for the creation of real-time interactive music performance systems,algorithmic compositionsoftware, and any other kind... | https://en.wikipedia.org/wiki/Hierarchical_Music_Specification_Language |
Anopen service interface definition(OSID) is a programmatic interface specification describing a service. These interfaces are specified by theOpen Knowledge Initiative(OKI) to implement aservice-oriented architecture(SOA) to achieveinteroperabilityamong applications across a varied base of underlying and changing tech... | https://en.wikipedia.org/wiki/Hierarchy_Open_Service_Interface_Definition |
Intheoretical physics, thehierarchy problemis the problem concerning the large discrepancy between aspects of the weak force and gravity.[1]There is no scientific consensus on why, for example, theweak forceis 1024times stronger thangravity.
A hierarchy problem[2]occurs when the fundamental value of some physical para... | https://en.wikipedia.org/wiki/Hierarchy_problem |
Aholonis something that is simultaneously a whole in and of itself, as well as a part of a larger whole. In this way, a holon can be considered asubsystemwithin a largerhierarchicalsystem.[1]
The holon represents a way to overcome thedichotomy between parts and wholes, as well as a way to account for both theself-asse... | https://en.wikipedia.org/wiki/Holarchy#Different_meanings |
Inmoral philosophy,instrumental and intrinsic valueare the distinction between what is ameans to an endand what is as anend in itself.[1]Things are deemed to haveinstrumental value(orextrinsic value[2]) if they help one achieve a particular end;intrinsic values, by contrast, are understood to be desirable in and of the... | https://en.wikipedia.org/wiki/Instrumental_value |
Layerorlayeredmay refer to: | https://en.wikipedia.org/wiki/Layer_(disambiguation) |
Multilevel models[a]arestatistical modelsofparametersthat vary at more than one level.[1]An example could be a model of student performance that contains measures for individual students as well as measures for classrooms within which the students are grouped. These models can be seen as generalizations oflinear models... | https://en.wikipedia.org/wiki/Multilevel_model |
Incombinatoricsandorder theory, amultitreemay describe either of two equivalent structures: adirected acyclic graph(DAG) in which there is at most one directed path between any twovertices, or equivalently in which thesubgraphreachable from any vertex induces anundirected tree, or apartially ordered set(poset) that doe... | https://en.wikipedia.org/wiki/Multitree |
Anordinary(fromLatinordinarius) is an officer of a church or civic authority who by reason of office hasordinary powerto execute laws.
Such officers are found in hierarchically organised churches ofWestern Christianitywhich have anecclesiastical legal system.[1]For example, diocesan bishops are ordinaries in theCathol... | https://en.wikipedia.org/wiki/Ordinary_(officer) |
Major recurring characters of theHalomultimedia franchise are organized below by their respective affiliations within the series' fictional universe. The franchise's central story revolves around conflict between humanity under the auspices of theUnited Nations Space Commandor UNSC, and an alien alliance known as theCo... | https://en.wikipedia.org/wiki/Characters_of_Halo#High_Prophets |
The following is a list of all of theCoptic Orthodox popeswho have led theCoptic Orthodox Churchand have succeeded the ApostleMark the Evangelistin the office ofBishop of Alexandria, who founded the Church in the 1st century, and marked the beginning ofChristianity in Africa.
TheCoptic Orthodox Churchis one of theOrie... | https://en.wikipedia.org/wiki/List_of_Coptic_Orthodox_Popes_of_Alexandria |
ThePeter principleis a concept inmanagementdeveloped byLaurence J. Peterwhich observes that people in ahierarchytend to rise to "a level of respective incompetence": employees are promoted based on their success in previous jobs until they reach a level at which they are no longercompetent, as skills in one job do not ... | https://en.wikipedia.org/wiki/Peter_Principle |
Incomputer science,hierarchical protection domains,[1][2]often calledprotection rings, are mechanisms to protect data and functionality from faults (by improvingfault tolerance) and malicious behavior (by providingcomputer security).
Computer operating systems provide different levels of access to resources. A protect... | https://en.wikipedia.org/wiki/Ring_(computer_security) |
Social dominance theory(SDT) is asocial psychologicaltheory ofintergroup relationsthat examines thecaste-like features[1]of group-basedsocial hierarchies, and how these hierarchies remain stable and perpetuate themselves.[2]According to the theory, group-based inequalities are maintained through three primary mechanism... | https://en.wikipedia.org/wiki/Social_dominance_theory |
Congestion games(CG) are a class of games ingame theory. They represent situations which commonly occur in roads,communication networks,oligopolymarkets andnatural habitats. There is a set of resources (e.g. roads or communication links); there are several players who need resources (e.g. drivers or network users); eac... | https://en.wikipedia.org/wiki/Congestion_game |
Anetwork partitionis a division of a computer network into relatively independentsubnets, either by design, to optimize them separately, or due to the failure of network devices. Distributed software must be designed to be partition-tolerant, that is, even after the network is partitioned, it still works correctly.
Fo... | https://en.wikipedia.org/wiki/Network_partition |
TheSeven Bridges of Königsbergis a historically notable problem in mathematics. Itsnegative resolutionbyLeonhard Euler, in 1736,[1]laid the foundations ofgraph theoryand prefigured the idea oftopology.[2]
The city ofKönigsberginPrussia(nowKaliningrad,Russia) was set on both sides of thePregel River, and included two l... | https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg |
A method for pruning dense networks to highlight key links
Relationships among a set of elements are often represented as a square matrix with entries representing the relations between all pairs of the elements. Relations such as distances, dissimilarities, similarities, relatedness, correlations, co-occurrences, co... | https://en.wikipedia.org/wiki/Pathfinder_network |
Ahuman disease networkis a network of human disorders anddiseaseswith reference to their genetic origins or other features. More specifically, it is the map of human disease associations referring mostly to diseasegenes. For example, in a human disease network, two diseases are linked if they share at least one associa... | https://en.wikipedia.org/wiki/Human_disease_network |
Abiological networkis a method of representing systems as complex sets of binary interactions or relations between various biological entities.[1]In general, networks or graphs are used to capture relationships between entities or objects.[1]A typicalgraphingrepresentation consists of a set ofnodesconnected byedges.
A... | https://en.wikipedia.org/wiki/Biological_network |
Network medicineis the application ofnetwork sciencetowards identifying, preventing, and treating diseases. This field focuses on usingnetwork topologyandnetwork dynamicstowards identifying diseases and developing medical drugs.Biological networks, such asprotein-protein interactionsandmetabolic pathways, are utilized ... | https://en.wikipedia.org/wiki/Network_medicine |
In mathematics, agraph partitionis the reduction of agraphto a smaller graph bypartitioningits set of nodes into mutually exclusive groups. Edges of the original graph that cross between the groups will produce edges in the partitioned graph. If the number of resulting edges is small compared to the original graph, the... | https://en.wikipedia.org/wiki/Graph_partition |
Inmathematics, atopological spaceis, roughly speaking, ageometrical spacein whichclosenessis defined but cannot necessarily be measured by a numericdistance. More specifically, a topological space is asetwhose elements are calledpoints, along with an additional structure called a topology, which can be defined as a set... | https://en.wikipedia.org/wiki/Topological_space |
In themathematicalfield oftopology, auniform spaceis asetwith additionalstructurethat is used to defineuniform properties, such ascompleteness,uniform continuityanduniform convergence. Uniform spaces generalizemetric spacesandtopological groups, but the concept is designed to formulate the weakest axioms needed for mos... | https://en.wikipedia.org/wiki/Uniform_space |
Inmathematics,Choquet theory, named afterGustave Choquet, is an area offunctional analysisandconvex analysisconcerned withmeasureswhich havesupporton theextreme pointsof aconvex setC. Roughly speaking, everyvectorofCshould appear as a weighted average of extreme points, a concept made more precise by generalizing the n... | https://en.wikipedia.org/wiki/Choquet_theory |
TheHewitt–Savage zero–one lawis atheoreminprobability theory, similar toKolmogorov's zero–one lawand theBorel–Cantelli lemma, that specifies that a certain type of event will eitheralmost surelyhappen or almost surely not happen. It is sometimes known as theSavage-Hewitt law for symmetric events. It is named afterEdwin... | https://en.wikipedia.org/wiki/Hewitt%E2%80%93Savage_zero%E2%80%93one_law |
In themathematical theoryoffunctional analysis, theKrein–Milman theoremis apropositionaboutcompactconvex setsinlocally convextopological vector spaces(TVSs).
Krein–Milman theorem[1]—Acompactconvexsubset of aHausdorfflocally convextopological vector spaceis equal to the closedconvex hullof itsextreme points.
This theo... | https://en.wikipedia.org/wiki/Krein%E2%80%93Milman_theorem |
Inmathematics, especially inprobability theoryandergodic theory, theinvariant sigma-algebrais asigma-algebraformed by sets which areinvariantunder agroup actionordynamical system. It can be interpreted as of being "indifferent" to the dynamics.
The invariant sigma-algebra appears in the study ofergodic systems, as wel... | https://en.wikipedia.org/wiki/Invariant_sigma-algebra |
SigSpec(acronym ofSIGnificance SPECtrum) is a statistical technique to provide the reliability of periodicities in a measured (noisy and not necessarily equidistant)time series.[1]It relies on the amplitudespectrumobtained by theDiscrete Fourier transform(DFT) and assigns a quantity called thespectral significance(freq... | https://en.wikipedia.org/wiki/SigSpec |
Inmathematicsandmultivariate statistics, thecentering matrix[1]is asymmetricandidempotent matrix, which when multiplied with a vector has the same effect as subtracting themeanof the components of the vector from every component of that vector.
Thecentering matrixof sizenis defined as then-by-nmatrix
whereIn{\display... | https://en.wikipedia.org/wiki/Centering_matrix |
Dykstra's algorithmis a method that computes a point in the intersection ofconvex sets, and is a variant of thealternating projectionmethod (also called theprojections onto convex setsmethod). In its simplest form, the method finds a point in the intersection of two convex sets by iteratively projecting onto each of t... | https://en.wikipedia.org/wiki/Dykstra%27s_projection_algorithm |
Inmathematics, aninvariant subspaceof alinear mappingT:V→Vi.e. from somevector spaceVto itself, is asubspaceWofVthat is preserved byT. More generally, an invariant subspace for a collection of linear mappings is a subspace preserved by each mapping individually.
Consider a vector spaceV{\displaystyle V}and a linear m... | https://en.wikipedia.org/wiki/Invariant_subspace |
Inlinear algebra,orthogonalizationis the process of finding asetoforthogonal vectorsthatspana particularsubspace. Formally, starting with alinearly independentset of vectors {v1, ... ,vk} in aninner product space(most commonly theEuclidean spaceRn), orthogonalization results in a set oforthogonalvectors {u1, ... ,uk} ... | https://en.wikipedia.org/wiki/Orthogonalization |
Inlinear algebra, thetraceof asquare matrixA, denotedtr(A),[1]is the sum of the elements on itsmain diagonal,a11+a22+⋯+ann{\displaystyle a_{11}+a_{22}+\dots +a_{nn}}. It is only defined for a square matrix (n×n).
The trace of a matrix is the sum of itseigenvalues(counted with multiplicities). Also,tr(AB) = tr(BA)for a... | https://en.wikipedia.org/wiki/Trace_(linear_algebra)#Properties |
Inmathematics,statistics,finance,[1]andcomputer science, particularly inmachine learningandinverse problems,regularizationis a process that converts theanswer to a problemto a simpler one. It is often used in solvingill-posed problemsor to preventoverfitting.[2]
Although regularization procedures can be divided in man... | https://en.wikipedia.org/wiki/Regularization_(mathematics)#Other_uses_of_regularization_in_statistics_and_machine_learning |
Inelectrical engineering, theaverage rectified value(ARV) of a quantity is theaverageof itsabsolute value. The ARV of an alternating current indicates which direct current would transport the same amount of electrical charge within the same period of time. On the other hand theRMSdescribes which direct current delivers... | https://en.wikipedia.org/wiki/Average_rectified_value |
Inmathematics,Pythagorean additionis abinary operationon thereal numbersthat computes the length of thehypotenuseof aright triangle, given its two sides. Like the more familiar addition and multiplication operations ofarithmetic, it is bothassociativeandcommutative.
This operation can be used in the conversion ofCarte... | https://en.wikipedia.org/wiki/Pythagorean_addition |
For the measurement of analternating currentthe signal is often converted into adirect currentof equivalent value, theroot mean square(RMS). Simple instrumentation and signal converters carry out this conversion by filtering the signal into anaverage rectified valueand applying a correction factor. The value of the cor... | https://en.wikipedia.org/wiki/True_RMS_converter |
Algorithms for calculating varianceplay a major role incomputational statistics. A key difficulty in the design of goodalgorithmsfor this problem is that formulas for thevariancemay involve sums of squares, which can lead tonumerical instabilityas well as toarithmetic overflowwhen dealing with large values.
A formula ... | https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance |
Instatistics, theresidual sum of squares(RSS), also known as thesum of squared residuals(SSR) or thesum of squared estimate of errors(SSE), is thesumof thesquaresofresiduals(deviations predicted from actual empirical values of data). It is a measure of the discrepancy between the data and an estimation model, such a... | https://en.wikipedia.org/wiki/Residual_sum_of_squares |
Ineconometricsand other applications of multivariatetime series analysis, avariance decompositionorforecast error variance decomposition(FEVD) is used to aid in the interpretation of avector autoregression(VAR) model once it has been fitted.[1]Thevariancedecomposition indicates the amount of information each variable c... | https://en.wikipedia.org/wiki/Variance_decomposition_of_forecast_errors |
Thehuman brainanatomicalregions are ordered following standardneuroanatomyhierarchies.Functional,connective, anddevelopmentalregions are listed in parentheses where appropriate.
Other areas that have been included in the limbic system include the:
2° (Spinomesencephalic tract→Superior colliculusofMidbrain tectum) | https://en.wikipedia.org/wiki/List_of_regions_in_the_human_brain |
Neural engineering(also known asneuroengineering) is a discipline withinbiomedical engineeringthat uses engineering techniques to understand, repair, replace, or enhance neural systems. Neural engineers are uniquely qualified to solve design problems at the interface of living neural tissue and non-living constructs.[1... | https://en.wikipedia.org/wiki/Neural_engineering |
Pulse-coupled networksorpulse-coupled neural networks(PCNNs) are neural models proposed by modeling a cat'svisual cortex, and developed for high-performancebiomimeticimage processing.[1]
In 1989, Eckhorn introduced a neural model to emulate the mechanism of cat's visual cortex.[2]The Eckhorn model provided a simple an... | https://en.wikipedia.org/wiki/Pulse-coupled_networks |
Anerve tractis a bundle of nerve fibers (axons) connectingnucleiof thecentral nervous system.[1][2][3]In theperipheral nervous system, this is known as anerve fascicle, and has associatedconnective tissue. The main nerve tracts in the central nervous system are of three types:association fibers,commissural fibers, andp... | https://en.wikipedia.org/wiki/Nerve_tract |
Inneuroanatomy, aneural pathwayis the connection formed byaxonsthat project fromneuronsto makesynapsesonto neurons in another location, to enableneurotransmission(the sending of a signal from one region of thenervous systemto another). Neurons are connected by a single axon, or by a bundle of axons known as anerve trac... | https://en.wikipedia.org/wiki/Neural_pathway |
Anerve plexusis aplexus(branching network) of intersectingnerves.[1]A nerve plexus is composed of afferent and efferent fibers that arise from the merging of the anterior rami of spinal nerves and blood vessels. There are fivespinal nerveplexuses, except in the thoracic region, as well as other forms ofautonomicplexuse... | https://en.wikipedia.org/wiki/Nerve_plexus |
Dual coneandpolar coneare closely related concepts inconvex analysis, a branch ofmathematics.
Thedual coneC*of asubsetCin alinear spaceXover thereals, e.g.Euclidean spaceRn, withdual spaceX*is the set
where⟨y,x⟩{\displaystyle \langle y,x\rangle }is theduality pairingbetweenXandX*, i.e.⟨y,x⟩=y(x){\displaystyle \langle... | https://en.wikipedia.org/wiki/Dual_cone |
Inmathematics,Farkas' lemmais a solvability theorem for a finitesystemoflinear inequalities. It was originally proven by the Hungarian mathematicianGyula Farkas.[1]Farkas'lemmais the key result underpinning thelinear programmingduality and has played a central role in the development ofmathematical optimization(alterna... | https://en.wikipedia.org/wiki/Farkas%27s_lemma |
Inmathematicsandstatistics,deviationserves as a measure to quantify the disparity between anobserved valueof a variable and another designated value, frequently the mean of that variable. Deviations with respect to thesample meanand thepopulation mean(or "true value") are callederrorsandresiduals, respectively. Thesign... | https://en.wikipedia.org/wiki/Deviation_(statistics) |
Instatistics,probable errordefines thehalf-rangeof an interval about acentral pointfor the distribution, such that half of the values from the distribution will lie within the interval and half outside.[1]Thus for asymmetric distributionit is equivalent to half theinterquartile range, or themedian absolute deviation. ... | https://en.wikipedia.org/wiki/Probable_error |
Themean absolute difference(univariate) is ameasure of statistical dispersionequal to the averageabsolute differenceof two independent values drawn from aprobability distribution. A related statistic is therelative mean absolute difference, which is the mean absolute difference divided by thearithmetic mean, and equal... | https://en.wikipedia.org/wiki/Mean_absolute_difference |
Empiricalmethods
Prescriptiveand policy
Convexityis a geometric property with a variety of applications ineconomics.[1]Informally, an economic phenomenon is convex when "intermediates (or combinations) are better than extremes". For example, an economic agent withconvex preferencespreferscombinationsof goods over ha... | https://en.wikipedia.org/wiki/Convexity_in_economics |
Ineconomics,non-convexityrefers to violations of theconvexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers withconvex preferences(that do not prefer extremes to in-between values) and convexbudget setsand on producers with convexproduction sets; for convex models, the predicte... | https://en.wikipedia.org/wiki/Non-convexity_(economics) |
This is alist of convexity topics, by Wikipedia page. | https://en.wikipedia.org/wiki/List_of_convexity_topics |
Moritz Werner Fenchel(German:[ˈfɛnçəl]; 3 May 1905 – 24 January 1988) was a German-Danishmathematicianknown for his contributions togeometryand tooptimization theory. Fenchel established the basic results ofconvex analysisand nonlinear optimization theory which would, in time, serve as the foundation fornonlinear prog... | https://en.wikipedia.org/wiki/Werner_Fenchel |
Inmathematical optimizationtheory,dualityor theduality principleis the principle thatoptimization problemsmay be viewed from either of two perspectives, theprimal problemor thedual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the pri... | https://en.wikipedia.org/wiki/Dual_problem |
In mathematics,Fenchel's duality theoremis a result in the theory of convex functions named afterWerner Fenchel.
Letƒbe aproper convex functiononRnand letgbe a proper concave function onRn. Then, if regularity conditions are satisfied,
whereƒ*is theconvex conjugateofƒ(also referred to as the Fenchel–Legendre transfor... | https://en.wikipedia.org/wiki/Fenchel%27s_duality_theorem |
Inmathematics, theLegendre transformation(orLegendre transform), first introduced byAdrien-Marie Legendrein 1787 when studying the minimal surface problem,[1]is aninvolutivetransformationonreal-valued functions that areconvexon a real variable. Specifically, if a real-valued multivariable function is convex on one of i... | https://en.wikipedia.org/wiki/Legendre_transformation |
Inmathematics,Young's inequality for productsis amathematical inequalityabout the product of two numbers.[1]The inequality is named afterWilliam Henry Youngand should not be confused withYoung's convolution inequality.
Young's inequality for products can be used to proveHölder's inequality. It is also widely used to e... | https://en.wikipedia.org/wiki/Young%27s_inequality_for_products |
Inmathematics, areal-valued functionis calledconvexif theline segmentbetween any two distinct points on thegraph of the functionlies above or on the graph between the two points. Equivalently, a function is convex if itsepigraph(the set of points on or above the graph of the function) is aconvex set.
In simple terms, ... | https://en.wikipedia.org/wiki/Convex_surface |
Inmathematics,Farkas' lemmais a solvability theorem for a finitesystemoflinear inequalities. It was originally proven by the Hungarian mathematicianGyula Farkas.[1]Farkas'lemmais the key result underpinning thelinear programmingduality and has played a central role in the development ofmathematical optimization(alterna... | https://en.wikipedia.org/wiki/Farkas%27_lemma |
In mathematics, and particularly infunctional analysis,Fichera's existence principleis an existence and uniqueness theorem for solution offunctional equations, proved byGaetano Ficherain 1954.[1]More precisely, given a generalvector spaceVand twolinear mapsfrom itontotwoBanach spaces, the principle states necessary and... | https://en.wikipedia.org/wiki/Fichera%27s_existence_principle |
TheM. Riesz extension theoremis atheoreminmathematics, proved byMarcel Riesz[1]during his study of theproblem of moments.[2]
LetE{\displaystyle E}be arealvector space,F⊂E{\displaystyle F\subset E}be avector subspace, andK⊂E{\displaystyle K\subset E}be aconvex cone.
Alinear functionalϕ:F→R{\displaystyle \phi :F\to \ma... | https://en.wikipedia.org/wiki/M._Riesz_extension_theorem |
Ingeometry, thehyperplane separation theoremis a theorem aboutdisjointconvex setsinn-dimensionalEuclidean space. There are several rather similar versions. In one version of the theorem, if both these sets areclosedand at least one of them iscompact, then there is ahyperplanein between them and even two parallel hyperp... | https://en.wikipedia.org/wiki/Separating_axis_theorem |
In mathematics, specifically infunctional analysisandHilbert spacetheory,vector-valued Hahn–Banach theoremsare generalizations of theHahn–Banach theoremsfrom linear functionals (which are always valued in thereal numbersR{\displaystyle \mathbb {R} }or thecomplex numbersC{\displaystyle \mathbb {C} }) to linear operator... | https://en.wikipedia.org/wiki/Vector-valued_Hahn%E2%80%93Banach_theorems |
Inconvex analysis,Popoviciu's inequalityis aninequalityaboutconvex functions. It is similar toJensen's inequalityand was found in 1965 byTiberiu Popoviciu,[1][2]a Romanian mathematician.
Letfbe a function from an intervalI⊆R{\displaystyle I\subseteq \mathbb {R} }toR{\displaystyle \mathbb {R} }. Iffisconvex, then for a... | https://en.wikipedia.org/wiki/Popoviciu%27s_inequality |
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