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Approximation theory | In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. What is meant by best and simpler will depend on the application.
A closely related topic is the approximation of functions by gener... |
Comparison of linear algebra libraries | The following tables provide a comparison of linear algebra software libraries, either specialized or general purpose libraries with significant linear algebra coverage.
== Dense linear algebra ==
=== General information ===
=== Matrix types and operations ===
Matrix types (special types like bidiagonal/tridiagon... |
Dominance-based rough set approach | The dominance-based rough set approach (DRSA) is an extension of rough set theory for multi-criteria decision analysis (MCDA), introduced by Greco, Matarazzo and Słowiński. The main change compared to the classical rough sets is the substitution for the indiscernibility relation by a dominance relation, which permits o... |
Predictable stopping time | In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time) is a specific type of "random time": a random variable whose value is interpreted as the time at which a given stochastic process exhibits a certain behav... |
Generalized Gauss–Newton method | The generalized Gauss–Newton method is a generalization of the least-squares method originally described by Carl Friedrich Gauss and of Newton's method due to Isaac Newton to the case of constrained nonlinear least-squares problems.
== References == |
Constructing skill trees | Constructing skill trees (CST) is a hierarchical reinforcement learning algorithm which can build skill trees from a set of sample solution trajectories obtained from demonstration. CST uses an incremental MAP (maximum a posteriori) change point detection algorithm to segment each demonstration trajectory into skills... |
Conflation (statistics) | In statistics, coalescence refers to the merging of independent probability density functions. It contrasts with the simpler, erroneous approach called conflation.
== Conflation ==
Conflation refers to the merging of independent probability density functions using simple multiplication of the constituent densities. T... |
Probabilistic metric space | In mathematics, probabilistic metric spaces are a generalization of metric spaces where the distance no longer takes values in the non-negative real numbers R ≥ 0, but in distribution functions.
Let D+ be the set of all probability distribution functions F such that F(0) = 0 (F is a nondecreasing, left continuous mappi... |
Category of modules | In algebra, given a ring R, the category of left modules over R is the category whose objects are all left modules over R and whose morphisms are all module homomorphisms between left R-modules. For example, when R is the ring of integers Z, it is the same thing as the category of abelian groups. The category of right ... |
Central tendency | In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.
Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s.
The most common measures of central tendency are the arithmetic mean... |
Crouzeix__apos__s conjecture | Crouzeix's conjecture is an unsolved problem in matrix analysis. It was proposed by Michel Crouzeix in 2004, and it can be stated as follows:
‖
f
(
A
)
‖
≤
2
sup
z
∈
W
... |
Phillips–Perron test | In statistics, the Phillips–Perron test (named after Peter C. B. Phillips and Pierre Perron) is a unit root test. That is, it is used in time series analysis to test the null hypothesis that a time series is integrated of order 1. It builds on the Dickey–Fuller test of the null hypothesis
ρ
... |
The Groundwork | The Groundwork was a privately held technology firm, run by Michael Slaby, that was formed in June 2014. Campaign finance disclosures revealed that Hillary Clinton's presidential campaign was a client of the Groundwork. Most of the Groundwork's employees are back-end software developers with experience at tech firms li... |
Specht__apos__s theorem | In mathematics, Specht's theorem gives a necessary and sufficient condition for two complex matrices to be unitarily equivalent. It is named after Wilhelm Specht, who proved the theorem in 1940.
Two matrices A and B with complex number entries are said to be unitarily equivalent if there exists a unitary matrix U such ... |
Node2vec | node2vec is an algorithm to generate vector representations of nodes on a graph. The node2vec framework learns low-dimensional representations for nodes in a graph through the use of random walks through a graph starting at a target node. It is useful for a variety of machine learning applications. node2vec follows the... |
Ordered Key-Value Store | An Ordered Key-Value Store (OKVS) is a type of data storage paradigm that can support multi-model database. An OKVS is an ordered mapping of bytes to bytes. An OKVS will keep the key-value pairs sorted by the key lexicographic order. OKVS systems provides different set of features and performance trade-offs. Most of th... |
KPZ fixed point | In probability theory, the KPZ fixed point is a Markov field and conjectured to be a universal limit of a wide range of stochastic models forming the universality class of a non-linear stochastic partial differential equation called the KPZ equation. Even though the universality class was already introduced in 1986 wit... |
Imitation learning | Imitation learning is a paradigm in reinforcement learning, where an agent learns to perform a task by supervised learning from expert demonstrations. It is also called learning from demonstration and apprenticeship learning.
It has been applied to underactuated robotics, self-driving cars, quadcopter navigation, helic... |
Brown–Forsythe test | The Brown–Forsythe test is a statistical test for the equality of group variances based on performing an Analysis of Variance (ANOVA) on a transformation of the response variable. When a one-way ANOVA is performed, samples are assumed to have been drawn from distributions with equal variance. If this assumption is not ... |
Conjugate transpose | In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an
m
×
n
{\displaystyle m\times n}
complex matrix
A
{\displaystyle \mathbf {A} }
is an
n
... |
Combinatorial data analysis | 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 given combinatorial construct reflects the observed data, or to search for a suitable combinatorial construct that does fit the data.
==... |
Digital Library of Mathematical Functions | The Digital Library of Mathematical Functions (DLMF) is an online project at the National Institute of Standards and Technology (NIST) to develop a database of mathematical reference data for special functions and their applications. It is intended as an update of Abramowitz's and Stegun's Handbook of Mathematical Func... |
Weight initialization | In deep learning, weight initialization or parameter initialization describes the initial step in creating a neural network. A neural network contains trainable parameters that are modified during training: weight initialization is the pre-training step of assigning initial values to these parameters.
The choice of wei... |
Mixture of experts | Mixture of experts (MoE) is a machine learning technique where multiple expert networks (learners) are used to divide a problem space into homogeneous regions. MoE represents a form of ensemble learning. They were also called committee machines.
== Basic theory ==
MoE always has the following components, but they are... |
Disorder problem | In the study of stochastic processes in mathematics, a disorder problem or quickest detection problem (formulated by Kolmogorov) is the problem of using ongoing observations of a stochastic process to detect as soon as possible when the probabilistic properties of the process have changed. This is a type of change dete... |
Donsker classes | A class of functions is considered a Donsker class if it satisfies Donsker's theorem, a functional generalization of the central limit theorem.
== Definition ==
Let
F
{\displaystyle {\mathcal {F}}}
be a collection of square integr... |
F-test of equality of variances | In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance.
Notionally, any F-test can be regarded as a comparison of two variances, but the specific case being discussed in this article is that of two populations, where the test statistic use... |
Artificial intelligence content detection | Artificial intelligence detection software aims to determine whether some content (text, image, video or audio) was generated using artificial intelligence (AI). However, this software is often unreliable.
== Accuracy issues ==
Many AI detection tools have been shown to be unreliable when generating AI-generated text... |
Fourth Industrial Revolution | "Fourth Industrial Revolution", "4IR", or "Industry 4.0", is a neologism describing rapid technological advancement in the 21st century. It follows the Third Industrial Revolution (the "Information Age"). The term was popularised in 2016 by Klaus Schwab, the World Economic Forum founder and former executive chairman, w... |
Quasi-stationary distribution | In probability a quasi-stationary distribution is a random process that admits one or several absorbing states that are reached almost surely, but is initially distributed such that it can evolve for a long time without reaching it. The most common example is the evolution of a population: the only equilibrium is when... |
Dependence relation | In mathematics, a dependence relation is a binary relation which generalizes the relation of linear dependence.
Let
X
{\displaystyle X}
be a set. A (binary) relation
◃
{\displaystyle \triangleleft }
between an element
... |
Differential-algebraic system of equations | In mathematics, a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system.
The set of the solutions of such a system is a differential algebraic variety, and corresponds to an ideal in a differential... |
Decision tree pruning | Pruning is a data compression technique in machine learning and search algorithms that reduces the size of decision trees by removing sections of the tree that are non-critical and redundant to classify instances. Pruning reduces the complexity of the final classifier, and hence improves predictive accuracy by the redu... |
Complex random variable | In probability theory and statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take are complex numbers. Complex random variables can always be considered as pairs of real random variables: their real and ima... |
Transition kernel | In the mathematics of probability, a transition kernel or kernel is a function in mathematics that has different applications. Kernels can for example be used to define random measures or stochastic processes. The most important example of kernels are the Markov kernels.
== Definition ==
Let
(... |
Deep reinforcement learning | Deep reinforcement learning (DRL) is a subfield of machine learning that combines principles of reinforcement learning (RL) and deep learning. It involves training agents to make decisions by interacting with an environment to maximize cumulative rewards, while using deep neural networks to represent policies, value fu... |
Catalog of articles in probability theory | This page lists articles related to probability theory. In particular, it lists many articles corresponding to specific probability distributions. Such articles are marked here by a code of the form (X:Y), which refers to number of random variables involved and the type of the distribution. For example (2:DC) indicates... |
Markov chain central limit theorem | In the mathematical theory of random processes, the Markov chain central limit theorem has a conclusion somewhat similar in form to that of the classic central limit theorem (CLT) of probability theory, but the quantity in the role taken by the variance in the classic CLT has a more complicated definition. See also the... |
Haynsworth inertia additivity formula | In mathematics, the Haynsworth inertia additivity formula, discovered by Emilie Virginia Haynsworth (1916–1985), concerns the number of positive, negative, and zero eigenvalues of a Hermitian matrix and of block matrices into which it is partitioned.
The inertia of a Hermitian matrix H is defined as the ordered triple
... |
Statistical model specification | In statistics, model specification is part of the process of building a statistical model: specification consists of selecting an appropriate functional form for the model and choosing which variables to include. For example, given personal income
y
{\displaystyle y}
together... |
Decision list | Decision lists are a representation for Boolean functions which can be easily learnable from examples. Single term decision lists are more expressive than disjunctions and conjunctions; however, 1-term decision lists are less expressive than the general disjunctive normal form and the conjunctive normal form.
The lang... |
Exponential dispersion model | In probability and statistics, the class of exponential dispersion models (EDM), also called exponential dispersion family (EDF), is a set of probability distributions that represents a generalisation of the natural exponential family.
Exponential dispersion models play an important role in statistical theory, in part... |
Choi__apos__s theorem on completely positive maps | In mathematics, Choi's theorem on completely positive maps is a result that classifies completely positive maps between finite-dimensional (matrix) C*-algebras. The theorem is due to Man-Duen Choi. An infinite-dimensional algebraic generalization of Choi's theorem is known as Belavkin's "Radon–Nikodym" theorem for comp... |
Blumenthal__apos__s zero–one law | In the mathematical theory of probability, Blumenthal's zero–one law, named after Robert McCallum Blumenthal, is a statement about the nature of the beginnings of right continuous Feller process. Loosely, it states that any right continuous Feller process on
[
0
,
∞
... |
Kruskal–Wallis test | The Kruskal–Wallis test by ranks, Kruskal–Wallis
H
{\displaystyle H}
test (named after William Kruskal and W. Allen Wallis), or one-way ANOVA on ranks is a non-parametric statistical test for testing whether samples originate from the same distribution. It is used for compari... |
EfficientNet | EfficientNet is a family of convolutional neural networks (CNNs) for computer vision published by researchers at Google AI in 2019. Its key innovation is compound scaling, which uniformly scales all dimensions of depth, width, and resolution using a single parameter.
EfficientNet models have been adopted in various com... |
Hardy distribution | In probability theory and statistics, the Hardy distribution is a discrete probability distribution that expresses the probability of the hole score for a given golf player. It is based on Hardy's (Hardy, 1945) basic assumption that there are three types of shots:
good
(
G
)
... |
List of numerical analysis topics | This is a list of numerical analysis topics.
== General ==
Validated numerics
Iterative method
Rate of convergence — the speed at which a convergent sequence approaches its limit
Order of accuracy — rate at which numerical solution of differential equation converges to exact solution
Series acceleration — methods to ... |
Vector quantization | Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. Developed in the early 1980s by Robert M. Gray, it was originally used for data compression. It works by dividing a large set of poin... |
Wasserstein GAN | The Wasserstein Generative Adversarial Network (WGAN) is a variant of generative adversarial network (GAN) proposed in 2017 that aims to "improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches".
Compared with the... |
Raleigh plot | Raleigh plots, or Rayleigh plots (also called circlegrams and closely related to circular histograms, phasor diagrams, and wind roses), are statistical graphics that serve as graphical representations for a Raleigh test that map a mean vector to a circular plot. Raleigh plots have many applications in the field of chro... |
Chauvenet__apos__s criterion | In statistical theory, Chauvenet's criterion (named for William Chauvenet) is a means of assessing whether one piece of experimental data from a set of observations is likely to be spurious – an outlier.
== Derivation ==
The idea behind Chauvenet's criterion finds a probability band that reasonably contains all n sam... |
AI_ML Development Platform | "AI/ML development platforms—such as PyTorch and Hugging Face—are software ecosystems that support the development and deployment of artificial intelligence (AI) and machine learning (ML) models." These platforms provide tools, frameworks, and infrastructure to streamline workflows for developers, data scientists, and ... |
Sequence analysis in social sciences | In social sciences, sequence analysis (SA) is concerned with the analysis of sets of categorical sequences that typically describe longitudinal data. Analyzed sequences are encoded representations of, for example, individual life trajectories such as family formation, school to work transitions, working careers, but th... |
Bayesian learning mechanisms | Bayesian learning mechanisms are probabilistic causal models used in computer science to research the fundamental underpinnings of machine learning, and in cognitive neuroscience, to model conceptual development.
Bayesian learning mechanisms have also been used in economics and cognitive psychology to study social lear... |
Spread of a matrix | In mathematics, and more specifically matrix theory, the spread of a matrix is the largest distance in the complex plane between any two eigenvalues of the matrix.
== Definition ==
Let
A
{\displaystyle A}
be a square matrix with eigenvalues
... |
Genetic Algorithm for Rule Set Production | Genetic Algorithm for Rule Set Production (GARP) is a computer program based on genetic algorithm that creates
ecological niche models for species. The generated models describe environmental conditions (precipitation, temperatures, elevation, etc.) under which the species should be able to maintain populations. As in... |
Eigendecomposition of a matrix | In linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decompositi... |
Moran process | A Moran process or Moran model is a simple stochastic process used in biology to describe finite populations. The process is named after Patrick Moran, who first proposed the model in 1958. It can be used to model variety-increasing processes such as mutation as well as variety-reducing effects such as genetic drift an... |
Gerald Tesauro | Gerald J. "Gerry" Tesauro is an American computer scientist and a researcher at IBM, known for his development of TD-Gammon, a backgammon program that taught itself to play at a world-championship level through self-play and temporal difference learning, an early success in reinforcement learning and neural networks. H... |
Directional component analysis | Directional component analysis (DCA) is a statistical method used in climate science for identifying representative patterns of variability in space-time data-sets such as historical climate observations, weather prediction ensembles or climate ensembles.
The first DCA pattern is a pattern of weather or climate variab... |
Stochastic thermodynamics | Stochastic thermodynamics is an emergent field of research in statistical mechanics that uses stochastic variables to better understand the non-equilibrium dynamics present in many microscopic systems such as colloidal particles, biopolymers (e.g. DNA, RNA, and proteins), enzymes, and molecular motors.
== Overview ==... |
L1-norm principal component analysis | L1-norm principal component analysis (L1-PCA) is a general method for multivariate data analysis.
L1-PCA is often preferred over standard L2-norm principal component analysis (PCA) when the analyzed data may contain outliers (faulty values or corruptions), as it is believed to be robust.
Both L1-PCA and standard PCA se... |
Cost-sensitive machine learning | Cost-sensitive machine learning is an approach within machine learning that considers varying costs associated with different types of errors. This method diverges from traditional approaches by introducing a cost matrix, explicitly specifying the penalties or benefits for each type of prediction error. The inherent di... |
Dynkin–Kruskal sequence | The Kruskal count (also known as Kruskal's principle, Dynkin–Kruskal count, Dynkin's counting trick, Dynkin's card trick, coupling card trick or shift coupling) is a probabilistic concept originally demonstrated by the Russian mathematician Evgenii Borisovich Dynkin in the 1950s or 1960s discussing coupling effects and... |
Sub-probability measure | In the mathematical theory of probability and measure, a sub-probability measure is a measure that is closely related to probability measures. While probability measures always assign the value 1 to the underlying set, sub-probability measures assign a value lesser than or equal to 1 to the underlying set.
== Definit... |
Risk-limiting audit | A risk-limiting audit (RLA) is a post-election tabulation auditing procedure which can limit the risk that the reported outcome in an election contest is incorrect. It generally involves (1) storing voter-verified paper ballots securely until they can be checked,
and (2) manually examining a statistical sample of the p... |
High-dimensional statistics | In statistical theory, the field of high-dimensional statistics studies data whose dimension is larger (relative to the number of datapoints) than typically considered in classical multivariate analysis. The area arose owing to the emergence of many modern data sets in which the dimension of the data vectors may be co... |
Extension neural network | Extension neural network is a pattern recognition method found by M. H. Wang and C. P. Hung in 2003 to classify instances of data sets. Extension neural network is composed of artificial neural network and extension theory concepts. It uses the fast and adaptive learning capability of neural network and correlation est... |
Spark (mathematics) | In mathematics, more specifically in linear algebra, the spark of a
m
×
n
{\displaystyle m\times n}
matrix
A
{\displaystyle A}
is the smallest integer
k
{\displaystyle k}
s... |
Eigenvalue perturbation | In mathematics, an eigenvalue perturbation problem is that of finding the eigenvectors and eigenvalues of a system
A
x
=
λ
x
{\displaystyle Ax=\lambda x}
that is perturbed from one with known eigenvectors and eigenvalues
... |
Adversarial machine learning | Adversarial machine learning is the study of the attacks on machine learning algorithms, and of the defenses against such attacks. A survey from May 2020 revealed practitioners' common feeling for better protection of machine learning systems in industrial applications.
Machine learning techniques are mostly designed t... |
Category of Markov kernels | In mathematics, the category of Markov kernels, often denoted Stoch, is the category whose objects are measurable spaces and whose morphisms are Markov kernels.
It is analogous to the category of sets and functions, but where the arrows can be interpreted as being stochastic.
Several variants of this category are used... |
Cochran__apos__s C test | Cochran's
C
{\displaystyle C}
test, named after William G. Cochran, is a one-sided upper limit variance outlier statistical test . The C test is used to decide if a single estimate of a variance (or a standard deviation) is significantly larger than a group of variances (or s... |
DALL-E | DALL-E, DALL-E 2, and DALL-E 3 (stylised DALL·E) are text-to-image models developed by OpenAI using deep learning methodologies to generate digital images from natural language descriptions known as prompts.
The first version of DALL-E was announced in January 2021. In the following year, its successor DALL-E 2 was rel... |
Cayley–Hamilton theorem | In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex numbers or the integers) satisfies its own characteristic equation.
The characteristic polynomial of an n × n matr... |
Total variation distance of probability measures | In probability theory, the total variation distance is a statistical distance between probability distributions, and is sometimes called the statistical distance, statistical difference or variational distance.
== Definition ==
Consider a measurable space
(
Ω
,
... |
Friedman test | The Friedman test is a non-parametric statistical test developed by Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row (or block) together, then considering the values of ranks by colum... |
Zero-shot learning | Zero-shot learning (ZSL) is a problem setup in deep learning where, at test time, a learner observes samples from classes which were not observed during training, and needs to predict the class that they belong to. The name is a play on words based on the earlier concept of one-shot learning, in which classification ca... |
Competitive learning | Competitive learning is a form of unsupervised learning in artificial neural networks, in which nodes compete for the right to respond to a subset of the input data. A variant of Hebbian learning, competitive learning works by increasing the specialization of each node in the network. It is well suited to finding clus... |
False precision | False precision (also called overprecision, fake precision, misplaced precision, excess precision, and spurious precision) occurs when numerical data are presented in a manner that implies better precision than is justified; since precision is a limit to accuracy (in the ISO definition of accuracy), this often leads to... |
Computer-assisted proof | A computer-assisted proof is a mathematical proof that has been at least partially generated by computer.
Most computer-aided proofs to date have been implementations of large proofs-by-exhaustion of a mathematical theorem. The idea is to use a computer program to perform lengthy computations, and to provide a proof th... |
Fast multipole method | The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the n-body problem. It does this by expanding the system Green's function using a multipole expansion, which allows one to group sources that lie close together and treat them as if they are ... |
Cyclical monotonicity | In mathematics, cyclical monotonicity is a generalization of the notion of monotonicity to the case of vector-valued function.
== Definition ==
Let
⟨
⋅
,
⋅
⟩
{\displaystyle \langle \cdot ,\cdot \rangle }
denote the inner product on an inner p... |
Dunnett__apos__s test | In statistics, Dunnett's test is a multiple comparison procedure developed by Canadian statistician Charles Dunnett to compare each of a number of treatments with a single control. Multiple comparisons to a control are also referred to as many-to-one comparisons.
== History ==
Dunnett's test was developed in 1955; an... |
Evolutionary multimodal optimization | In applied mathematics, multimodal optimization deals with optimization tasks that involve finding all or most of the multiple (at least locally optimal) solutions of a problem, as opposed to a single best solution. Evolutionary multimodal optimization is a branch of evolutionary computation, which is closely related t... |
Càdlàg | In mathematics, a càdlàg (French: continue à droite, limite à gauche), RCLL ("right continuous with left limits"), or corlol ("continuous on (the) right, limit on (the) left") function is a function defined on the real numbers (or a subset of them) that is everywhere right-continuous and has left limits everywhere. Càd... |
Resource-dependent branching process | A branching process (BP) (see e.g. Jagers (1975)) is a mathematical model to describe the development of a population. Here population is meant in a general sense, including a human population, animal populations, bacteria and others which reproduce in a biological sense, cascade process, or particles which split in... |
Error level analysis | Error level analysis (ELA) is the analysis of compression artifacts in digital data with lossy compression such as JPEG.
== Principles ==
When used, lossy compression is normally applied uniformly to a set of data, such as an image, resulting in a uniform level of compression artifacts.
Alternatively, the data may co... |
Artificial intelligence | Artificial intelligence (AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in computer science that develops and studies methods and software that enable m... |
Category__colon__Google DeepMind | This category contains major Google DeepMind inventions, generally open source |
Butcher group | In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by Hairer & Wanner (1974), is an infinite-dimensional Lie group first introduced in numerical analysis to study solutions of non-linear ordinary differential equations by the Runge–Kutta method. It arose from an algebraic for... |
Antieigenvalue theory | In applied mathematics, antieigenvalue theory was developed by Karl Gustafson from 1966 to 1968. The theory is applicable to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization.
The antieigenvectors
x
{\displaystyle x}
are the vectors most tu... |
Technology mining | Tech mining or technology mining refers to applying text mining methods to technical documents. For patent analysis purposes, it is named ‘patent mining’. Porter, as one of the pioneers in technology mining, defined ‘tech mining’ in his book as follows: “the application of text mining tools to science and technology in... |
Biomedical data science | Biomedical data science is a multidisciplinary field which leverages large volumes of data to promote biomedical innovation and discovery. Biomedical data science draws from various fields including Biostatistics, Biomedical informatics, and machine learning, with the goal of understanding biological and medical data. ... |
GCD matrix | In mathematics, a greatest common divisor matrix (sometimes abbreviated as GCD matrix) is a matrix that may also be referred to as Smith's matrix. The study was initiated by H.J.S. Smith (1875). A new inspiration was begun from the paper of Bourque & Ligh (1992). This led to intensive investigations on singularity and... |
Sargan–Hansen test | The Sargan–Hansen test or Sargan's
J
{\displaystyle J}
test is a statistical test used for testing over-identifying restrictions in a statistical model. It was proposed by John Denis Sargan in 1958, and several variants were derived by him in 1975. Lars Peter Hansen re-worked... |
Radial basis function network | In the field of mathematical modeling, a radial basis function network is an artificial neural network that uses radial basis functions as activation functions. The output of the network is a linear combination of radial basis functions of the inputs and neuron parameters. Radial basis function networks have many uses,... |
Stochastic analysis on manifolds | In mathematics, stochastic analysis on manifolds or stochastic differential geometry is the study of stochastic analysis over smooth manifolds. It is therefore a synthesis of stochastic analysis (the extension of calculus to stochastic processes) and of differential geometry.
The connection between analysis and stochas... |
Kantorovich theorem | The Kantorovich theorem, or Newton–Kantorovich theorem, is a mathematical statement on the semi-local convergence of Newton's method. It was first stated by Leonid Kantorovich in 1948. It is similar to the form of the Banach fixed-point theorem, although it states existence and uniqueness of a zero rather than a fixed ... |
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