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In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as convergence rate, precision, robustness and general performance.
Here some test functions are presented with the aim of giving an idea about the different situations that op... | Wikipedia/Keane's_bump_function |
Estimation of distribution algorithms (EDAs), sometimes called probabilistic model-building genetic algorithms (PMBGAs), are stochastic optimization methods that guide the search for the optimum by building and sampling explicit probabilistic models of promising candidate solutions. Optimization is viewed as a series o... | Wikipedia/Estimation_of_distribution_algorithm |
In computer science and operations research, a memetic algorithm (MA) is an extension of an evolutionary algorithm (EA) that aims to accelerate the evolutionary search for the optimum. An EA is a metaheuristic that reproduces the basic principles of biological evolution as a computer algorithm in order to solve challen... | Wikipedia/Memetic_algorithm |
In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as convergence rate, precision, robustness and general performance.
Here some test functions are presented with the aim of giving an idea about the different situations that op... | Wikipedia/Test_functions_for_optimization |
The population model of an evolutionary algorithm (EA) describes the structural properties of its population to which its members are subject. A population is the set of all proposed solutions of an EA considered in one iteration, which are also called individuals according to the biological role model. The individuals... | Wikipedia/Population_model_(evolutionary_algorithm) |
Crossover in evolutionary algorithms and evolutionary computation, also called recombination, is a genetic operator used to combine the genetic information of two parents to generate new offspring. It is one way to stochastically generate new solutions from an existing population, and is analogous to the crossover that... | Wikipedia/Crossover_(evolutionary_algorithm) |
The Fly Algorithm is a computational method within the field of evolutionary algorithms, designed for direct exploration of 3D spaces in applications such as computer stereo vision, robotics, and medical imaging. Unlike traditional image-based stereovision, which relies on matching features to construct 3D information,... | Wikipedia/Fly_algorithm |
Selection is a genetic operator in an evolutionary algorithm (EA). An EA is a metaheuristic inspired by biological evolution and aims to solve challenging problems at least approximately. Selection has a dual purpose: on the one hand, it can choose individual genomes from a population for subsequent breeding (e.g., usi... | Wikipedia/Selection_(evolutionary_algorithm) |
In mathematical optimization, the firefly algorithm is a metaheuristic proposed by Xin-She Yang and inspired by the flashing behavior of fireflies.
== Algorithm ==
In pseudocode the algorithm can be stated as:
Begin
1) Objective function:
f
(
x
... | Wikipedia/Firefly_algorithm |
In computer science and operations research, Genetic fuzzy systems are fuzzy systems constructed by using genetic algorithms or genetic programming, which mimic the process of natural evolution, to identify its structure and parameter.
When it comes to automatically identifying and building a fuzzy system, given the hi... | Wikipedia/Genetic_fuzzy_systems |
In mathematics and computer science, an algorithm ( ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use co... | Wikipedia/Computer_algorithm |
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,... | Wikipedia/Radial_basis_network |
In mathematics a radial basis function (RBF) is a real-valued function
φ
{\textstyle \varphi }
whose value depends only on the distance between the input and some fixed point, either the origin, so that
φ
(
x
... | Wikipedia/Radial_basis_functions |
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives (differentiability class) it has over its domain.
A function of class
C
k
{\displaystyle C^{k}}
is a fu... | Wikipedia/Smooth_approximation |
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation
f
(
x
)
=
L
1
+
e
−
... | Wikipedia/Standard_logistic_function |
Communication-avoiding algorithms minimize movement of data within a memory hierarchy for improving its running-time and energy consumption. These minimize the total of two costs (in terms of time and energy): arithmetic and communication. Communication, in this context refers to moving data, either between levels of m... | Wikipedia/Communication-avoiding_algorithm |
The Academy of Military Sciences (Chinese: 中国人民解放军军事科学院) is the highest-level research institute of the People's Liberation Army (PLA). It is headquartered in Beijing. The academy was founded in March 1958 and as of 2002, its staff included approximately 500 researchers, making it the largest research institution in th... | Wikipedia/People's_Liberation_Army_Academy_of_Military_Sciences |
Interior-point methods (also referred to as barrier methods or IPMs) are algorithms for solving linear and non-linear convex optimization problems. IPMs combine two advantages of previously-known algorithms:
Theoretically, their run-time is polynomial—in contrast to the simplex method, which has exponential run-time i... | Wikipedia/Interior_point_method |
The Bradley–Terry model is a probability model for the outcome of pairwise comparisons between items, teams, or objects. Given a pair of items i and j drawn from some population, it estimates the probability that the pairwise comparison i > j turns out true, as
where pi is a positive real-valued score assigned to indi... | Wikipedia/Plackett–Luce_model |
Reinforcement learning (RL) is an interdisciplinary area of machine learning and optimal control concerned with how an intelligent agent should take actions in a dynamic environment in order to maximize a reward signal. Reinforcement learning is one of the three basic machine learning paradigms, alongside supervised le... | Wikipedia/Exploration_(reinforcement_learning) |
The Bradley–Terry model is a probability model for the outcome of pairwise comparisons between items, teams, or objects. Given a pair of items i and j drawn from some population, it estimates the probability that the pairwise comparison i > j turns out true, as
where pi is a positive real-valued score assigned to indi... | Wikipedia/Bradley–Terry_model |
The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The s... | Wikipedia/Statistical_entropy |
Inductive reasoning refers to a variety of methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but with some degree of probability. Unlike deductive reasoning (such as mathematical induction), where the conclusion is certain, given the premises are correct, inductive r... | Wikipedia/Inductive_inference |
Algorithmic information theory (AIT) is a branch of theoretical computer science that concerns itself with the relationship between computation and information of computably generated objects (as opposed to stochastically generated), such as strings or any other data structure. In other words, it is shown within algori... | Wikipedia/Algorithmic_Information_Theory |
In computability theory, super-recursive algorithms are posited as a generalization of hypercomputation: hypothetical algorithms that are more powerful, that is, compute more than Turing machines.
The term was introduced by Mark Burgin, whose book Super-recursive algorithms develops their theory and presents several ma... | Wikipedia/Super-recursive_algorithm |
System integration is defined in engineering as the process of bringing together the component sub-systems into one system (an aggregation of subsystems cooperating so that the system is able to deliver the overarching functionality) and ensuring that the subsystems function together as a system, and in information tec... | Wikipedia/Systems_integration |
The core idea of artificial intelligence systems integration is making individual software components, such as speech synthesizers, interoperable with other components, such as common sense knowledgebases, in order to create larger, broader and more capable A.I. systems. The main methods that have been proposed for int... | Wikipedia/Constructionist_design_methodology |
The hierarchical hidden Markov model (HHMM) is a statistical model derived from the hidden Markov model (HMM). In an HHMM, each state is considered to be a self-contained probabilistic model. More precisely, each state of the HHMM is itself an HHMM.
HHMMs and HMMs are useful in many fields, including pattern recognitio... | Wikipedia/Hierarchical_hidden_Markov_model |
The layered hidden Markov model (LHMM) is a statistical model derived from the hidden Markov model (HMM).
A layered hidden Markov model (LHMM) consists of N levels of HMMs, where the HMMs on level i + 1 correspond to observation symbols or probability generators at level i.
Every level i of the LHMM consists of Ki HMM... | Wikipedia/Layered_hidden_Markov_model |
The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time, given the history of evidence. The process is also known as filtering. The forward algorithm is closely related to, but distinct from, the Viterbi algorithm.
== I... | Wikipedia/Forward_algorithm |
A trellis is a graph whose nodes are ordered into vertical slices (time) with every node at almost every time connected to at least one node at an earlier and at least one node at a later time. The earliest and latest times in the trellis have only one node (hence the "almost" in the preceding sentence).
Trellises are ... | Wikipedia/Trellis_(graph) |
A hidden semi-Markov model (HSMM) is a statistical model with the same structure as a hidden Markov model except that the unobservable process is semi-Markov rather than Markov. This means that the probability of there being a change in the hidden state depends on the amount of time that has elapsed since entry into th... | Wikipedia/Hidden_semi-Markov_model |
In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property). Generally, this assumption enables reasoning and computation... | Wikipedia/Markov_model |
The forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations/emissions
o
1
:
T
:=
... | Wikipedia/Forward-backward_algorithm |
In statistics, a maximum-entropy Markov model (MEMM), or conditional Markov model (CMM), is a graphical model for sequence labeling that combines features of hidden Markov models (HMMs) and maximum entropy (MaxEnt) models. An MEMM is a discriminative model that extends a standard maximum entropy classifier by assuming ... | Wikipedia/Maximum_entropy_Markov_model |
Time-inhomogeneous hidden Bernoulli model (TI-HBM) is an alternative to hidden Markov model (HMM) for automatic speech recognition. Contrary to HMM, the state transition process in TI-HBM is not a Markov-dependent process, rather it is a generalized Bernoulli (an independent) process. This difference leads to eliminati... | Wikipedia/Hidden_Bernoulli_model |
The following outline is provided as an overview of, and topical guide to, machine learning:
Machine learning (ML) is a subfield of artificial intelligence within computer science that evolved from the study of pattern recognition and computational learning theory. In 1959, Arthur Samuel defined machine learning as a "... | Wikipedia/Machine_learning_algorithms |
The Shuttle Radar Topography Mission (SRTM) is an international research effort that obtained digital elevation models on a near-global scale from 56°S to 60°N,: 4820 to generate the most complete high-resolution digital topographic database of Earth prior to the release of the ASTER GDEM in 2009. SRTM consisted of a ... | Wikipedia/Shuttle_Radar_Topography_Mission |
Drug repositioning (also called drug repurposing) involves the investigation of existing drugs for new therapeutic purposes.
== Repurposing achievements ==
Repurposing generics can have groundbreaking effects for patients: 35% of 'transformative' drugs approved by the US FDA are repurposed products. Repurposing is es... | Wikipedia/Drug_repurposing |
In topological graph theory, an embedding (also spelled imbedding) of a graph
G
{\displaystyle G}
on a surface
Σ
{\displaystyle \Sigma }
is a representation of
G
{\displaystyle G}
on
... | Wikipedia/Graph_embedding |
A capsule neural network (CapsNet) is a machine learning system that is a type of artificial neural network (ANN) that can be used to better model hierarchical relationships. The approach is an attempt to more closely mimic biological neural organization.
The idea is to add structures called "capsules" to a convolution... | Wikipedia/Capsule_neural_network |
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalise to unseen data, and thus perform tasks without explicit instructions. Within a subdiscipline in machine learning, advances in the field of deep ... | Wikipedia/Machine_learning_algorithm |
In the statistical analysis of time series, autoregressive–moving-average (ARMA) models are a way to describe a (weakly) stationary stochastic process using autoregression (AR) and a moving average (MA), each with a polynomial. They are a tool for understanding a series and predicting future values. AR involves regress... | Wikipedia/ARMA_model |
A probabilistic logic network (PLN) is a conceptual, mathematical and computational approach to uncertain inference. It was inspired by logic programming and it uses probabilities in place of crisp (true/false) truth values, and fractional uncertainty in place of crisp known/unknown values. In order to carry out effect... | Wikipedia/Probabilistic_logic_network |
In control engineering and system identification, a state-space representation is a mathematical model of a physical system that uses state variables to track how inputs shape system behavior over time through first-order differential equations or difference equations. These state variables change based on their curren... | Wikipedia/State_Space_Model |
Reinforcement learning (RL) is an interdisciplinary area of machine learning and optimal control concerned with how an intelligent agent should take actions in a dynamic environment in order to maximize a reward signal. Reinforcement learning is one of the three basic machine learning paradigms, alongside supervised le... | Wikipedia/Actor-critic_method |
The proposition in probability theory known as the law of total expectation, the law of iterated expectations (LIE), Adam's law, the tower rule, and the smoothing property of conditional expectation, among other names, states that if
X
{\displaystyle X}
is a random variable ... | Wikipedia/Law_of_iterated_expectation |
A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the re... | Wikipedia/Policy_function |
In statistics, the rational quadratic covariance function is used in spatial statistics, geostatistics, machine learning, image analysis, and other fields where multivariate statistical analysis is conducted on metric spaces. It is commonly used to define the statistical covariance between measurements made at two poin... | Wikipedia/Rational_quadratic_covariance_function |
In statistics, the Matérn covariance, also called the Matérn kernel, is a covariance function used in spatial statistics, geostatistics, machine learning, image analysis, and other applications of multivariate statistical analysis on metric spaces. It is named after the Swedish forestry statistician Bertil Matérn. It ... | Wikipedia/Matérn_covariance_function |
In computer science, the Knuth–Morris–Pratt algorithm (or KMP algorithm) is a string-searching algorithm that searches for occurrences of a "word" W within a main "text string" S by employing the observation that when a mismatch occurs, the word itself embodies sufficient information to determine where the next match c... | Wikipedia/Knuth–Morris–Pratt_algorithm |
A* (pronounced "A-star") is a graph traversal and pathfinding algorithm that is used in many fields of computer science due to its completeness, optimality, and optimal efficiency. Given a weighted graph, a source node and a goal node, the algorithm finds the shortest path (with respect to the given weights) from sourc... | Wikipedia/A*_search_algorithm |
In computer science, the Boyer–Moore string-search algorithm is an efficient string-searching algorithm that is the standard benchmark for practical string-search literature. It was developed by Robert S. Boyer and J Strother Moore in 1977. The original paper contained static tables for computing the pattern shifts wit... | Wikipedia/Boyer–Moore_string-search_algorithm |
In mathematical optimization and computer science, heuristic (from Greek εὑρίσκω "I find, discover") is a technique designed for problem solving more quickly when classic methods are too slow for finding an exact or approximate solution, or when classic methods fail to find any exact solution in a search space. This i... | Wikipedia/Heuristic_function |
The Journal of Computer and System Sciences (JCSS) is a peer-reviewed scientific journal in the field of computer science. JCSS is published by Elsevier, and it was started in 1967. Many influential scientific articles have been published in JCSS; these include five papers that have won the Gödel Prize. Its managing ed... | Wikipedia/Journal_of_Computer_and_System_Sciences |
The nearest neighbour algorithm was one of the first algorithms used to solve the travelling salesman problem approximately. In that problem, the salesman starts at a random city and repeatedly visits the nearest city until all have been visited. The algorithm quickly yields a short tour, but usually not the optimal on... | Wikipedia/Nearest_neighbour_algorithm |
SAMV (iterative sparse asymptotic minimum variance) is a parameter-free superresolution algorithm for the linear inverse problem in spectral estimation, direction-of-arrival (DOA) estimation and tomographic reconstruction with applications in signal processing, medical imaging and remote sensing. The name was coined in... | Wikipedia/SAMV_(algorithm) |
The algebraic reconstruction technique (ART) is an iterative reconstruction technique used in computed tomography. It reconstructs an image from a series of angular projections (a sinogram). Gordon, Bender and Herman first showed its use in image reconstruction; whereas the method is known as Kaczmarz method in numeric... | Wikipedia/Algebraic_Reconstruction_Technique |
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the r... | Wikipedia/Inverse_discrete_Fourier_transform |
The algebraic reconstruction technique (ART) is an iterative reconstruction technique used in computed tomography. It reconstructs an image from a series of angular projections (a sinogram). Gordon, Bender and Herman first showed its use in image reconstruction; whereas the method is known as Kaczmarz method in numeric... | Wikipedia/Algebraic_reconstruction_technique |
In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency and phase information about a wave then we may reconstruct the original wave precisely.
The the... | Wikipedia/Inverse_Fourier_transform |
Industrial Tomography Systems plc, occasionally abbreviated to ITOMS or simply ITS, is a manufacturer of process visualization systems based upon the principles of tomography. Headquartered in Manchester, UK, the company provides instrumentation to a variety of organisations across a range of sectors; including oil ref... | Wikipedia/Industrial_Tomography_Systems |
In computer programming, a parameter, a.k.a. formal argument, is a variable that represents an argument, a.k.a. actual argument, a.k.a. actual parameter, to a subroutine call.. A function's signature defines its parameters. A call invocation involves evaluating each argument expression of a call and associating the re... | Wikipedia/Parameters_(computer_science) |
Differential privacy (DP) is a mathematically rigorous framework for releasing statistical information about datasets while protecting the privacy of individual data subjects. It enables a data holder to share aggregate patterns of the group while limiting information that is leaked about specific individuals. This is ... | Wikipedia/Differential_privacy |
The scale-invariant feature transform (SIFT) is a computer vision algorithm to detect, describe, and match local features in images, invented by David Lowe in 1999. Applications include object recognition, robotic mapping and navigation, image stitching, 3D modeling, gesture recognition, video tracking, individual iden... | Wikipedia/Scale-invariant_feature_transform |
Sparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications have found wide use in image processing, signal processing, machine learning, medical imaging, and more.
== Sparse d... | Wikipedia/Sparse_approximation |
In computer science, a convolutional deep belief network (CDBN) is a type of deep artificial neural network composed of multiple layers of convolutional restricted Boltzmann machines stacked together. Alternatively, it is a hierarchical generative model for deep learning, which is highly effective in image processing ... | Wikipedia/Convolutional_deep_belief_network |
Dropout and dilution (also called DropConnect) are regularization techniques for reducing overfitting in artificial neural networks by preventing complex co-adaptations on training data. They are an efficient way of performing model averaging with neural networks. Dilution refers to randomly decreasing weights towards ... | Wikipedia/Dropout_(neural_networks) |
The cerebral cortex, also known as the cerebral mantle, is the outer layer of neural tissue of the cerebrum of the brain in humans and other mammals. It is the largest site of neural integration in the central nervous system, and plays a key role in attention, perception, awareness, thought, memory, language, and consc... | Wikipedia/Cortical_neuron |
In network science, a sparse network has much fewer links than the possible maximum number of links within that network (the opposite is a dense network). The study of sparse networks is a relatively new area primarily stimulated by the study of real networks, such as social and computer networks.
The notion of much fe... | Wikipedia/Sparse_network |
In statistical physics, Glauber dynamics is a way to simulate the Ising model (a model of magnetism) on a computer.
The algorithm is named after Roy J. Glauber.
== The algorithm ==
The Ising model is an abstract model for the magnetic interaction of neighboring atoms. It is conventionally considered on a two-dimensio... | Wikipedia/Glauber_dynamics |
Bidirectional recurrent neural networks (BRNN) connect two hidden layers of opposite directions to the same output. With this form of generative deep learning, the output layer can get information from past (backwards) and future (forward) states simultaneously. Invented in 1997 by Schuster and Paliwal, BRNNs were intr... | Wikipedia/Bidirectional_recurrent_neural_networks |
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs.
== Definition ==
In formal terms, a directed graph is an ordered pair G = (V, A) where
V is a set whose elements are called vertices, no... | Wikipedia/Directed_cyclic_graph |
In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the i-th approximation (called an "iterate") is derived from the previous ones.
A specific implementation with termination... | Wikipedia/Iterative_algorithm |
In time series modeling, a nonlinear autoregressive exogenous model (NARX) is a nonlinear autoregressive model which has exogenous inputs. This means that the model relates the current value of a time series to both:
past values of the same series; and
current and past values of the driving (exogenous) series — that i... | Wikipedia/Nonlinear_autoregressive_exogenous_model |
A language model is a model of the human brain's ability to produce natural language. Language models are useful for a variety of tasks, including speech recognition, machine translation, natural language generation (generating more human-like text), optical character recognition, route optimization, handwriting recogn... | Wikipedia/Language_Modeling |
A recursive neural network is a kind of deep neural network created by applying the same set of weights recursively over a structured input, to produce a structured prediction over variable-size input structures, or a scalar prediction on it, by traversing a given structure in topological order. These networks were fir... | Wikipedia/Recursive_neural_network |
A text-to-video model is a machine learning model that uses a natural language description as input to produce a video relevant to the input text. Advancements during the 2020s in the generation of high-quality, text-conditioned videos have largely been driven by the development of video diffusion models.
== Models =... | Wikipedia/Text-to-Video_model |
Vector space model or term vector model is an algebraic model for representing text documents (or more generally, items) as vectors such that the distance between vectors represents the relevance between the documents. It is used in information filtering, information retrieval, indexing and relevancy rankings. Its fir... | Wikipedia/Vector_space_model |
In linguistics, coreference, sometimes written co-reference, occurs when two or more expressions refer to the same person or thing; they have the same referent. For example, in Bill said Alice would arrive soon, and she did, the words Alice and she refer to the same person.
Co-reference is often non-trivial to determi... | Wikipedia/Coreference_resolution |
In statistical classification, Bayes error rate is the lowest possible error rate for any classifier of a random outcome (into, for example, one of two categories) and is analogous to the irreducible error.
A number of approaches to the estimation of the Bayes error rate exist. One method seeks to obtain analytical bou... | Wikipedia/Bayes_error_rate |
Generalized regression neural network (GRNN) is a variation to radial basis neural networks. GRNN was suggested by D.F. Specht in 1991.
GRNN can be used for regression, prediction, and classification. GRNN can also be a good solution for online dynamical systems.
GRNN represents an improved technique in the neural netw... | Wikipedia/General_regression_neural_network |
A probabilistic neural network (PNN) is a feedforward neural network, which is widely used in classification and pattern recognition problems. In the PNN algorithm, the parent probability distribution function (PDF) of each class is approximated by a Parzen window and a non-parametric function. Then, using PDF of each... | Wikipedia/Probabilistic_neural_network |
Quantum neural networks are computational neural network models which are based on the principles of quantum mechanics. The first ideas on quantum neural computation were published independently in 1995 by Subhash Kak and Ron Chrisley, engaging with the theory of quantum mind, which posits that quantum effects play a r... | Wikipedia/Quantum_neural_networks |
In mathematics, a radial function is a real-valued function defined on a Euclidean space
R
n
{\displaystyle \mathbb {R} ^{n}}
whose value at each point depends only on the distance between that po... | Wikipedia/Radial_function |
The activating function is a mathematical formalism that is used to approximate the influence of an extracellular field on an axon or neurons. It was developed by Frank Rattay and is a useful tool to approximate the influence of functional electrical stimulation (FES) or neuromodulation techniques on target neurons. It... | Wikipedia/Activating_function |
In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a retur... | Wikipedia/Fold_function |
In mathematics, a ridge function is any function
f
:
R
d
→
R
{\displaystyle f:\mathbb {R} ^{d}\rightarrow \mathbb {R} }
that can be written as the... | Wikipedia/Ridge_function |
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex-valued. For example, a wave function mi... | Wikipedia/Quantum_function |
In computer programming, a software framework is a software abstraction that provides generic functionality which developers can extend with custom code to create applications. It establishes a standard foundation for building and deploying software, offering reusable components and design patterns that handle common p... | Wikipedia/Framework_(computer_science) |
A language model is a model of the human brain's ability to produce natural language. Language models are useful for a variety of tasks, including speech recognition, machine translation, natural language generation (generating more human-like text), optical character recognition, route optimization, handwriting recogn... | Wikipedia/Language_modeling |
Recurrent neural networks (RNNs) are a class of artificial neural networks designed for processing sequential data, such as text, speech, and time series, where the order of elements is important. Unlike feedforward neural networks, which process inputs independently, RNNs utilize recurrent connections, where the outpu... | Wikipedia/Elman_network |
In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it can be used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its ow... | Wikipedia/Autoregressive_models |
In computer science, contextualization is the process of identifying the data relevant to an entity (e.g., a person or a city) based on the entity's contextual information.
== Definition ==
Context or contextual information is any information about any entity that can be used to effectively reduce the amount of reaso... | Wikipedia/Contextualization_(computer_science) |
In mathematics, low-rank approximation refers to the process of approximating a given matrix by a matrix of lower rank. More precisely, it is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constr... | Wikipedia/Low-rank_approximation |
An evaluation function, also known as a heuristic evaluation function or static evaluation function, is a function used by game-playing computer programs to estimate the value or goodness of a position (usually at a leaf or terminal node) in a game tree. Most of the time, the value is either a real number or a quantize... | Wikipedia/Evaluation_function |
In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular, it is commonly used in support vector machine classification.
The RBF kernel on two samples
x
∈
... | Wikipedia/Radial_basis_function_kernel |
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often ... | Wikipedia/Dense_graph |
In mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other. It is possible to derive an evaluation order or the absence of an evaluation order that respects the given dependencies from the dependency graph.
== Defini... | Wikipedia/Dependency_graph |
Price's model (named after the physicist Derek J. de Solla Price) is a mathematical model for the growth of citation networks. It was the first model which generalized the Simon model to be used for networks, especially for growing networks. Price's model belongs to the broader class of network growing models (together... | Wikipedia/Price's_model |
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