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Markov-based processes with variable "memory"
processes, variable-order Markov (VOM) models are an important class of models that extend the well known Markov chain models. In contrast to the Markov chain
Variable-order_Markov_model
Statistical Markov model
probability theory, a hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent (or hidden) Markov process (referred to
Hidden_Markov_model
Statistical tool to model changing systems
simplest Markov model is the Markov chain. It models the state of a system with a random variable that changes through time. In this context, the Markov property
Markov_model
Hierarchical hidden Markov model Maximum-entropy Markov model Variable-order Markov model Markov renewal process Markov chain mixing time Markov kernel Piecewise-deterministic
List of things named after Andrey Markov
List_of_things_named_after_Andrey_Markov
Random process independent of past history
equation Quantum Markov chain Semi-Markov process Stochastic cellular automaton Telescoping Markov chain Variable-order Markov model Sean Meyn; Richard
Markov_chain
Probabilistic model
like hidden Markov models, neural networks and newer models such as variable-order Markov models can be considered special cases of Bayesian networks
Graphical_model
Overview of and topical guide to machine learning
theory Statistical relational learning Tanagra Transfer learning Variable-order Markov model Version space learning Waffles Weka Loss function Loss functions
Outline_of_machine_learning
the predictions of many underlying variable order Markov models, where each such model is constructed using zero-order conditional probability estimators
Context_tree_weighting
Generalization of Markov jump processes
\forall n\geq 1,\forall t\geq 0} Markov process Renewal theory Variable-order Markov model Hidden semi-Markov model Medhi, J. (1982). Stochastic processes
Markov_renewal_process
Technique for the generative modeling of a continuous probability distribution
diffusion models, also known as diffusion-based generative models or score-based generative models, are a class of latent variable generative models. A diffusion
Diffusion_model
Calculation of complex statistical distributions
such Markov chains, including the Metropolis–Hastings algorithm. Markov chain Monte Carlo methods create samples from a continuous random variable, with
Markov_chain_Monte_Carlo
Mathematical model for sequential decision making under uncertainty
A Markov decision process (MDP) is a mathematical model for sequential decision making when outcomes are uncertain. It is a type of stochastic decision
Markov_decision_process
Stochastic chain family
Variable Length Markov Chains. Named by Bühlmann and Wyner as “variable length Markov chains” (VLMC), these chains are also known as “variable-order Markov
Stochastic chains with memory of variable length
Stochastic_chains_with_memory_of_variable_length
Probabilistic logic
A Markov logic network (MLN) is a probabilistic logic which applies the ideas of a Markov network to first-order logic, defining probability distributions
Markov_logic_network
theory Varadhan's lemma Variable Variable kernel density estimation Variable-order Bayesian network Variable-order Markov model Variable rules analysis Variance
List_of_statistics_articles
Regression models accounting for possible errors in independent variables
errors-in-variables model or a measurement error model is a regression model that accounts for measurement errors in the independent variables. In contrast
Errors-in-variables_model
Algorithm in mathematics
inference in hidden Markov models, is numerically unstable due to its recursive calculation of joint probabilities. As the number of variables grows, these joint
Baum–Welch_algorithm
Topics referred to by the same term
raising awareness of persecutions of Christians around the world A Variable-order Markov model An abbreviation of vomit A German word, the contraction of von
VOM
Probability concept
A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential
Continuous-time_Markov_chain
Class of statistical modeling methods
another generalization of CRFs, the semi-Markov conditional random field (semi-CRF), which models variable-length segmentations of the label sequence
Conditional_random_field
In statistics and Markov modeling, an ancestral graph is a type of mixed graph used to provide a graphical representation for the result of marginalizing
Ancestral_graph
Collection of random variables
-dimensional Euclidean space, which results in collections of random variables known as Markov random fields. A martingale is a discrete-time or continuous-time
Stochastic_process
Matrix used to describe the transitions of a Markov chain
stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability
Stochastic_matrix
Variable-order Bayesian network (VOBN) models provide an important extension of both the Bayesian network models and the variable-order Markov models
Variable-order Bayesian network
Variable-order_Bayesian_network
Examples of the probabilistic construct
contains examples of Markov chains and Markov processes in action. All examples are in the countable state space. For an overview of Markov chains in general
Examples_of_Markov_chains
Statistics models class
statistics, a generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth
Generalized_additive_model
Inference algorithm for probabilistic graphical models
Variable elimination (VE) is a simple and general exact inference algorithm in probabilistic graphical models, such as Bayesian networks and Markov random
Variable_elimination
Class of statistical models
constant change in the response variable (i.e. a linear-response model). This is appropriate when the response variable can vary, to a good approximation
Generalized_linear_model
Model for generating observable data in probability and statistics
triplets etc. Types of generative models are: Gaussian mixture model (and other types of mixture model) Hidden Markov model Probabilistic context-free grammar
Generative_model
Probability concept
discrete-time Markov chain (DTMC) is a sequence of random variables, known as a stochastic process, in which the value of the next variable depends only
Discrete-time_Markov_chain
Software for finding prokaryotic genes
compared to fixed-order Markov model. There was a comparison made between interpolated Markov model used by GLIMMER and fifth order Markov model in the paper
GLIMMER
Probabilistic problem-solving algorithm
the variable is parameterized, mathematicians often use a Markov chain Monte Carlo (MCMC) sampler. The central idea is to design a judicious Markov chain
Monte_Carlo_method
Statistical concept
distributed random variables. The resulting model is termed a hidden Markov model and is one of the most common sequential hierarchical models. Numerous extensions
Mixture_model
Principle in kinetic systems
balance in kinetics seem to be clear. A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary
Detailed_balance
Taxonomy of statistical data elements
specifically to cases where each random variable is only correlated with nearby variables (as in a Markov model). This is a particular case of a Bayes
Statistical_data_type
Hidden Markov model algorithm
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
Forward_algorithm
non-negative values. The model is a particular type of piecewise deterministic Markov process and can also be viewed as a Markov reward model with boundary conditions
Fluid_queue
Performance metric in football and hockey
represented by including an additional variable in the score. Continuing Example 1, suppose the model includes a pressure variable P {\displaystyle P} scaled from
Expected_goals
Probabilistic graphical representation of causal relationships
and possibly cyclic, graphs such as Markov networks. Suppose we want to model the dependencies between three variables: the sprinkler (or more appropriately
Bayesian_network
Type of machine learning model
the variables are C {\displaystyle C} is the cost of training the model, in FLOPs. N {\displaystyle N} is the number of parameters in the model. D {\displaystyle
Large_language_model
Concept in probability and statistics
different from a Markov sequence, where the probability distribution for the nth random variable is a function of the previous random variable in the sequence
Independent and identically distributed random variables
Independent_and_identically_distributed_random_variables
Stochastic process modeling random walk with friction
Ornstein–Uhlenbeck process is a stationary Gauss–Markov process, which means that it is a Gaussian process, a Markov process, and is temporally homogeneous. In
Ornstein–Uhlenbeck_process
Semi-Markov process Stochastic matrix / anl Telegraph process / (U:B) Variable-order Markov model Wiener process / Gau scl Normal distribution / spd Abstract Wiener
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Mathematical models of changing DNA
A number of different Markov models of DNA sequence evolution have been proposed. These substitution models differ in terms of the parameters used to
Models_of_DNA_evolution
Statistical term
independent variable and back is counted once only. Bayesian network Causality Causal loop diagram Hidden Markov model Latent variable model Path coefficient
Path_analysis_(statistics)
Statistics concept
specify graphical models such as, for instance, Bayesian networks, dynamic Bayesian networks, Kalman filters or hidden Markov models. Indeed, Bayesian
Bayesian_programming
Type of statistical model
on the values of the individual-level variables. Thus, the problem with using a random-coefficients model in order to analyze hierarchical data is that
Multilevel_model
Monte Carlo algorithm
For example, in a hidden Markov model, a blocked Gibbs sampler might sample from all the latent variables making up the Markov chain in one go, using the
Gibbs_sampling
Representation of a type of random process
sources. The model specifies output variables that are dependent linearly on their own previous values on a stochastic basis. The model is in the form
Autoregressive_model
Quantum algorithm in computer science
evaluating the Jones polynomial. This is done by means of the Markov trace. The "Markov trace" is a trace operator defined on the Temperley–Lieb algebra
Aharonov–Jones–Landau algorithm
Aharonov–Jones–Landau_algorithm
Set of statistical processes for estimating the relationships among variables
In statistical modeling, regression analysis is a statistical method for estimating the relationship between a dependent variable (often called the outcome
Regression_analysis
Statistical modeling method
independent variable). A model with exactly one explanatory variable is a simple linear regression; a model with two or more explanatory variables is a multiple
Linear_regression
Field of machine learning
assume knowledge of an exact mathematical model of the Markov decision process, and they target large Markov decision processes where exact methods become
Reinforcement_learning
Analysis of sets of categorical sequences
distribution models. See also Markov model. Probabilistic Suffix Tree (PST) also known as variable-order Markov model or variable-length Markov model. Event
Sequence analysis in social sciences
Sequence_analysis_in_social_sciences
Mathematical model of a system in control engineering
mathematical model of a physical system that uses state variables to track how inputs shape system behavior over time through first-order differential
State-space_representation
PSL uses "soft" logic as its logical component and Markov random fields as its statistical model. PSL provides sophisticated inference techniques for
Probabilistic_soft_logic
Mathematical methods used in Bayesian inference and machine learning
complex statistical models consisting of observed variables (usually termed "data") as well as unknown parameters and latent variables, with various sorts
Variational_Bayesian_methods
Approximation method in statistics
cases. The Gauss–Markov theorem. In a linear model in which the errors have expectation zero conditional on the independent variables, are uncorrelated
Least_squares
Iterative method for finding maximum likelihood estimates in statistical models
(MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing
Expectation–maximization algorithm
Expectation–maximization_algorithm
Method for estimating the unknown parameters in a linear regression model
regression model by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values
Ordinary_least_squares
Statistical model for a binary dependent variable
logistic model (or logit model) is a statistical model that models the log-odds of an event as a linear combination of one or more independent variables. In
Logistic_regression
Linear dependency situation in a regression model
refers to a situation where the predictive variables have a nearly exact linear relationship. The Gauss–Markov theorem assumes absence of perfect multicollinearity
Multicollinearity
Algorithm that estimates unknowns from a series of measurements over time
basis is a hidden Markov model such that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions
Kalman_filter
Type of simulation
consumption, and so on. System modeling approaches: Finite-state machines and Markov chains Stochastic process and a special case, Markov process Queueing theory
Discrete-event_simulation
Equation from probability theory
over the nuisance variable. (Note that nothing yet has been assumed about the temporal (or any other) ordering of the random variables—the above equation
Chapman–Kolmogorov_equation
Statistical model containing both fixed effects and random effects
mixed model, mixed-effects model or mixed error-component model is a statistical model containing both fixed effects and random effects. These models are
Mixed_model
Problem in network theory
Markov logic networks (MLNs) is a probabilistic graphical model defined over Markov networks. These networks are defined by templated first-order logic-like
Link_prediction
Branch of statistics
studies, and Markov chain Monte Carlo methods to quantify uncertainty. Jin et al. (2017) proposed a widely adopted Bayesian MMM framework that models the carryover
Causal_inference
Statistical model for time series data
249), a Markov chain in the Markov-chain driven threshold autoregressive model (Tong and Lim, 1980, p. 285), which is now also known as the Markov switching
SETAR_(model)
Conditional independence of exchangeable observations
exist exchangeable random variables that are not statistically independent, for example the Pólya urn model. A random variable X has a Bernoulli distribution
De_Finetti's_theorem
Monte Carlo algorithm
statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples
Metropolis–Hastings_algorithm
Statistical method
a special case of errors-in-variables models. The correlation between a variable and a given factor, called the variable's factor loading, indicates the
Factor_analysis
Regression analysis for modeling ordinal data
for predicting an ordinal variable, i.e. a variable whose value exists on an arbitrary scale where only the relative ordering between different values
Ordinal_regression
Statistics concept
in which the relationship between the independent variable x and the dependent variable y is modeled as a polynomial in x. Polynomial regression fits a
Polynomial_regression
Least squares approximation of linear functions to data
distributed random variables. A generalization of the LTF is the Quadratic Template Fit, which assumes a second order regression of the model, requires predictions
Linear_least_squares
Graphical tool in probability
among variables on top of a Markov tree which is generally too parsimonious to summarize the dependence among variables. A vine V on n variables is a nested
Vine_copula
Finds likely sequence of hidden states
often called the Viterbi path. It is most commonly used with hidden Markov models (HMMs). For example, if a doctor observes a patient's symptoms over
Viterbi_algorithm
Type of statistical model
Simultaneous equations models are a type of statistical model in which the dependent variables are functions of other dependent variables, rather than just
Simultaneous_equations_model
Time at which a random variable stops exhibiting a behavior of interest
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
Stopping_time
Inference algorithm for hidden Markov models
an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations/emissions
Forward–backward_algorithm
Type of stochastic recurrent neural network
of binary pairwise Markov random field (undirected probabilistic graphical model) with multiple layers of hidden random variables. It is a network of
Boltzmann_machine
Mathematical model of ferromagnetism in statistical mechanics
mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins"
Ising_model
Algorithm
Slice sampling is a type of Markov chain Monte Carlo algorithm for pseudo-random number sampling, i.e. for drawing random samples from a statistical distribution
Slice_sampling
Resource problem in machine learning
"Optimal adaptive policies for Markov decision processes" Burnetas and Katehakis studied the much larger model of Markov Decision Processes under partial
Multi-armed_bandit
Mathematical model used for classification or regression
Y ) {\displaystyle P(X,Y)} on a given observable variable X and target variable Y; A generative model can be used to "generate" random instances (outcomes)
Discriminative_model
Type of stochastic process
countably-infinite-order graph G {\displaystyle G} and a local state space, a compact metric space S {\displaystyle S} . More precisely IPS are continuous-time Markov jump
Interacting_particle_system
Necessary condition for optimality associated with dynamic programming
equation – Optimality condition in optimal control theory Markov decision process – Mathematical model for sequential decision making under uncertainty Optimal
Bellman_equation
Artificial intelligence model paradigm
In artificial intelligence, a foundation model (FM), also known as large x model (LxM, where "x" is a variable representing any text, image, sound, etc
Foundation_model
Overview of and topical guide to statistics
theorem Concentration inequality Convergence of random variables Computational statistics Markov chain Monte Carlo Bootstrapping (statistics) Jackknife
Outline_of_statistics
models for compatibility. DVE input language: a system is described as Network of Extended Finite State Machines communicating via shared variables and
List_of_model_checking_tools
Planning programming language
non-propositional state-variables (which may be n-ary: true, false, unknown, or anything else). It introduces a temporal model given with modal operators
Planning Domain Definition Language
Planning_Domain_Definition_Language
Statistical model used in machine learning
method using the change-of-variable law of probabilities to transform a simple distribution into a complex one. The direct modeling of likelihood provides
Flow-based_generative_model
Theorem in cybernetics
agents, modeled as goal-conditioned policies in environments governed by fully observable Markov processes, inherently encode a predictive model of their
Good_regulator_theorem
Probability distribution
by a random variable describing the time until absorption of a Markov process with one absorbing state. Each of the states of the Markov process represents
Phase-type_distribution
Mathematical theorem
factorizations of Pr ( U ) {\displaystyle \Pr(U)} . The local Markov property implies that for any random variable x ∈ U {\displaystyle x\in U} , that there exists
Hammersley–Clifford_theorem
the nominal scale and as categorical variables. Bowker's test of symmetry Categorical distribution, general model Chi-squared test Cochran–Armitage test
List of analyses of categorical data
List_of_analyses_of_categorical_data
System for reasoning about vagueness
Gene Expression Programming, Support Vector Machine, Wavelets, Hidden Markov Models, Fuzzy Logic with C++, Java and SymbolicC++ Programs (4 ed.). World
Fuzzy_logic
Projection of data onto lower-dimensional manifolds
intrinsic variables of that manifold will represent the robot's position and orientation. Invariant manifolds are of general interest for model order reduction
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Special type of continuous-time Markov process
of continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths"
Birth–death_process
Regression for more than two discrete outcomes
it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a
Multinomial logistic regression
Multinomial_logistic_regression
VARIABLE ORDER-MARKOV-MODEL
VARIABLE ORDER-MARKOV-MODEL
Male
German
 Serbian and Slovene form of Greek Markos, MARKO means "defense" or "of the sea." Also in use by the Basques, Bulgarians, Dutch, Finnish, Germans, and Romani. Compare with another form of Marko.
Male
English
 English form of Latin Marcus, MARKUS means "defense" or "of the sea." Compare with another form of Markus.
Male
Hebrew
(יַעֲקׄב) Variant spelling of Hebrew Yaaqob, YAAKOV means "supplanter."Â
Surname or Lastname
English
English : topographic name for someone who lived by a market, Middle English market.
Male
English
 Pet form of English Mark, MARKO means "defense" or "of the sea." Compare with another form of Marko.
Surname or Lastname
English
English : variant of Cordier.Catalan : occupational name for a maker of cord or string, from an agent derivative of Catalan corda ‘string’, ‘cord’.
Male
German
 German form of Latin Marcus, MARKUS means "defense" or "of the sea." Compare with another form of Markus.
Surname or Lastname
English
English : variant spelling of Marks.
Male
Finnish
Finnish form of Greek Markos, MARKKU means "defense" or "of the sea."
Female
Japanese
(舞å) Japanese name MAIKO means "dancing child."
Surname or Lastname
English
English : topographic name for someone who lived at the edge of a village or by some other boundary, Middle English border, from Old French bordure ‘edge’.
Female
English
Pet form of French Marguerite, MARGOT means "pearl."
Male
Swedish
Old Swedish form of Old Norse Oddr, ODDER means "point of a weapon."
Male
Greek
(ΜάÏκος) Greek form of Latin Marcus, MARKOS means "defense" or "of the sea." In the New Testament bible, this is the name of the author of the second Gospel.
Female
Japanese
(真里å) Japanese name MARIKO means "true village child."
Surname or Lastname
English
English : from a pet form of the personal name Mary (Marie) or possibly sometimes from a pet form of the much less common male personal name Mark 1.Jewish (eastern Ashkenazic) : patronymic from the Yiddish personal name Marke, a variant of Mark.
Surname or Lastname
English and Dutch
English and Dutch : patronymic from Mark 1.English : variant of Mark 2.German and Jewish (western Ashkenazic) : reduced form of Markus, German spelling of Marcus (see Mark 1).
Female
English
English variant spelling of French Margot, MARGO means "pearl."
Male
Spanish
Portuguese and Spanish form of Latin Marcus, MARCOS means "defense" or "of the sea."
Boy/Male
Russian
Of Mars; the god of war.
VARIABLE ORDER-MARKOV-MODEL
VARIABLE ORDER-MARKOV-MODEL
Girl/Female
Latin
Feminine of Arsenio.
Boy/Male
Tamil
Narottam | நரோதà¯à®¤à®®
Best among men, Lord Vishnu
Boy/Male
Arabic, Hindu, Indian, Muslim, Pashtun
The Biblical Ezra
Girl/Female
Indian
Fairy faced
Boy/Male
British, English
From the Bright Stream
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Kind
Boy/Male
Australian, Vietnamese
Aware
Boy/Male
Arabic, Muslim
Companion of Prophet Muhammad
Boy/Male
Muslim/Islamic
Jurist Scholar of religious laws
Girl/Female
Australian, Russian
Born at Christmas; The Russian Form of the English Natalie; Abbreviation of Natasha
VARIABLE ORDER-MARKOV-MODEL
VARIABLE ORDER-MARKOV-MODEL
VARIABLE ORDER-MARKOV-MODEL
VARIABLE ORDER-MARKOV-MODEL
VARIABLE ORDER-MARKOV-MODEL
n.
An invariable quantity; a constant.
n.
A body of persons having some common honorary distinction or rule of obligation; esp., a body of religious persons or aggregate of convents living under a common rule; as, the Order of the Bath; the Franciscan order.
a.
Designated or distinguished by, or as by, a mark; hence; noticeable; conspicuous; as, a marked card; a marked coin; a marked instance.
n.
Rank; degree; thus, the order of a curve or surface is the same as the degree of its equation.
a.
Liable to vary; too susceptible of change; mutable; fickle; unsteady; inconstant; as, the affections of men are variable; passions are variable.
a.
Friendly; kindly; sweet; gracious; as, an amiable temper or mood; amiable ideas.
n.
A quantity which may increase or decrease; a quantity which admits of an infinite number of values in the same expression; a variable quantity; as, in the equation x2 - y2 = R2, x and y are variables.
a.
Invariable.
n.
To give an order to; to command; as, to order troops to advance.
n.
Arable land; plow land.
a.
Having value or worth; possessing qualities which are useful and esteemed; precious; costly; as, a valuable horse; valuable land; a valuable cargo.
n.
That which is variable; that which varies, or is subject to change.
a.
Worthy; estimable; deserving esteem; as, a valuable friend; a valuable companion.
a.
Having the capacity of varying or changing; capable of alternation in any manner; changeable; as, variable winds or seasons; a variable quantity.
a.
Arable; tillable.
n.
To give an order for; to secure by an order; as, to order a carriage; to order groceries.
adv.
In a variable manner.
v. t.
To represent by parable.
n.
Right arrangement; a normal, correct, or fit condition; as, the house is in order; the machinery is out of order.
v. i.
To give orders; to issue commands.