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Mathematical function
In physics and mathematics, a random field is a random function over an arbitrary domain (usually a multi-dimensional space such as R n {\displaystyle
Random_field
Set of random variables
physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property
Markov_random_field
Class of statistical modeling methods
Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured
Conditional_random_field
Concept in statistics
In statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF
Gaussian_random_field
Collection of random variables
theory and related fields a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random variables in a probability
Stochastic_process
Type of random mathematical object
statistics and related fields, a Poisson point process (also known as: Poisson random measure, Poisson random point field and Poisson point field) is a type of
Poisson_point_process
Apparent lack of pattern or predictability in events
and information entropy. The fields of mathematics, probability, and statistics use formal definitions of randomness, typically assuming that there
Randomness
Physical quantities taking values at each point in space and time
are nowhere differentiable. Random fields are indexed sets of random variables; a continuous random field is a random field that has a set of functions
Field_(physics)
functions, processes, fields, series, transformations, and also sets or collections of sets. The modern-day usage of “random element” frequently assumes
Random_element
Tree-based ensemble machine learning methods
Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that works by creating a multitude
Random_forest
hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields have an underlying
Hidden_Markov_random_field
Statistical tool to model changing systems
a Markov random field, each state depends on its neighbors in any of multiple directions. A Markov random field may be visualized as a field or graph
Markov_model
Concept in statistical mechanics
statistical mechanics, the Gaussian free field (GFF) is a Gaussian random field, a central model of random surfaces (random height functions). The discrete version
Gaussian_free_field
Process forming a path from many random steps
and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer
Random_walk
Matrix-valued random variable
distribution. Random matrix theory (RMT) is the study of properties of random matrices, often as they become large. RMT provides techniques like mean-field theory
Random_matrix
Overview of and topical guide to machine learning
machines Random Forests Ensembles of classifiers Bootstrap aggregating (bagging) Boosting (meta-algorithm) Ordinal classification Conditional Random Field ANOVA
Outline_of_machine_learning
Mathematical concept
case of a random field on a lattice. The idea of a Gibbs measure is, however, much more general than this. The definition of a Gibbs random field on a lattice
Gibbs_measure
Mathematical theorem
by a Markov network (also known as a Markov random field). It is the fundamental theorem of random fields. It states that a probability distribution that
Hammersley–Clifford_theorem
Process of making something random
the occurrence of a set of measured values is random. Randomization is widely applied in various fields, especially in scientific research, statistical
Randomization
Variable representing a random phenomenon
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which
Random_variable
function is defined is a time interval (time series) or a region of space (random field). Familiar examples of time series include stock market and exchange
List of stochastic processes topics
List_of_stochastic_processes_topics
Subset of variables that contains all the useful information
as a Bayesian network or Markov random field. A Markov blanket of a random variable Y {\displaystyle Y} in a random variable set S = { X 1 , … , X n
Markov_blanket
thus result in a net-zero magnetization. The randomness of dipoles in a dipole glass creates local fields resulting in short-range order but no long-range
Dipole_glass
Function in probability theory
describes how much two random variables change together (their covariance) with varying spatial or temporal separation. For a random field or stochastic process
Covariance_function
Statistical method
Random sample consensus (RANSAC) is an iterative method to estimate parameters of a mathematical model from a set of observed data that contains outliers
Random_sample_consensus
Memoryless property of a stochastic process
such as a hidden Markov model. A Markov random field extends this property to two or more dimensions or to random variables defined for an interconnected
Markov_property
Statistical Markov model
model is the linear-chain conditional random field. This uses an undirected graphical model (aka Markov random field) rather than the directed graphical
Hidden_Markov_model
Type of stochastic recurrent neural network
the context of cognitive science. It is also classified as a Markov random field. Boltzmann machines are theoretically intriguing because of the locality
Boltzmann_machine
Cryptographic device
hardware random number generator (HRNG), true random number generator (TRNG), non-deterministic random bit generator (NRBG), or physical random number generator
Hardware random number generator
Hardware_random_number_generator
Probabilistic model
distributions are commonly used, namely, Bayesian networks and Markov random fields. Both families encompass the properties of factorization and independences
Graphical_model
Partitioning a digital image into segments
721–741, Vol. 6, No. 6. A. Bouman and M. Shapiro (2002): "A multiscale Random field model for Bayesian image segmentation", IEEE Transactions on Image Processing
Image_segmentation
Representation of a type of random process
an autoregressive (AR) model is a modelled representation of a type of random process. It can be used to describe time-varying processes from many natural
Autoregressive_model
Supervised machine learning techniques
exploited in a sequence model such as a hidden Markov model or conditional random field that predicts the entire tag sequence for a sentence (rather than just
Structured_prediction
Process of removing noise from a signal
using a weighted average of the overlapping pixels. Shrinkage fields is a random field-based machine learning technique that brings performance comparable
Noise_reduction
Field of applied statistics
Spatial statistics is a field of applied statistics dealing with spatial data. It involves stochastic processes (random fields, point processes), sampling
Spatial_statistics
Statistics models class
reduction) or by finding sparse representations of the smooths using Markov random fields, which are amenable to the use of sparse matrix methods for computation
Generalized_additive_model
Machine-learning and computational-neuroscience conference
evaluate randomness in the reviewing process. Several researchers interpreted the result. Regarding whether the decision in NIPS is completely random or not
Conference on Neural Information Processing Systems
Conference_on_Neural_Information_Processing_Systems
Random change in the energy inside a volume
temporary random change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. They are minute random fluctuations
Quantum_fluctuation
Similarity measure for number sequences
products between two random unit vectors in RD". CrossValidated. Graham L. Giller (2012). "The Statistical Properties of Random Bitstreams and the Sampling
Cosine_similarity
Model for a random simple path
mathematics, loop-erased random walk is a model for a random simple path with important applications in combinatorics, physics and quantum field theory. It is intimately
Loop-erased_random_walk
A random function – of either one variable (a random process), or two or more variables (a random field) – is called Gaussian if every finite-dimensional
Large deviations of Gaussian random functions
Large_deviations_of_Gaussian_random_functions
Random number book first published in 1955
consisting primarily of a random number table, was an important 20th century work in the field of statistics and random numbers. It was produced starting
A Million Random Digits with 100,000 Normal Deviates
A_Million_Random_Digits_with_100,000_Normal_Deviates
Estimation in statistical mathematics
and volumetric neuroimaging data using linear mixed effects models and random field theory, but more generally in the fitlme package for modeling linear
Restricted_maximum_likelihood
French computer scientist (born 1960)
methods, and the Graph Transformer Networks method (similar to conditional random field), which he applied to handwriting recognition and Optical character recognition
Yann_LeCun
Spatial statistics function
_{2}))-E[Z(\mathbf {s} _{1})-Z(\mathbf {s} _{2})])^{2}\right].} If the spatial random field has constant mean μ {\displaystyle \mu } , this is equivalent to the
Variogram
Subset of artificial intelligence
algorithms like Random forest.[clarification needed] Some statisticians have adopted methods from machine learning, producing the field of statistical
Machine_learning
Method of interpolation
frameworks: kriging is made for estimation of a single realization of a random field, while regression models are based on multiple observations of a multivariate
Kriging
Automated recognition of patterns and regularities in data
of experts, hierarchical mixture of experts Bayesian networks Markov random fields Unsupervised: Multilinear principal component analysis (MPCA) Kalman
Pattern_recognition
Algorithmic production of digital images
such as through use of a noncausal nonparametric multiscale Markov random field. Patch-based texture synthesis creates a new texture by copying and stitching
Texture_synthesis
2025 fantasy novel by Philip Pullman
with Penguin Random House and Alfred A. Knopf. The Rose Field is set directly after The Secret Commonwealth, published in 2019. The "Rose Field" of the title
The_Rose_Field
3D reconstruction technique
A neural radiance field (NeRF) is a neural field for reconstructing a three-dimensional representation of a scene from two-dimensional images. The NeRF
Neural_radiance_field
Machine learning technique
through transfer learning both prior to any learning (compared to standard random weight distribution) and at the end of the learning process (asymptote)
Transfer_learning
Technique for the generative modeling of a continuous probability distribution
data as generated by a diffusion process, whereby a new datum performs a random walk with drift through the space of all possible data. A trained diffusion
Diffusion_model
Approximation of physical behavior
probability theory, mean-field theory (MFT) or self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying
Mean-field_theory
Stochastic process in probability theory
it represents the motion of a point whose successive displacements are random, in which displacements in pairwise disjoint time intervals are independent
Lévy_process
Value used to initialize a pseudo-random number generator
the pseudorandom numbers generated. The choice of a good random seed is crucial in the field of computer security. When a secret encryption key is pseudorandomly
Random_seed
Image segmentation algorithm
The random walker algorithm is an algorithm for image segmentation. In the first description of the algorithm, a user interactively labels a small number
Random_walker_algorithm
Condensed matter physicist
of the three-dimensional random field Ising model". Hill made magnetic scattering studies of the three-dimensional random-field Ising model, specifically
John_Peter_Hill
Uses of an apparent lack of pattern or predictability in events
Randomness has multiple uses in science, art, statistics, cryptography, gaming, gambling, and other fields. For example, random assignment in randomized
Applications_of_randomness
Algorithm for statistical inference on graphical models
inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for each unobserved node (or
Belief_propagation
Operator in probability theory
covariance function of a function-valued random element (in special cases is called random process or random field) z is C o v ( x , y ) = ∫ z ( x ) z (
Covariance_operator
neuroimaging analysis, an estimate of the number of resels together with random field theory is used in statistical inference. Keith Worsley has proposed an
Resel
(F:C) Harris chain / (L:DC) Hidden Markov model / (F:D) Hidden Markov random field Hunt process / (U:R) Kalman filter / (F:C) Kolmogorov backward equation /
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Generalization of the one-dimensional normal distribution to higher dimensions
(univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination
Multivariate normal distribution
Multivariate_normal_distribution
Topics referred to by the same term
characterized by a pseudo-randomized acquisition strategy Markov random field, in physics and probability, a random field that satisfies Markov properties
MRF
Difficulties arising when analyzing data with many aspects ("dimensions")
a random point from a large finite random set with high probability even if this set is exponentially large: the number of elements in this random set
Curse_of_dimensionality
American electrical engineer
Transformation of Random Fields, studied random fields of three types: continuous-parameter Markov random fields, continuous-parameter random fields admitting
Bruce_Hajek
Solution to a stochastic differential equation
subjected to random displacements due to collisions with other particles, which is called Brownian motion. The position of the particle is then random; its probability
Diffusion_process
Random set of points on a space with random number and random position
probability theory, a point process or point field is a set of a random number of mathematical points randomly located on a mathematical space such as the
Point_process
Concept in probability and statistics
finds application in many fields, such as data mining and signal processing. Statistics commonly deals with random samples. A random sample can be thought
Independent and identically distributed random variables
Independent_and_identically_distributed_random_variables
Form of computer data storage
Random-access memory (RAM; /ræm/) is a form of electronic computer memory that can be read and changed in any order, typically used to store working data
Random-access_memory
Graph generated by a random process
at random. The aim of the study in this field is to determine at what stage a particular property of the graph is likely to arise. Different random graph
Random_graph
the field, see list of mathematical probabilists and list of statisticians. Probability Randomness, Pseudorandomness, Quasirandomness Randomization, hardware
List_of_probability_topics
Method of image segmentation
background using a Gaussian mixture model. This is used to construct a Markov random field over the pixel labels, with an energy function that prefers connected
GrabCut
Model-free reinforcement learning algorithm
finite Markov decision process, given infinite exploration time and a partly random policy. "Q" refers to the function that the algorithm computes: the expected
Q-learning
Method in natural language processing
the introduction of latent semantic analysis in the late 1980s and the random indexing approach for collecting word co-occurrence contexts. In 2000, Bengio
Word_embedding
Class of hallucination
few minutes, one becomes aware of an apparent disorganized motion, a random field of lightness or darkness that overlays the redness or blackness of closed
Closed-eye_hallucination
Method in machine learning
between statistical variables in a dataset. This makes random forests particularly useful in such fields as banking, healthcare, the stock market, and e-commerce
Bootstrap_aggregating
Shrinkage fields is a random field-based machine learning technique that aims to perform high quality image restoration (denoising and deblurring) using
Shrinkage Fields (image restoration)
Shrinkage_Fields_(image_restoration)
Type of artificial neural network
a neural field (also known as implicit neural representation, neural implicit, or coordinate-based neural network), is a mathematical field that is fully
Neural_field
Optimization algorithm
Christopher D. Manning (2008). Efficient, Feature-based, Conditional Random Field Parsing. Proc. Annual Meeting of the ACL. LeCun, Yann A., et al. "Efficient
Stochastic_gradient_descent
in machine learning. He is best known for proposing the Conditional Random Fields with Andrew McCallum and Fernando C.N. Pereira. In 2017, Lafferty was
John_D._Lafferty
Objective full-reference image quality assessment
non-overlapping blocks are assumed to be independent of each other and that the random field S {\displaystyle {\mathcal {S}}} is independent of U {\displaystyle {\mathcal
Visual_information_fidelity
Concept in machine learning
Non-independent and identically distributed random (non-IID) data Time leakage (for example, splitting a time-series dataset randomly instead of newer data in test
Leakage_(machine_learning)
Statistics and machine learning technique
the models they combine. Although perhaps non-intuitive, more random algorithms (like random decision trees) can be used to produce a stronger ensemble than
Ensemble_learning
Machine learning paradigm
{\displaystyle X=\left\{x_{1},\ldots x_{N}\right\}} of N {\displaystyle N} random samples containing one positive sample from p ( x t + k ∣ c t ) {\displaystyle
Self-supervised_learning
Stochastic process
smooth. It is also studied in statistical mechanics in the context of random fields. For a continuous real-valued semimartingale ( B s ) s ≥ 0 {\displaystyle
Local_time_(mathematics)
American computer scientist
John D. Lafferty and Fernando Pereira, McCallum developed conditional random fields, first described in a paper presented at the International Conference
Andrew_McCallum
Optimization technique
Bayesian statistical context of smoothing noisy images, using a Markov random field as the image prior distribution, they showed with a mathematically beautiful
Graph cuts in computer vision and artificial intelligence
Graph_cuts_in_computer_vision_and_artificial_intelligence
Concept 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
Complex_random_variable
chain random field theory, which extends a single Markov chain into a multi-dimensional random field for geostatistical modeling. A Markov chain random field
Markov_chain_geostatistics
logic network Markov chain approximation method Markov matrix Markov random field Lempel–Ziv–Markov chain algorithm Markov partition Markov property Markov
List of things named after Andrey Markov
List_of_things_named_after_Andrey_Markov
Numerical method that reduces the complexity of computationally intensive simulations
turbulences, is to decompose a random vector field u(x, t) into a set of deterministic spatial functions Φk(x) modulated by random time coefficients ak(t) so
Proper orthogonal decomposition
Proper_orthogonal_decomposition
Randomly determined process
stochastic process is also referred to as a random process. Stochasticity is used in many different fields, including actuarial science, image processing
Stochastic
Nonparametric spectral estimation method
(1946)–Loève (1945, 1978) spectral decomposition of time series and random fields and in the Mañé (1981)–Takens (1981) embedding theorem. SSA can be an
Singular_spectrum_analysis
Technique for setting initial values of trainable parameters in a neural network
gradient is likely nonzero at initialization, avoiding the dying ReLU problem. Random initialization means sampling the weights from a normal distribution or
Weight_initialization
Field using controlled experiments to study financial behaviour and market dynamics
provides for more accurate assessment of causality. Controlled field experiments also randomize treatments but do so in real world applications. Average effects
Experimental_finance
Term used in composite materials theory
description of the material involves Statistical Volume Element (SVE) and random fields. The property of interest can include mechanical properties such as
Representative elementary volume
Representative_elementary_volume
Form of scientific experiment
A randomized controlled trial (RCT) is a type of statistical experiment designed to evaluate the efficacy or safety of an intervention by minimizing bias
Randomized_controlled_trial
vector space over the field of complex numbers. If Z 1 , … , Z n {\displaystyle Z_{1},\ldots ,Z_{n}} are complex-valued random variables, then the n-tuple
Complex_random_vector
RANDOM FIELD
RANDOM FIELD
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
Surname or Lastname
English
English : variant of Ransom.
Surname or Lastname
English
English : variant of Brandon.
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Male
English
Pet form of English Randall and Randolph, both RANDY means "shield-wolf." Compare with feminine Randy.
Boy/Male
English
Son of Rand.
Boy/Male
English American
Son of Rand.
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Female
English
Short form of English Miranda, RANDA means "worthy of admiration."Â
Female
English
Pet form of English Miranda, RANDY means "worthy of admiration."Â Compare with masculine Randy.Â
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
Surname or Lastname
English or Scottish
English or Scottish : unexplained. Possibly, as Black suggests, a reduced form of Langdon.French : from the old Germanic personal name element Lando (see Land), via the oblique case, Landonis.
Male
Norwegian
 Norwegian form of Old Norse Arnþórr, ANDOR means "eagle of Thor." Compare with another form of Andor.
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
Surname or Lastname
English
English : patronymic from Rand 1.
Male
Hungarian
 Variant spelling of Hungarian András, ANDOR means "man; warrior." Compare with another form of Andor.
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
RANDOM FIELD
RANDOM FIELD
Boy/Male
Celebrity, Indian, Malayalam
Lord Ganesha
Female
Hungarian
Pet form of Hungarian Jolán, JOLÃNKA means "violet flower."
Girl/Female
Indian
Collection of pomes ir song, Tagores poems which got nobel prize, An offering of songs
Female
Egyptian
, the sister of the scribe Thoth.
Boy/Male
Arabic, Muslim
Adorer of the Prophet Muhammad
Girl/Female
Tamil
Cloud
Female
Chinese
flowery tuber.
Boy/Male
Muslim
Help, Victory
Boy/Male
Arabic, Muslim
Nobility; Good Manners
Girl/Female
Arabic, Muslim, Sindhi
Dazzling; Bright
RANDOM FIELD
RANDOM FIELD
RANDOM FIELD
RANDOM FIELD
RANDOM FIELD
a.
Going at random or by chance; done or made at hazard, or without settled direction, aim, or purpose; hazarded without previous calculation; left to chance; haphazard; as, a random guess.
imp. & p. p.
of Ransom
n.
To redeem from captivity, servitude, punishment, or forfeit, by paying a price; to buy out of servitude or penalty; to rescue; to deliver; as, to ransom prisoners from an enemy.
adv.
At random; hit or miss. (Obs.)
n.
Ransom; release.
n.
A roving motion; course without definite direction; want of direction, rule, or method; hazard; chance; -- commonly used in the phrase at random, that is, without a settled point of direction; at hazard.
n.
Anything driven at random.
n.
Random.
n.
Distance to which a missile is cast; range; reach; as, the random of a rifle ball.
v. i.
To extend or grow at random.
v. i.
To wander at random; to scatter.
n.
Ransom.
adv.
In a random manner.
n.
To exact a ransom for, or a payment on.
n.
Extra hazard; chance; accident; random.
p. pr. & vb. n.
of Ransom
v. i.
To go or stray at random.
n.
The release of a captive, or of captured property, by payment of a consideration; redemption; as, prisoners hopeless of ransom.
a.
Cruising at random on the ocean.