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information retrieval, divergence from randomness (DFR) is a generalization of one of the very first models, Harter's 2-Poisson indexing-model. It is one type
Divergence-from-randomness model
Divergence-from-randomness_model
Topics referred to by the same term
organisation in Germany Dihydroflavonol 4-reductase, an enzyme class Divergence-from-randomness model, in information retrieval Dounreay Fast Reactor, Scotland Dual
DFR
Topics referred to by the same term
association football in England Harter's 2-Poisson indexing-model, a divergence-from-randomness model used in information retrieval PLL (disambiguation) PL
PL2_(disambiguation)
Collection of statistical models
when applied to data from non-randomized experiments or observational studies, model-based analysis lacks the warrant of randomization. For observational
Analysis_of_variance
Finding information for an information need
Uncertain inference Language models Divergence-from-randomness model Latent Dirichlet allocation Feature-based retrieval models view documents as vectors
Information_retrieval
Measure of difference between two points
class of divergences. When the points are interpreted as probability distributions – notably as either values of the parameter of a parametric model or as
Bregman_divergence
Mathematical statistics distance measure
mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence), denoted D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel
Kullback–Leibler_divergence
Function that measures dissimilarity between two probability distributions
information geometry, a divergence is a kind of statistical distance: a binary function which establishes the separation from one probability distribution
Divergence_(statistics)
Machine learning technique
the KL divergence (a measure of statistical distance between distributions) between the model being fine-tuned and the initial supervised model. By choosing
Reinforcement learning from human feedback
Reinforcement_learning_from_human_feedback
Model for generating observable data in probability and statistics
Generative models are often contrasted with discriminative models, which focus on predicting outputs from inputs directly. Generative model approaches
Generative_model
Apparent lack of pattern or predictability in events
as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance
Randomness
Interactions among inertial, elastic, and aerodynamic forces
simple models (e.g. single aileron on an Euler-Bernoulli beam), control reversal speeds can be derived analytically as for torsional divergence. Control
Aeroelasticity
Type of mathematical model
statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger
Statistical_model
Distance between two statistical objects
pseudometrics on distributions Kullback–Leibler divergence Rényi divergence Jensen–Shannon divergence Ball divergence Bhattacharyya distance (despite its name
Statistical_distance
Concept in information theory
the min-entropy is used in the context of randomness extractors. Let X {\displaystyle X} be a discrete random variable with possible outcomes in the set
Rényi_entropy
Concept in genetics
but also natural selection, gene flow, and mutation contribute to this divergence. This potential for relatively rapid changes in the colony's gene frequency
Genetic_drift
Variable representing a random phenomenon
object which depends on random events. The term 'random variable' in its mathematical definition refers to neither randomness nor variability but instead
Random_variable
Generalization of the one-dimensional normal distribution to higher dimensions
vector space, and the result has units of nats. The Kullback–Leibler divergence from N 1 ( μ 1 , Σ 1 ) {\displaystyle {\mathcal {N}}_{1}({\boldsymbol {\mu
Multivariate normal distribution
Multivariate_normal_distribution
Quantifying marketing influence
comparing MTA outputs to results from randomized experiments have found substantial discrepancies, with attribution models systematically misallocating credit
Attribution_(marketing)
Model in theoretical ecology and statistical mechanics
The random generalized Lotka–Volterra model (rGLV) is an ecological model and random set of coupled ordinary differential equations where the parameters
Random generalized Lotka–Volterra model
Random_generalized_Lotka–Volterra_model
Mathematical formalization of card shuffling
cards, the Gilbert–Shannon–Reeds model describes the probabilities obtained from a certain mathematical model of randomly cutting and then riffling a deck
Gilbert–Shannon–Reeds_model
Description of the behaviour of bosons
information retrieval. The method is one of a collection of DFR ("Divergence From Randomness") models, the basic notion being that Bose–Einstein statistics may
Bose–Einstein_statistics
Probabilistic model
graph expresses the conditional dependence structure between random variables. Graphical models are commonly used in probability theory, statistics—particularly
Graphical_model
Statistical concept
mixture models, where members of the population are sampled at random. Conversely, mixture models can be thought of as compositional models, where the
Mixture_model
Process of making something random
Randomization is the process of making something random. Randomization is not haphazard; instead, a random process is a sequence of random variables describing
Randomization
Mathematical methods used in Bayesian inference and machine learning
Kullback–Leibler divergence (KL-divergence) of Q from P as the choice of dissimilarity function. This choice makes this minimization tractable. The KL-divergence is
Variational_Bayesian_methods
Experiment using randomness in some aspect, usually to aid in removal of bias
(according to the law of large numbers). Randomization also produces ignorable designs, which are valuable in model-based statistical inference, especially
Randomized_experiment
randomization procedure. The model for the response is Y i , j = μ + T i + r a n d o m e r r o r {\displaystyle Y_{i,j}=\mu +T_{i}+\mathrm {random\
Completely_randomized_design
Process of using data analysis for predicting population data from sample data
(first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model. Konishi and Kitagawa state
Statistical_inference
Algorithm for modelling sequential data
needing double the amount of embedding-related parameters and to avoid divergence during training. This practice is called weight tying. A positional encoding
Transformer_(deep_learning)
Probabilistic problem-solving algorithm
random sampling for obtaining numerical results, conceptualized by Polish mathematician Stanisław Ulam. The underlying concept is to use randomness to
Monte_Carlo_method
Degradation of AI models trained on synthetic data
degradation of machine learning models from uncurated synthetic data, or from training on the outputs of another model, such as a prior versions of itself
Model_collapse
Statistical model for a binary dependent variable
Kullback–Leibler divergence. This leads to the intuition that by maximizing the log-likelihood of a model, you are minimizing the KL divergence of your model from the
Logistic_regression
Class of statistical models
linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be
Generalized_linear_model
Technique for the generative modeling of a continuous probability distribution
making biased random steps that are a sum of pure randomness (like a Brownian walker) and gradient descent down the potential well. The randomness is necessary:
Diffusion_model
Statistical model allowing for frequent zero values
conceived of as the basic count model upon which a variety of other count models are based." In a Poisson model, "… the random variable y {\displaystyle y}
Zero-inflated_model
Form of scientific experiment
physiological effects of treatments from various psychological sources of bias.[citation needed] The randomness in the assignment of participants to
Randomized_controlled_trial
Branch of statistics
Cox proportional hazards regression Parametric survival models Survival trees Survival random forests The following terms are commonly used in survival
Survival_analysis
Chart of correlation statistics
processes. The randomness assumption is critically important for the following three reasons: Most standard statistical tests depend on randomness. The validity
Correlogram
Form of causal modeling that fit networks of constructs to data
Structural equation modeling (SEM) is a diverse set of methods used by scientists for both observational and experimental research. SEM is used mostly
Structural_equation_modeling
Statistical method that summarizes and/or integrates data from multiple sources
to assume that random-effects analysis accounts for all uncertainty about the way effects can vary from trial to trial. Newer models of meta-analysis
Meta-analysis
Task of selecting a statistical model from a set of candidate models
Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. In the context
Model_selection
Statistical modeling method
regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Most commonly, the conditional
Linear_regression
Divergent sum of positive unit fractions
_{i=1}^{n-1}2H_{i}=O(n\log n).} The divergence of the harmonic series corresponds in this application to the fact that, in the comparison model of sorting used for quicksort
Harmonic_series_(mathematics)
Parametric model in survival analysis
accelerated failure time model (AFT model) is a parametric model that provides an alternative to the commonly used proportional hazards models. Whereas a proportional
Accelerated failure time model
Accelerated_failure_time_model
Machine learning technique for privacy-preserving training
privacy budgets, which can reduce model accuracy. DP-SGD has become a de facto standard for privacy-preserving learning from large datasets. It is used in
Differentially private stochastic gradient descent
Differentially_private_stochastic_gradient_descent
Class of statistical survival models
Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one
Proportional_hazards_model
Statistical test
time series are different from zero. Instead of testing randomness at each distinct lag, it tests the "overall" randomness based on a number of lags,
Ljung–Box_test
Selection of data points in statistics
estimate the accuracy of results. Simple random sampling can be vulnerable to sampling error because the randomness of the selection may result in a sample
Sampling_(statistics)
Mathematical model used for classification or regression
Discriminative models, also referred to as conditional models, are a class of models frequently used for classification. In machine learning, it typically models the
Discriminative_model
Type of statistical model
theory is possible. For the regression case, the statistical model is as follows. Given a (random) sample ( Y i , X i 1 , … , X i p ) , i = 1 , … , n {\displaystyle
Linear_model
Model of the evolution of genetic incompatibility
modes of divergence. For instance, if divergence is due to different selection pressures, thus causing natural selection to act, or to random genetic drift
Bateson–Dobzhansky–Muller model
Bateson–Dobzhansky–Muller_model
Statistical distribution for dependence between random variables
/ model the dependence (inter-correlation) between random variables. Their name, introduced by applied mathematician Abe Sklar in 1959, comes from the
Copula_(statistics)
Statistical model used in time series analysis
commonly normal random variables. The notation ARMA(p, q) refers to the model with p autoregressive terms and q moving-average terms. This model contains the
Autoregressive moving-average model
Autoregressive_moving-average_model
Statistical concept
values. Graphical models can be used to describe the missing data mechanism in detail. Values in a data set are missing completely at random (MCAR) if the
Missing_data
Fundamental theorem in probability theory and statistics
sums of independent random variables. Reading, MA: Addison-wesley. Nolan, John P. (2020). Univariate stable distributions, Models for Heavy Tailed Data
Central_limit_theorem
Overview of and topical guide to statistics
Sufficient statistic Ancillary statistic Minimal sufficiency Kullback–Leibler divergence Nuisance parameter Order statistic Bayesian inference Bayes' theorem Bayes
Outline_of_statistics
Mathematical function for the probability a given outcome occurs in an experiment
probability distribution. With this source of uniform pseudo-randomness, realizations of any random variable can be generated. For example, suppose U has a
Probability_distribution
Concept in information theory
appeared n times in the test sample of size N). By the definition of KL divergence, it is also equal to H ( p ~ ) + D K L ( p ~ ‖ q ) {\displaystyle H({\tilde
Perplexity
Measure of goodness of fit for a statistical model
generalized linear models. Deviance can be related to Kullback–Leibler divergence. The unit deviance d ( y , μ ) {\displaystyle d(y,\mu )} is a bivariate
Deviance_(statistics)
Probability distribution
hold.[proof] For non-normal random variables uncorrelatedness does not imply independence. The Kullback–Leibler divergence of one normal distribution X
Normal_distribution
Measure of divergence between populations
measure of the genetic divergence between species or between populations within a species, whether the distance measures time from common ancestor or degree
Genetic_distance
Statistical hypothesis test
Ryabko, B. Ya.; Stognienko, V. S.; Shokin, Yu. I. (2004). "A new test for randomness and its application to some cryptographic problems" (PDF). Journal of
Chi-squared_test
Statistical linear model
general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that
General_linear_model
Concept in statistics
"Controlling Variability in Split-Merge Systems". Analytical and Stochastic Modeling Techniques and Applications (PDF). Lecture Notes in Computer Science. Vol
Range_(statistics)
Class of artificial neural network
W} , is the contrastive divergence (CD) algorithm due to Hinton, originally developed to train PoE (product of experts) models. The algorithm performs
Restricted_Boltzmann_machine
Statistical method
estimator by resampling (often with replacement) one's data or a model which is estimated from the data. Bootstrapping assigns measures of accuracy (bias,
Bootstrapping_(statistics)
Statistical model used in machine learning
training a deep learning model, the goal with normalizing flows is to minimize the Kullback–Leibler divergence between the model's likelihood and the target
Flow-based_generative_model
Deep learning generative model to encode data representation
optimize this model, one needs to know two terms: the "reconstruction error", and the Kullback–Leibler divergence (KL-D). Both terms are derived from the free
Variational_autoencoder
Design of experiments to collect similar contexts together
trials for any K-factor randomized block design are simply the cell indices of a k dimensional matrix. The model for a randomized block design with one
Blocking_(statistics)
Discrete probability distribution
The directed Kullback–Leibler divergence of P = Pois ( λ ) {\displaystyle P=\operatorname {Pois} (\lambda )} from P 0 = Pois ( λ 0 ) {\displaystyle
Poisson_distribution
Model in statistical genetics
coalescent model also provides a framework for using genomic data to address a number of biological problems, such as estimation of species divergence times
Multispecies coalescent process
Multispecies_coalescent_process
Metric on a smooth statistical manifold
relative entropy (i.e., the Kullback–Leibler divergence); specifically, it is the Hessian of the divergence. Alternately, it can be understood as the metric
Fisher_information_metric
Function related to statistics and probability theory
likelihood) gives the relative merit of various statistical models for describing a data set. Often the models being compared are parameterized by a parameter, with
Likelihood_function
Fusion of natural selection with Mendelian inheritance
push them away from adaptive peaks, which would in turn allow natural selection to push them towards new adaptive peaks. Wright's model appealed to field
Modern synthesis (20th century)
Modern_synthesis_(20th_century)
Distribution of an uncertain quantity
based criterion, such as KL divergence or log-likelihood function for binary supervised learning problems and mixture model problems. Philosophical problems
Prior_probability
Probability distribution
The directed Kullback–Leibler divergence in nats of e λ {\displaystyle e^{\lambda }} ("approximating" distribution) from e λ 0 {\displaystyle e^{\lambda
Exponential_distribution
Time series model
econometrics, the autoregressive conditional heteroskedasticity (ARCH) model is a statistical model for time series data that describes the variance of the current
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
Randomization Randomized block design Randomized controlled trial Randomized decision rule Randomized experiment Randomized response Randomness Randomness tests
List_of_statistics_articles
Lower bound on the log-likelihood of some observed data
Kullback-Leibler divergence (KL divergence) term which decreases the ELBO due to an internal part of the model being inaccurate despite good fit of the model overall
Evidence_lower_bound
Experimental design that is optimal with respect to some statistical criterion
Kirstine Smith. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with
Optimal_experimental_design
Method of estimating the parameters of a statistical model, given observations
linear regression model maximizes the likelihood when the random errors are assumed to have normal distributions with the same variance. From the perspective
Maximum_likelihood_estimation
Number of values in the final calculation of a statistic that are free to vary
most often used in the context of linear models (linear regression, analysis of variance), where certain random vectors are constrained to lie in linear
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Notion in statistics
of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of
Fisher_information
Process involving chance used in research for allocating experimental subjects to groups
statistics. More advanced statistical modeling can be used to adapt the inference to the sampling method. Randomization was emphasized in the theory of statistical
Random_assignment
Probability Randomness, Pseudorandomness, Quasirandomness Randomization, hardware random number generator Random number generation Random sequence Uncertainty
List_of_probability_topics
British statistician and geneticist (1919–2000)
objective randomization procedures. Kempthorne's randomization-analysis has influenced the causal model of Donald Rubin; in turn, Rubin's randomization-based
Oscar_Kempthorne
Probability distribution
distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling
Binomial_distribution
Set of statistical processes for estimating the relationships among variables
line case, given a random sample from the population, we estimate the population parameters and obtain the sample linear regression model: y ^ i = β ^ 0 +
Regression_analysis
Transport of dissolved species from the highest to the lowest concentration region
is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios. Therefore
Diffusion
Type of statistical model
A partially linear model is a form of semiparametric model, since it contains parametric and nonparametric elements. Application of the least squares
Partially_linear_model
Sequence of data points over time
forecasting is the use of a model to predict future values based on previously observed values. Generally, time series data is modeled as a stochastic process
Time_series
Concept in machine learning
Double descent in statistics and machine learning is the phenomenon where a model's error rate on the test set initially decreases with the number of parameters
Double_descent
Statistical theorem
and the restricted model is therefore not nested within the larger model. As a demonstration, they set either one or two random effects variances to
Wilks'_theorem
Subfield of information theory and computer science
to distinguish it from other stronger notions of randomness (2-randomness, 3-randomness, etc.). In addition to Martin-Löf randomness concepts, there are
Algorithmic information theory
Algorithmic_information_theory
Ratio of competing statistical models
competing statistical models represented by their evidence, and is used to quantify the support for one model over the other. The models in question can have
Bayes_factor
Sampling from a population which can be partitioned into subpopulations
interest, between the towns). Instead, if we choose to take a random sample of 10, 20 and 30 from Town A, B and C respectively, then we can produce a smaller
Stratified_sampling
Lattice model of statistical mechanics
thermodynamic limit, there is no divergence in the specific heat. Indeed, like the one-dimensional Ising model, the one-dimensional XY model has no phase transitions
Classical_XY_model
Method of statistical sampling
attributes or characteristics, known as strata, then followed by simple random sampling from the stratified groups, where each element within the same subgroup
Stratified_randomization
Design of tasks
may be represented with a general linear model, with the design matrix W {\displaystyle W} having entries from { − 1 , 0 , 1 } {\displaystyle \{-1,0,1\}}
Design_of_experiments
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DIVERGENCE FROM-RANDOMNESS-MODEL
DIVERGENCE FROM-RANDOMNESS-MODEL
DIVERGENCE FROM-RANDOMNESS-MODEL
DIVERGENCE FROM-RANDOMNESS-MODEL
DIVERGENCE FROM-RANDOMNESS-MODEL
DIVERGENCE FROM-RANDOMNESS-MODEL
DIVERGENCE FROM-RANDOMNESS-MODEL
DIVERGENCE FROM-RANDOMNESS-MODEL
DIVERGENCE FROM-RANDOMNESS-MODEL
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