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Family of optimization algorithms
(Stochastic) variance reduction is an algorithmic approach to minimizing functions that can be decomposed into finite sums. By exploiting the finite sum
Stochastic_variance_reduction
Statistical measure of how far values spread from their average
In probability theory and statistics, variance is a measure of dispersion, meaning it is a measure of how far a set of numbers are spread out from their
Variance
Optimization algorithm
Differentially private stochastic gradient descent Linear classifier Online machine learning Stochastic hill climbing Stochastic variance reduction ⊙ {\displaystyle
Stochastic_gradient_descent
Topics referred to by the same term
survey for Asteroseismology and Galactic Archaeology SAGA, a stochastic variance reduction algorithm for mathematical optimisation SAGA, a European quantum
Saga_(disambiguation)
Property of a model
In statistics and machine learning, the bias–variance tradeoff describes the relationship between a model's complexity, the accuracy of its predictions
Bias–variance_tradeoff
Projection of data onto lower-dimensional manifolds
Nonlinear dimensionality reduction (NLDR), also known as manifold learning, is any of various related techniques that aim to project high-dimensional
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Process of reducing the number of random variables under consideration
dimensionality reduction, principal component analysis, performs a linear mapping of the data to a lower-dimensional space in such a way that the variance of the
Dimensionality_reduction
Technique used in stochastic gradient variational inference
optimization of parametric probability models using stochastic gradient descent, and the variance reduction of estimators. It was developed in the 1980s in
Reparameterization_trick
Family of iterative methods
Stochastic gradient descent Stochastic variance reduction Toulis, Panos; Airoldi, Edoardo (2015). "Scalable estimation strategies based on stochastic
Stochastic_approximation
Collection of statistical models
Analysis of variance (ANOVA) is a family of statistical methods used to compare the means of two or more groups by analyzing variance. Specifically, ANOVA
Analysis_of_variance
Optimization and sampling technique
approximate samples from the posterior as by balancing variance from the injected Gaussian noise and stochastic gradient computation.[citation needed] SGLD is
Stochastic gradient Langevin dynamics
Stochastic_gradient_Langevin_dynamics
Distribution estimation technique
importance weighted variational autoencoders. Importance sampling is a variance reduction technique that can be used in the Monte Carlo method. The idea behind
Importance_sampling
Statistical property
all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Measure of covariance of components of a random vector
matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between
Covariance_matrix
Linear regression model with a single explanatory variable
mean β and variance σ 2 / ∑ i ( x i − x ¯ ) 2 , {\textstyle \sigma ^{2}\left/\sum _{i}(x_{i}-{\bar {x}})^{2}\right.,} where σ2 is the variance of the error
Simple_linear_regression
Statistical property quantifying how much a collection of data is spread out
statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data
Statistical_dispersion
Non-parametric method for testing whether samples originate from the same distribution
the one-way analysis of variance (ANOVA). A significant Kruskal–Wallis test indicates that at least one sample stochastically dominates one other sample
Kruskal–Wallis_test
Differential equations involving stochastic processes
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution
Stochastic differential equation
Stochastic_differential_equation
analysis Variance Variance decomposition of forecast errors Variance gamma process Variance inflation factor Variance-gamma distribution Variance reduction Variance-stabilizing
List_of_statistics_articles
Measure of the joint variability
behavior. The magnitude of the covariance is the geometric mean of the variances that are shared for the two random variables, where a larger magnitude
Covariance
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
distribution) are considered low-variance, while those with CV > 1 (such as a hyper-exponential distribution) are considered high-variance[citation needed]. Some
Coefficient_of_variation
Unbiased statistical estimator minimizing variance
minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than
Minimum-variance unbiased estimator
Minimum-variance_unbiased_estimator
Mathematical framework for investment risk
Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of financial assets such that the expected
Modern_portfolio_theory
Statistical hypothesis test
statistical test that compares variances. It is used to determine if the variances of two samples, or if the ratios of variances among multiple samples, are
F-test
Sampling from a population which can be partitioned into subpopulations
In computational statistics, stratified sampling is a method of variance reduction when Monte Carlo methods are used to estimate population statistics
Stratified_sampling
Risk reduction technique
asset with the lowest variance of return, even if the assets' returns are uncorrelated. For example, let asset X have stochastic return x {\displaystyle
Diversification_(finance)
Statistical property
has its own mean and variance. Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided
Standard_error
Experimental design that is optimal with respect to some statistical criterion
designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to
Optimal_experimental_design
Method of data analysis
dimensionality reduction can be a very useful step for visualising and processing high-dimensional datasets, while still retaining as much of the variance in the
Principal_component_analysis
Measure of variation in statistics
data set or probability distribution is the square root of its variance (the variance being the average of the squared deviations from the mean). A useful
Standard_deviation
Time series model
the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms; often the variance is
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
Class of stochastic process
strong/strongly stationary process) is a stochastic process whose statistical properties, such as mean and variance, do not change over time. More formally
Stationary_process
Vietnamese-American computer scientist and applied mathematician
a wide class of variance-reduced optimization methods. The SARAH algorithm has been included in graduate-level courses on stochastic optimization and
Lam_Nguyen
Statistical method
( i , m ) {\displaystyle (i,m)} th unobserved stochastic error term with mean zero and finite variance. In matrix notation X − M = L F + ε {\displaystyle
Factor_analysis
Measure of linear correlation
{\displaystyle r_{xy}} by substituting estimates of the covariances and variances based on a sample into the formula above. Given paired data { ( x 1 ,
Pearson correlation coefficient
Pearson_correlation_coefficient
Procedure to estimate standard deviation from a sample
settings of α as a function of sample size n. Changing α alters the variance reduction ratio of the filter, which is known to be V R R = α 2 − α {\displaystyle
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Statistical measure to determine how suited data is for factor analysis
The statistic is a measure of the proportion of variance among variables that might be common variance. The higher the proportion, the higher the KMO-value
Kaiser–Meyer–Olkin_test
Population dynamics concept
This results in the acceleration or reduction of the rate of extinction depending on the intensity of stochasticity. There is a negative correlation between
Environmental_stochasticity
Fundamental theorem in probability theory and statistics
with expected value (average) μ {\displaystyle \mu } and finite positive variance σ 2 {\displaystyle \sigma ^{2}} , and let X ¯ n {\displaystyle {\bar {X}}_{n}}
Central_limit_theorem
Statistical method
estimated from the data. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates. This
Bootstrapping_(statistics)
Number of values in the final calculation of a statistic that are free to vary
intermediate steps in the estimation of the parameter itself. For example, if the variance is to be estimated from a random sample of N {\textstyle N} independent
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Normalized measure of the dispersion of a probability distribution
dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized
Index_of_dispersion
Statistical measure of the magnitude of a phenomenon
expectation and variance of the effect sizes. In some cases large sample approximations for the variance are used. One suggestion for the variance of Hedges'
Effect_size
Tree-based ensemble machine learning methods
subspace method, which, in Ho's formulation, is a way to implement the "stochastic discrimination" approach to classification proposed by Eugene Kleinberg
Random_forest
Machine learning paradigm
the sum of the bias and the variance of the learning algorithm. Generally, there is a tradeoff between bias and variance. A learning algorithm with low
Supervised_learning
{x} )}}} The ratio of the variance and the arithmetic mean was proposed as a test statistic by Clapham. Since the variance is always ≥0 the contraharmonic
Contraharmonic_mean
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
Covariance and correlation
processes, because the mean or variance may not exist. Let ( X t , Y t ) {\displaystyle (X_{t},Y_{t})} represent a pair of stochastic processes that are jointly
Cross-correlation
Test used in statistics
statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance. Notionally, any F-test can
F-test of equality of variances
F-test_of_equality_of_variances
Class of reinforcement learning algorithms
REINFORCE have been introduced, under the title of variance reduction. A common way for reducing variance is the REINFORCE with baseline algorithm, based
Policy_gradient_method
Correlation of a signal with a time-shifted copy of itself, as a function of shift
interchangeably. The definition of the autocorrelation coefficient of a stochastic process is ρ X X ( t 1 , t 2 ) = K X X ( t 1 , t 2 ) σ t 1 σ t 2 = E
Autocorrelation
Family of statistical methods based on sampling of available data
The jackknife, originally used for bias reduction, is more of a specialized method and only estimates the variance of the point estimator. This can be enough
Resampling_(statistics)
Statistical estimator for ratio of means
size, mx is the mean of the x variate and sx2 and sy2 are the sample variances of the x and y variates respectively. A computationally simpler but slightly
Ratio_estimator
Overview of and topical guide to machine learning
error reduction (RIPPER) Rprop Rule-based machine learning Self-organizing map Skill chaining Sparse PCA State–action–reward–state–action Stochastic gradient
Outline_of_machine_learning
Numerical integration process
called quasi-random sequences or sub-random sequences) to achieve variance reduction. This is in contrast to the regular Monte Carlo method or Monte Carlo
Quasi-Monte_Carlo_method
Study of convergence properties of statistical estimators
}}_{n})_{n\in \mathbb {N} }} to θ 0 {\displaystyle \theta _{0}} is of stochastic order 1 / a n {\displaystyle 1/a_{n}} (also written O p ( 1 / a n ) {\displaystyle
Asymptotic theory (statistics)
Asymptotic_theory_(statistics)
Statistical measure of variability
estimator of scale than the sample variance or standard deviation, it works better with distributions without a mean or variance, such as the Cauchy distribution
Median_absolute_deviation
Procedure for comparing multivariate sample means
In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate sample means. As a multivariate procedure, it is used
Multivariate analysis of variance
Multivariate_analysis_of_variance
Single measure of some attribute of a sample
statistics. Some include: Sample mean, sample median, and sample mode Sample variance and sample standard deviation Sample quantiles besides the median, e.g
Statistic
Statistical method for resampling
therefore, a form of resampling. It is especially useful for bias and variance estimation. The jackknife pre-dates other common resampling methods such
Jackknife_resampling
Non-parametric statistical test
repeated measures analysis of variance by ranks. In its use of ranks it is similar to the Kruskal–Wallis one-way analysis of variance by ranks. The Friedman
Friedman_test
Study of uncertainty in the output of a mathematical model or system
the sensitivity measures can be hard to interpret. Stochastic code: A code is said to be stochastic when, for several evaluations of the code with the
Sensitivity_analysis
Middle quantile of a data set or probability distribution
the minimum-variance mean (for large normal samples), which is to say the variance of the median will be ~50% greater than the variance of the mean.
Median
Approximation method in statistics
calculation is similar in both cases. Polynomial least squares describes the variance in a prediction of the dependent variable as a function of the independent
Least_squares
Statistical test used to test homoscedasticity
"homogeneity of variance"), that is, if multiple samples are from populations with equal variances. Some statistical tests, such as the analysis of variance, assume
Bartlett's_test
Probability distribution
a normal family as a compound distribution when marginalizing over the variance parameter. Student's t distribution has the probability density function
Student's_t-distribution
Inverse of the average of the inverses of a set of numbers
Assuming that the variance is not infinite and that the central limit theorem applies to the sample then using the delta method, the variance is Var ( H
Harmonic_mean
the performance of subset simulation (and other variance-reduction techniques) in a set of stochastic mechanics benchmark problems. Chapter 4 of Phoon
Subset_simulation
Statistical hypothesis test
t-tests, though strictly speaking that name should only be used if the variances of the two populations are also assumed to be equal; the form of the test
Student's_t-test
Statistical hypothesis test
exactly is the test that the variance of a normally distributed population has a given value based on a sample variance. Such tests are uncommon in practice
Chi-squared_test
Metric for fit of statistical models
Pearson's chi-square test). In the analysis of variance, one of the components into which the variance is partitioned may be a lack-of-fit sum of squares
Goodness_of_fit
Method used in statistics, pattern recognition, and other fields
more commonly, for dimensionality reduction before later classification. LDA is closely related to analysis of variance (ANOVA) and regression analysis
Linear_discriminant_analysis
Estimate of an interval in which future observations will fall
future observation X in a normal distribution N(μ,σ2) with known mean and variance may be calculated from γ = P ( ℓ < X < u ) = P ( ℓ − μ σ < X − μ σ < u
Prediction_interval
Statistical relationship
variables of a numerical dataset normalized to the square root of their variances. Equivalently, Pearson's correlation coefficient can be calculated by
Correlation
Type of mathematical model
of the variables are stochastic. In the above example with children's heights, ε is a stochastic variable; without that stochastic variable, the model
Statistical_model
Effect of variables' uncertainties on the uncertainty of a function based on them
of the standard deviation, σ, which is the positive square root of the variance. The value of a quantity and its error are then expressed as an interval
Propagation_of_uncertainty
Class of statistical models
response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized
Generalized_linear_model
Nonparametric test of the null hypothesis
responses with the alternative hypothesis being that one distribution is stochastically greater than the other. That is to say that the probability of a random
Mann–Whitney_U_test
Process of selecting a portfolio
giving a property of mean-variance efficient portfolios Portfolio theory, for the formulas Risk parity / Tail risk parity Stochastic portfolio theory Universal
Portfolio_optimization
General linear model that blends ANOVA and regression
decomposes the variance in the DV into variance explained by the CV(s), variance explained by the categorical IV, and residual variance. Intuitively, ANCOVA
Analysis_of_covariance
Technique for setting initial values of trainable parameters in a neural network
Philipp (2018-07-03). "Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients". Proceedings of the 35th International Conference on
Weight_initialization
Branch of statistics
commonly used in statistics include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. Statistical data
Mathematical_statistics
Statistical property
of transformations); for example, the sample variance is a biased estimator for the population variance. These are all illustrated below. An unbiased
Bias_of_an_estimator
Statistical model validation technique
Steiner, Gerald; Salzer, Reiner; Sowa, Michael G. (October 2005). "Variance reduction in estimating classification error using sparse datasets". Chemometrics
Cross-validation_(statistics)
Mathematical function for the probability a given outcome occurs in an experiment
and stochastics. New York: Springer. p. 57. ISBN 9780387878584. see Lebesgue's decomposition theorem Erhan, Çınlar (2011). Probability and stochastics. New
Probability_distribution
Probability distribution of the possible sample outcomes
compute one value of a statistic (for example, the sample mean or sample variance) per sample, the sampling distribution is the probability distribution
Sampling_distribution
Smooth function in statistics
statistics, the variance function is a smooth function that depicts the variance of a random quantity as a function of its mean. The variance function is
Variance_function
Statistical test
Z-tests if the sample size is large or the population variance is known. If the population variance is unknown (and therefore has to be estimated from the
Z-test
Statistical modeling method
response and explanatory variables with the best fit or least error, i.e. variance. After developing such a model, if additional values of the explanatory
Linear_regression
Probabilistic problem-solving algorithm
2 {\displaystyle s^{2}} be the estimated variance, sometimes called the "sample" variance; it is the variance of the results obtained from a relatively
Monte_Carlo_method
Machine learning algorithm
discretization before being applied. The variance reduction of a node N is defined as the total reduction of the variance of the target variable Y due to the
Decision_tree_learning
Signal processing technique
contrast, the parametric approaches assume that the underlying stationary stochastic process has a certain structure that can be described using a small number
Spectral_density_estimation
Probabilistic measurement methods
risk-management decisions. This state of affairs can be mitigated by variance reduction techniques. A simple technique is, for every sample path obtained
Monte Carlo methods in finance
Monte_Carlo_methods_in_finance
Fourth standardized moment in statistics
For non-normal samples, the variance of the sample variance depends on the kurtosis; for details, please see variance. Pearson's definition of kurtosis
Kurtosis
Criterion for model selection
intercept, the q {\displaystyle q} slope parameters, and the constant variance of the errors; thus, k = q + 2 {\displaystyle k=q+2} . The BIC can be derived
Bayesian information criterion
Bayesian_information_criterion
Model for generating observable data in probability and statistics
(Bernoulli) / Binomial / Poisson regressions Partition of variance Analysis of variance (ANOVA) Analysis of variance (ANCOVA)] MANOVA Degrees of freedom Categorical /
Generative_model
Method of machine learning
maximize ad revenue, portfolio optimization, shortest path prediction (with stochastic weights, e.g. traffic on roads for a maps application), spam filtering
Online_machine_learning
Sequence of data points over time
previously observed values. Generally, time series data is modeled as a stochastic process. While regression analysis is often employed in such a way as
Time_series
Experiment methodology
bandit Multivariate testing Randomized controlled trial Scientific control Stochastic dominance Test statistic Two-proportion Z-test Young, Scott W. H. (August
A/B_testing
Mathematical analysis technique
parameters are the mean and variance of the PDF. Essentially, the mean is the location of the PDF on the real number line, and the variance is a description of
Experimental uncertainty analysis
Experimental_uncertainty_analysis
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STOCHASTIC VARIANCE-REDUCTION
STOCHASTIC VARIANCE-REDUCTION
Girl/Female
English
Modern blend of Ava and Ana.
Girl/Female
American, Australian, Chinese, Dutch, Finnish, French, German, Greek, Latin, Swedish
The Holy One; Black Beauty; Dark One; Very Holy Woman; Similar to Ariadne; Utterly Pure
Girl/Female
American, British, English, German
Bearer of Good News; Modern Blend of Ava and Ana
Female
Dutch
, Marie Anne.
Female
French
French form of Latin Ariadne, ARIANNE means "utterly pure."
Boy/Male
Latin
Fidde.
Female
English
French form of Latin Marianna, MARIANNE means "like Marius."
Girl/Female
Greek French
Holy one.
Female
French
French form of Latin Ariadne, ARIANE means "utterly pure."
Boy/Male
American, British, English
Blend of Darell and Clarence
Surname or Lastname
Variant spelling of Dutch Dils.English
Variant spelling of Dutch Dils.English : infrequent variant of Dill.
Girl/Female
American, Australian, British, Chinese, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Hebrew, Latin, Lebanese, Netherlands, Norse, Swedish, Swiss
Bitter; Sea of Bitterness; A Combination of Marie and Anne; Rebelliousnesses Wished for Child; A Blend of Marie Star of the Sea and Anne; Star of the Sea
Girl/Female
Australian, British, English, French, German, Hebrew, Lebanese
Variant of Mary Bitter; Bitter; Beloved
Girl/Female
Latin
Mythological Ariadne who aided Theseus to escape from the Cretan labyrinth.
Girl/Female
French
Bitter.
Girl/Female
British, Danish, English, Scandinavian, Swedish
Pure; Abbreviation of Katherine
Girl/Female
Scandinavian
Abbreviation of Katherine. Pure.
Surname or Lastname
Variant of Nicolai 2.English
Variant of Nicolai 2.English : variant of Nicholas.
Surname or Lastname
English and Scottish (of Norman origin)
English and Scottish (of Norman origin) : habitational name from Valence in Drôme, France, which probably has the same origin as Valencia.
Girl/Female
Norse American Latin Russian French
Bitter grace.
STOCHASTIC VARIANCE-REDUCTION
STOCHASTIC VARIANCE-REDUCTION
STOCHASTIC VARIANCE-REDUCTION
STOCHASTIC VARIANCE-REDUCTION
STOCHASTIC VARIANCE-REDUCTION
STOCHASTIC VARIANCE-REDUCTION
STOCHASTIC VARIANCE-REDUCTION
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