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Mathematical procedure for reducing the variance of statistical estimators
mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained
Variance_reduction
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
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
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
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
Statistical technique
components with higher variances (the ones based on eigenvectors corresponding to the higher eigenvalues of the sample variance-covariance matrix of the
Principal component regression
Principal_component_regression
Vietnamese-American computer scientist and applied mathematician
multiple names: authors list (link) "Variance Reduction Methods" (PDF). Princeton University. "Lecture 7: Variance Reduction" (PDF). EPFL. Nguyen, Lam M.; Hoang
Lam_Nguyen
Technique used in stochastic gradient variational inference
parametric probability models using stochastic gradient descent, and the variance reduction of estimators. It was developed in the 1980s in operations research
Reparameterization_trick
Technique for increasing the precision of estimates in Monte Carlo experiments
The control variates method is a variance reduction technique used in Monte Carlo methods. It exploits information about the errors in estimates of known
Control_variates
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
Statistical technique
Boca Raton: Chapman & Hall/CRC. p. 25. Liao, JG; Rohde, C (2022). "Variance reduction in the inverse probability weighted estimators for the average treatment
Inverse_probability_weighting
Monte Carlo method
In statistics, the antithetic variates method is a variance reduction technique used in Monte Carlo methods. Considering that the error in the simulated
Antithetic_variates
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
Hashing technique
In computer science, consistent hashing is a special kind of hashing technique such that when a hash table is resized, only n / m {\displaystyle n/m} keys
Consistent_hashing
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
Topics referred to by the same term
in a free group, a word with no adjacent generator-inverse pairs Variance reduction, a procedure used to increase the precision of the estimates that
Reduction
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
Concept in mathematical modelling
different populations: "'Explained variance' explains nothing."[page needed] Analysis of variance Variance reduction Variance-based sensitivity analysis Kent
Explained_variation
Type of image blur produced by a Gaussian function
smoothing process, obeying a semi-group property over additions of the variance of the kernel, or describing the effect of Brownian motion over a spatial
Gaussian_blur
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
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
attractive for complex systems where it is difficult to use other variance reduction or rare-event sampling techniques that require prior information about
Subset_simulation
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
Machine learning strategy
overlapping partitions for labeling. Variance reduction: label those points that would minimize output variance, which is one of the components of error
Active learning (machine learning)
Active_learning_(machine_learning)
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
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
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 algorithm
classifier Online machine learning Stochastic hill climbing Stochastic variance reduction ⊙ {\displaystyle \odot } denotes the element-wise product. Bottou
Stochastic_gradient_descent
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
Topics referred to by the same term
for Asteroseismology and Galactic Archaeology SAGA, a stochastic variance reduction algorithm for mathematical optimisation SAGA, a European quantum communication
Saga_(disambiguation)
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
Software package for simulating nuclear processes
surface source; geometry and output tally plotters; a collection of variance reduction techniques; a flexible tally structure; and an extensive collection
Monte Carlo N-Particle Transport Code
Monte_Carlo_N-Particle_Transport_Code
analyzing black box systems, and unlike the importance sampling method of variance reduction, does not require detailed knowledge of the system. The basic idea
Line_sampling
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)
Measure of frequency stability in clocks and oscillators
The Allan variance (AVAR), also known as two-sample variance, is a measure of frequency stability in clocks, oscillators and amplifiers. It is named after
Allan_variance
Systems describing the emergence of resource sharing in nature
tolerated by other members of a group. This developed in response to variance-reduction models, as reciprocal behavior might have socially related taboos
Evolutionary models of food sharing
Evolutionary_models_of_food_sharing
Question in geometric probability
they act to reduce the total variance in the estimator that is an average of the two of them. This method of variance reduction is known as the antithetic
Buffon's_needle_problem
Numerical technique
Carlo Monte Carlo method in statistical physics Monte Carlo method Variance reduction Press et al. 2007, Chap. 4 Press et al. 2007, Chap. 7 Newman & Barkema
Monte_Carlo_integration
Algorithm
\mathrm {E} _{g}(f;N)={1 \over N}\sum _{i}^{N}{f(x_{i})}/g(x_{i}).} The variance of the new estimate is then V a r g ( f ; N ) = V a r ( f / g ; N ) {\displaystyle
VEGAS_algorithm
analysis Variance Variance decomposition of forecast errors Variance gamma process Variance inflation factor Variance-gamma distribution Variance reduction Variance-stabilizing
List_of_statistics_articles
chi-squared test and Fisher's exact test. Paired difference test Variance reduction Randomized block design Gosall, Narinder Kaur Gosall, Gurpal Singh
Paired_data
Subtle energy channels described in yoga and Tantra
Niharika (2013). "Effects of yoga practice on acumeridian energies: Variance reduction implies benefits for regulation". International Journal of Yoga. 6
Nadi_(yoga)
Ensemble learning method
January 2015. Arcing [Boosting] is more successful than bagging in variance reduction Zhou Zhi-Hua (2012). Ensemble Methods: Foundations and Algorithms
Boosting_(machine_learning)
Type of simulation
techniques: Computer experiment Computer simulation Monte Carlo method Variance reduction Pseudo-random number generator Software: List of computer simulation
Discrete-event_simulation
Machine learning method
P. (1993), Improving regression estimation: Averaging methods for variance reduction with extensions to general convex measure optimization Wolpert, D
Ensemble averaging (machine learning)
Ensemble_averaging_(machine_learning)
Concept in probability theory
management terms it means that there is minimal (or eventually no) variance reduction from diversification. For extensions of comonotonicity, see Jouini
Comonotonicity
Australian statistician & academic
Hwa Yang FRSN is an Australian statistician known for her work on variance reduction for microarrays, and for inferring proteins from mass spectrometry
Jean_Yang
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
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
Mathematical framework for investment risk
creating a "free lunch" of risk reduction without necessarily sacrificing expected return. The MPT is a mean-variance theory, and it compares the expected
Modern_portfolio_theory
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
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
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
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)
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 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
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 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
Exact statistical hypothesis test
{\displaystyle \alpha \times 100\%} significance level. To exploit variance reduction with paired samples, a paired permutation test must be applied, see
Permutation_test
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
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
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
Finite difference equation
process, and as the control variate for application in simulation variance reduction. Hoffman, Joe (2001), "Chapter 9. Elliptic partial differential equations"
Discrete_Poisson_equation
random variable as a sum of other random variables Indexed search Variance reduction techniques: Antithetic variates Control variates Importance sampling
List of numerical analysis topics
List_of_numerical_analysis_topics
Designated link between a hedging instrument and the risk it offsets
hedge to be deemed effective, the R squared must be better than 0.8. "Variance-reduction test". Also a comparison of the forecast values or cash flows of the
Hedge_relationship
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
Process of removing noise from a signal
Noise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort
Noise_reduction
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
Technique to make a model more generalizable and transferable
Bias–variance tradeoff Matrix regularization Regularization by spectral filtering Regularized least squares Lagrange multiplier Variance reduction L-curve
Regularization_(mathematics)
Non-parametric method for testing whether samples originate from the same distribution
parametric equivalent of the Kruskal–Wallis test is the one-way analysis of variance (ANOVA). A significant Kruskal–Wallis test indicates that at least one
Kruskal–Wallis_test
Statistical method
estimated from the data. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates. This
Bootstrapping_(statistics)
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
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
Family of iterative methods
Dvoretzky published in 1956. Stochastic gradient descent Stochastic variance reduction Toulis, Panos; Airoldi, Edoardo (2015). "Scalable estimation strategies
Stochastic_approximation
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
Statistical method
the variance in the matrix is to be accounted for (including variance unique to each variable, variance common among variables, and error variance). That
Factor_analysis
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
Measure of the shape of a function
the first moment is the expected value, the second central moment is the variance, the third standardized moment is the skewness, and the fourth standardized
Moment_(mathematics)
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
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
Topics referred to by the same term
non-fiction book by Giles Milton Russian roulette integration, a variance reduction technique in Monte Carlo integration/simulation Russian Roulette (Accept
Russian Roulette (disambiguation)
Russian_Roulette_(disambiguation)
Estimator for quality of a statistical model
(with zero mean), then the model has three parameters: b0, b1, and the variance of the Gaussian distributions. Thus, when calculating the AIC value of
Akaike_information_criterion
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
Phenomenon in machine learning
architectural asymmetry, stop-gradient operations, variance regularization, and redundancy reduction objectives, as seen in methods such as SimCLR, BYOL
Representation_collapse
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)
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
Statistical method that summarizes and/or integrates data from multiple sources
As such, this statistical approach involves extracting effect sizes and variance measures from various studies. By combining these effect sizes the statistical
Meta-analysis
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
Mathematical algorithm
is reduced by increasing the number of paths sampled, or by using variance reduction methods. The WoS theoretically provides exact (or unbiased) simulations
Walk-on-spheres_method
Statistical considerations on how many observations to make
intervals and risk of errors in statistical hypothesis testing. using a target variance for an estimate to be derived from the sample eventually obtained, i.e
Sample_size_determination
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
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 transformation
variable whose distribution is approximately normally distributed, with a variance that is stable over different values of r. Given a set of N bivariate sample
Fisher_transformation
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
Correlation of a signal with a time-shifted copy of itself, as a function of shift
defined. Suppose that the process has mean μ t {\displaystyle \mu _{t}} and variance σ t 2 {\displaystyle \sigma _{t}^{2}} at time t {\displaystyle t} , for
Autocorrelation
Range to estimate an unknown parameter
{\displaystyle \mu } and variance σ 2 . {\displaystyle \sigma ^{2}.} Define the sample mean X ¯ {\displaystyle {\bar {X}}} and unbiased sample variance S 2 {\displaystyle
Confidence_interval
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
Nonparametric test of the null hypothesis
whether or not the population variances are suspected to be different. Rank transformations do not preserve variances, but variances are recomputed from samples
Mann–Whitney_U_test
Concept in inferential statistics
Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments Kurtosis L-moments Skewness Count data
Statistical_significance
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
VARIANCE REDUCTION
VARIANCE REDUCTION
Boy/Male
Latin
Fidde.
Female
Dutch
, Marie Anne.
Female
French
French form of Latin Ariadne, ARIANE means "utterly pure."
Boy/Male
American, British, English
Blend of Darell and Clarence
Girl/Female
Greek French
Holy one.
Girl/Female
English
Modern blend of Ava and Ana.
Girl/Female
Scandinavian
Abbreviation of Katherine. Pure.
Surname or Lastname
Variant spelling of Dutch Dils.English
Variant spelling of Dutch Dils.English : infrequent variant of Dill.
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
British, Danish, English, Scandinavian, Swedish
Pure; Abbreviation of Katherine
Surname or Lastname
Variant of Nicolai 2.English
Variant of Nicolai 2.English : variant of Nicholas.
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
Australian, British, English, French, German, Hebrew, Lebanese
Variant of Mary Bitter; Bitter; Beloved
Girl/Female
American, British, English, German
Bearer of Good News; Modern Blend of Ava and Ana
Girl/Female
French
Bitter.
Female
French
French form of Latin Ariadne, ARIANNE means "utterly pure."
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
Norse American Latin Russian French
Bitter grace.
Girl/Female
Latin
Mythological Ariadne who aided Theseus to escape from the Cretan labyrinth.
Female
English
French form of Latin Marianna, MARIANNE means "like Marius."
VARIANCE REDUCTION
VARIANCE REDUCTION
Girl/Female
Indian
Wise; Respectful
Boy/Male
Hindu
Fresh air, Cool
Boy/Male
American, Australian, British, Christian, English, Jamaican, Scottish
From Scotland; A Gael; Diminutive of Scott; A Scotsman
Boy/Male
British, English, Gaelic, Irish
Sword Friend; Polished Chief
Girl/Female
Hindu
Rich or from hadria, Gem, Goddess Lakshmi, Graceful, Singer
Girl/Female
Indian
Unique, Matchless
Boy/Male
Hindu, Indian, Punjabi, Sikh
Best Protector
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sikh, Sindhi, Telugu
Lord Vishnu; Poet; Saint; A Godly Person
Boy/Male
Muslim
Slave of the firm, Servant of the strong (Allah)
Surname or Lastname
English
English : variant of Carter.French : Breton variant of Chartier.
VARIANCE REDUCTION
VARIANCE REDUCTION
VARIANCE REDUCTION
VARIANCE REDUCTION
VARIANCE REDUCTION
n.
Something which differs in form from another thing, though really the same; as, a variant from a type in natural history; a variant of a story or a word.
n.
The quality or state of being variant; change of condition; variation.
n.
That which is variable; that which varies, or is subject to change.
a.
Discordant; at variance; disagreeing; contrary; different.
a.
Having the capacity of varying or changing; capable of alternation in any manner; changeable; as, variable winds or seasons; a variable quantity.
v. t. & i.
To unite again; to join after separation or variance.
n.
A disagreement or difference between two parts of the same legal proceeding, which, to be effectual, ought to agree, -- as between the writ and the declaration, or between the allegation and the proof.
v. t.
To furnish with a valance; to decorate with hangings or drapery.
a.
Liable to vary; too susceptible of change; mutable; fickle; unsteady; inconstant; as, the affections of men are variable; passions are variable.
v.
Reconciliation; agreement after variance; harmony; concord.
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.
p. pr. & vb. n.
of Valance
n.
Disunion; difference in opinion or feeling; discord; variance; alienation.
n.
Quarrel; strife; cause of variance; difference.
n.
Disagreeing; incongruous; being at variance; clashing; opposing; not harmonious.
variant
of Disarray.
n.
Difference that produce dispute or controversy; disagreement; dissension; discord; dispute; quarrel.
a.
Varying in from, character, or the like; variable; different; diverse.
n.
Conversation; discourse; talk; diction; phrase; as, in legal parlance; in common parlance.
n.
Alt. of Valiancy