This study reviews techniques to estimate volatility and price Variance Swaps.
problem Estimating historical volatility and pricing Variance Swaps.
method Review of existing techniques.
result Discussion of various methods to estimate volatility and price Variance Swaps.
This work proposes using zero-variance control variates to reduce variance in pathwise gradient estimators for variational inference.
problem Pathwise gradient estimators in variational inference have high variance, leading to inefficient optimization.
method Apply zero-variance control variates to pathwise gradient estimators.
result Zero-variance control variates can significantly reduce the variance of pathwise gradient estimators without requiring complex assumptions.
Jackknife variance estimation validated for generalized U-statistics.
problem Uncertainty quantification for subsampling-based estimators.
method Jackknife variance estimation for generalized U-statistics with row-wise Lr weak law. result Jackknife and delete-d variance estimators are ratio-consistent for generalized U-statistics. VarGrad reduces variance in ELBO gradient estimation for variational inference.
problem Improving the variance of gradient estimators in variational inference.
method VarGrad uses a new log-variance loss to estimate the ELBO gradient, achieving lower variance than the score function method.
result VarGrad offers a lower variance gradient estimator compared to other methods.
Paper improves confidence intervals and variance estimation for deep learning models.
problem Improving confidence intervals and variance estimation in deep learning models.
method Residual-based framework for conditional variance estimation; robust bootstrap procedure for confidence intervals.
result First non-asymptotic bounds for variance estimation using ReLU networks.
The paper develops estimators for variance in graph structures using fused lasso.
problem Variance estimation in graph-structured problems.
method Developed linear time estimator for homoscedastic case and total variation regularization estimator for heteroscedastic case.
result Minimax rates and consistency for variance estimation in various graph structures.
New estimator accurately estimates mean of real-valued distributions without variance knowledge.
problem Estimating the mean of real-valued distributions without prior variance knowledge.
method Introduces a novel estimator that converges sub-Gaussian and works across distributions with bounded variance.
result The estimator achieves accuracy of σ·(1+o(1))√(2log(1/δ)/n) with parameters n, δ, and σ².
In this paper, we propose a random projection approach to estimate variance in kernel ridge regression. Our approach leads to a consistent estimator of the true variance, while being computationally more efficient. Our variance estimator is optimal for a large family of kernels, including cubic splines and Gaussian ker…
Bayesian methods reduce variance in subspace identification for small data sets.
problem High variance in traditional subspace identification methods for large models or small sample sizes.
method Investigation of Bayesian estimation solutions (regularized and shrinkage estimators) for subspace identification.
result Bayesian estimators reduce estimation risk by up to 40% compared to traditional methods.
Improves gradient estimation for discrete distributions with variance reduction techniques.
problem Excessive variance in gradient estimation for discrete distributions.
method Stein operators for discrete distributions and control variates.
result Substantially lower variance in gradient estimation.
Paper introduces VDE, a variance-reduced determinant estimator.
problem Estimating determinants with low variance and efficiency.
method Combines variational inference and spherical normalizing flows.
result VDE achieves zero variance in ideal cases, requiring only one sample.
Novel estimator reduces diffusion model variance.
problem High variance in score function estimation for diffusion models.
method Uses nearest neighbour samples to estimate the score function.
result Significant decrease in variance, leading to improved model performance.
Paper proposes robust estimators for heavy-tailed data with infinite variance.
problem Developing robust estimators for heavy-tailed data with infinite variance.
method Proposes two robust estimators: ridge log-truncated M-estimator and elastic net log-truncated M-estimator.
result Demonstrates robustness of log-truncated estimations over standard estimations through simulations and real data analysis.
Estimates Markov chain variance efficiently without storing samples.
problem Estimating the asymptotic variance of Markov chain functions.
method Linear stochastic approximation of Poisson equation solution.
result Optimal MSE convergence rate with finite sample guarantees.
Kernel ridge regression imputation with consistent variance estimation for handling missing data.
problem Handling missing data in statistical analysis.
method Kernel ridge regression imputation combined with entropy method for variance estimation.
result Root-n consistency of the imputation estimator in a Sobolev space setting.
We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within n subsequent time-step intervals. The main characteristics of some of the introduced estimators is to take into account the information on the occurrence times of the high a…
A new gradient estimator reduces variance near boundaries for binary latent variables.
problem Explosive gradient variance near boundaries in binary latent variable models.
method Introduces a new gradient estimator (bitflip-1) and an aggregated estimator (UGC) that uses either bitflip-1 or DisARM for each coordinate.
result UGC has uniformly lower variance than DisARM and achieves optimal optimization objectives.
We study the variance of the REINFORCE policy gradient estimator in environments with continuous state and action spaces, linear dynamics, quadratic cost, and Gaussian noise. These simple environments allow us to derive bounds on the estimator variance in terms of the environment and noise parameters. We compare the pr…
The paper estimates variance of random sections on complex manifolds.
problem Estimating variance of random holomorphic sections on compact Kahler manifolds.
method Analyzes a sequence of smooth Hermitian holomorphic line bundles on a compact Kahler manifold X, considering specific probability measures.
result Provides variance estimates for various measures including Gaussian and Fubini-Study measures.
A new method reduces variance in training discrete latent variable models.
problem High variance in stochastic gradient estimators for discrete latent variable models.
method Double control variates for score function estimators using Taylor expansions.
result Our method can have lower variance compared to other estimators.
Learning in models with discrete latent variables is challenging due to high variance gradient estimators. Generally, approaches have relied on control variates to reduce the variance of the REINFORCE estimator. Recent work (Jang et al. 2016, Maddison et al. 2016) has taken a different approach, introducing a continuou…
Paper improves Gumbel-Softmax estimator variance reduction.
problem Challenges in gradient estimation for models with discrete latent variables.
method Rao-Blackwellization applied to straight-through Gumbel-Softmax estimator.
result Reduces mean squared error and variance of Gumbel-Softmax estimator.
Normal distributions ensure asymptotic variance reduction in moment matching Monte Carlo.
problem Asymptotic variance reduction in general integration problems.
method Characterization of conditions for asymptotic variance reduction using normal distributions.
result Asymptotic variance reduction is guaranteed for normal distributions in moment matching Monte Carlo.
The paper provides concentration inequalities for Markov chain variance estimators.
problem Estimating the variance of Markov chains with concentration properties.
method Martingale decomposition method for uniformly geometrically ergodic Markov chains.
result Explicit control of the p-th moment of the OBM estimator difference and dependence on p and mixing time.
This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables with unknown, possibly changing, mean value but fixed variance. The main assumpt…
New Riemannian optimization improves variance estimation in mixed models.
problem Challenges in estimating variance parameters in linear mixed models due to constraints.
method Formulated as an optimization problem on a Riemannian manifold, using Riemannian gradient and Hessian.
result Yields higher quality variance parameter estimates compared to existing methods.
The paper explores the trade-off between bias and variance in high-dimensional models.
problem Understanding the unavoidable trade-off between bias and variance in high-dimensional statistical models.
method Proposes a general strategy to obtain lower bounds on the variance of estimators with a specified bias, and applies it to various statistical models.
result Shows the extent to which the bias-variance trade-off is unavoidable and quantifies the performance loss for methods that do not balance it.
Algorithm estimates common mean from Gaussian variables with unknown variances.
problem Estimating common mean from Gaussian variables with different unknown variances.
method Intuitive and efficient algorithm using Subset-of-Signals model as benchmark.
result Improved estimation error by polynomial factors compared to previous work.
New method reduces density estimation variance for multivariate data.
problem Efficient multivariate density estimation with reduced dimensionality.
method Variance-Reduced Sketching (VRS) framework for multivariate density estimation.
result VRS framework significantly improves density estimation over existing methods.
We analyze the variance of Fisher information estimators in deep learning models.
problem Understanding the variance of Fisher information in deep learning models.
method Investigated two unbiased and consistent estimators of Fisher information matrix.
result The variance of estimators is influenced by the model's parametric structure.
Paper develops efficient mechanisms for estimating variance and covariance under differential privacy in the add-remove model.
problem Estimating variance and covariance under differential privacy in the add-remove model.
method Developed mechanisms based on the Bézier mechanism, a novel moment-release framework.
result Proved minimax optimality of the Bézier-based estimator in the high-privacy regime and demonstrated its better utility in instance-wise analysis.
U-statistics improve gradient estimation in importance-weighted variational inference.
problem High variance in gradient estimation for importance-weighted variational inference.
method Use U-statistics to average base gradient estimators on overlapping batches of size m, achieving lower variance.
result U-statistic variance reduction leads to modest to significant improvements in inference performance.
Machine learning reduces variance in online experiment results.
problem Reducing variance in randomized controlled trials.
method Machine learning regression-adjusted treatment effect estimator (MLRATE).
result MLRATE reduces estimator variance by over 70% in A/A tests.
New unbiased variance estimator for random forests using Hoeffding decomposition.
problem Uncertainty quantification in random forests with large kernel sizes and small sample sizes.
method Proposes a new Hoeffding decomposition view for variance estimation, establishing unbiased estimators and ratio consistency.
result Establishes the ratio consistency of the proposed variance estimator, justifying confidence interval coverage rates.
Two Fisher information matrix estimators are analyzed for neural networks, focusing on their variances and trade-offs.
problem Estimating the Fisher information matrix in neural networks due to its high computational cost.
method Examined two popular diagonal Fisher information matrix estimators and their variances in neural networks for regression and classification.
result The variances of the estimators depend on the non-linearity with respect to different parameter groups and should not be neglected.
The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al. 2012), bearing a simple estimator with pleasing computational and statistical properties. Being able to efficiently estimate the variance of this estimator is very helpful to vario…
Paper tackles bias-variance trade-off in missing data, proposing a dynamic framework.
problem Missing data in practical applications deteriorates model performance.
method Develops a fine-grained dynamic learning framework to jointly optimize bias and variance.
result Theoretical and empirical validation of joint bias-variance optimization.
Hutch++ optimizes trace estimation for generative models, reducing variance and improving quality.
problem High variance and scalability issues in Hutchinson estimators for generative models.
method Hutch++ is an optimal stochastic trace estimator designed to minimize training variance while maintaining transport optimality.
result Hutch++ leads to higher quality generations and effective variance reduction in various applications.
Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE ex…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose the natural lasso estimator for the error variance, which maximizes a penalized …
Paper proposes a method to estimate variance reduction in DNN training using importance sampling.
problem Challenges in assessing variance reduction during DNN training using importance sampling.
method Proposes a method for estimating variance reduction using minibatches sampled under importance sampling.
result Demonstrates consistent reduction in variance, improved training efficiency, and enhanced model accuracy.
Optimizes survey design for private mean estimation with reduced variance.
problem Minimizing variance in private mean estimation with privacy constraints.
method Formulates optimal survey design as an optimization problem, determining optimal subsampling sizes to minimize variance.
result Identifies the first privacy-aware stratified sampling scheme that minimizes variance under different privacy mechanisms.
Off-policy policy estimators that use importance sampling (IS) can suffer from high variance in long-horizon domains, and there has been particular excitement over new IS methods that leverage the structure of Markov decision processes. We analyze the variance of the most popular approaches through the viewpoint of con…
Paper explores robust regression methods and their bias-variance trade-off.
problem Understanding the trade-off between robust estimation and optimization methods.
method Examines traditional outlier-resistant robust estimation and robust optimization.
result Both methods follow converse strategies due to a bias-variance trade-off.
A novel k-NN method estimates conditional mean and variance efficiently.
problem Joint estimation of conditional mean and variance.
method Integrates k-NN with automated variance selection.
result Achieves fast convergence rates and improved precision.
Optimal estimator derived for partially observable LTI systems.
problem Optimal estimator for partially observable LTI systems.
method State-space representation for derivation of optimal estimator.
result Derivation of minimum error variance estimator for partially observable LTI systems.
We show a connection between the Fourier spectrum of Boolean functions and the REINFORCE gradient estimator for binary latent variable models. We show that REINFORCE estimates (up to a factor) the degree-1 Fourier coefficients of a Boolean function. Using this connection we offer a new perspective on variance reduction…
Meta-learning variance reduced via Laplace approximation for regression tasks.
problem High variance in meta-learning due to limited support data for each task.
method Laplace approximation to estimate posterior variance and reduce gradient estimate variance.
result Effective variance reduction in meta-learning, improving generalization performance.