arXiv research

NP-PROV separates mean and variance spaces to improve function uncertainty.

We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some restrictions imposed on the functional class fast convergence rates can be achieved incl…

In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A distinctive feature of the proposed approach is its ability to significantly reduce th…

SignSVRG improves SignSGD by reducing variance, achieving similar convergence rates.

The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.

This paper connects nonpositive sectional curvature of a Riemannian manifold with the displacement convexity of the variance functional on the space $P(M)$ of probability measures over $M$. We show that $M$ has nonpositive sectional curvature and has trivial topology (i.e, is homeomorphic to $\mathbf{R}^n$) if and only…

Paper solves a control problem with robust methods.

Estimates generalization gap for overparameterized models using Langevin approximation.

This paper describes another extension of the Local Variance Gamma model originally proposed by P. Carr in 2008, and then further elaborated on by Carr and Nadtochiy, 2017 (CN2017), and Carr and Itkin, 2018 (CI2018). As compared with the latest version of the model developed in CI2018 and called the ELVG (the Expanded …

A new QHR model extends HR model with a quadratic variance function.

VA-OPE improves OPE by incorporating variance information, achieving tighter error bounds.

The paper analyzes the bias-variance tradeoff for Bregman divergences.

We present an actor-critic framework for MDPs where the objective is the variance-adjusted expected return. Our critic uses linear function approximation, and we extend the concept of compatible features to the variance-adjusted setting. We present an episodic actor-critic algorithm and show that it converges almost su…

Novel estimator reduces diffusion model variance.

This work proposes using zero-variance control variates to reduce variance in pathwise gradient estimators for variational inference.

New method optimizes portfolio weights as functions, outperforming traditional approaches.

VarGrad reduces variance in ELBO gradient estimation for variational inference.

Estimates variance function using aggregation methods in regression models.

Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on problems arising in continuous control, we propose a functional regularization appr…

The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function parameters are usually learned using maximum likelihood, which can lead to overfitt…

Empirical study finds variance swap rate is affine in spot variance for S&P500 data.

New simulations advise caution in choosing principal components for multivariate functional data.

Estimates Markov chain variance efficiently without storing samples.

New algorithms reduce contextual bandits' regret without knowing reward noise variances.

This paper explores the non-convex composition optimization in the form including inner and outer finite-sum functions with a large number of component functions. This problem arises in some important applications such as nonlinear embedding and reinforcement learning. Although existing approaches such as stochastic gr…

Risk management in dynamic decision problems is a primary concern in many fields, including financial investment, autonomous driving, and healthcare. The mean-variance function is one of the most widely used objective functions in risk management due to its simplicity and interpretability. Existing algorithms for mean-…

Improves gradient estimation for discrete distributions with variance reduction techniques.

Optimizes MCMC chains with neural control variates.

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with conventional stochastic variance reduced gradient (SVRG) algorithm that uses two reference …

Contextual bandits study how reward variance affects regret bounds.

Study tight offline learning bounds for linear MDPs using variance information.

The paper proposes a new method to calibrate option pricing models that accurately match both volatility surfaces and variance term structures.

Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.

Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.

We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the sample size n. The bounds lead us to consider sample variance penalization, a nov…

PS-IG improves feature attribution by reducing noise and variance.

New algorithm reduces variance in Monte Carlo simulations using deep neural networks and policy gradients.

Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance unbiased estimators of derivatives at any order. Our objective is compatible with arbit…

Paper improves Gumbel-Softmax estimator variance reduction.

Policy gradient methods are very attractive in reinforcement learning due to their model-free nature and convergence guarantees. These methods, however, suffer from high variance in gradient estimation, resulting in poor sample efficiency. To mitigate this issue, a number of variance-reduction approaches have been prop…

New method reduces density estimation variance for multivariate data.

This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the exponential dispersion model. This compact integral form simplifies derivations of many pr…

Delta Variances efficiently estimate epistemic uncertainty in neural networks.

Adversarial training leads to large generalization gap, decomposed into bias and variance.

A novel k-NN method estimates conditional mean and variance efficiently.

We prove that if a geodesic metric measure space satisfies a comparison condition for isoperimetric profile and if the observable variance is maximal, then the space is foliated by minimal geodesics, where the observable variance is defined to be the supremum of the variance of 1-Lipschitz functions on the space. Our r…

With a new deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the `global' mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reductio…

Paper develops a new estimator for MDPs' risk functionals with lower variance and bias.