Related papers: An unbiased ray-marching transmittance estimator
This paper develops a flexible method for decreasing the variance of estimators for complex experiment effect metrics (e.g. ratio metrics) while retaining asymptotic unbiasedness. This method uses the auxiliary information about the…
We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has…
Several statistics-based detectors, based on unimodal matrix models, for determining the number of sources in a field are designed. A new variance ratio statistic is proposed, and its asymptotic distribution is analyzed. The variance ratio…
We examine the problem of estimating the trace of a matrix $A$ when given access to an oracle which computes $x^\dagger A x$ for an input vector $x$. We make use of the basis vectors from a set of mutually unbiased bases, widely studied in…
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…
A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…
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…
Standard practice obtains an unbiased variance estimator by dividing by $N-1$ rather than $N$. Yet if only half the data are used to compute the mean, dividing by $N$ can still yield an unbiased estimator. We show that an alternative mean…
Building upon recent developments of force-based estimators with a reduced variance for the computation of densities, radial distribution functions or local transport properties from molecular simulations, we show that the variance can be…
We propose the use of U-statistics to reduce variance for gradient estimation in importance-weighted variational inference. The key observation is that, given a base gradient estimator that requires $m > 1$ samples and a total of $n > m$…
Random sampling is an essential tool in the processing and transmission of data. It is used to summarize data too large to store or manipulate and meet resource constraints on bandwidth or battery power. Estimators that are applied to the…
We present a new Unbiased Minimal Variance (UMV) estimator for the purpose of reconstructing the large--scale structure of the universe from noisy, sparse and incomplete data. Similar to the Wiener Filter (WF), the UMV estimator is derived…
Many signal processing algorithms for distributed sensors are capable of improving their performance if the positions of sensors are known. In this paper, we focus on estimators for inferring the relative geometry of distributed arrays and…
Given an implicit $n\times n$ matrix $A$ with oracle access $x^TA x$ for any $x\in \mathbb{R}^n$, we study the query complexity of randomized algorithms for estimating the trace of the matrix. This problem has many applications in quantum…
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.…
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which…
Bessel's correction adjusts the denominator in the sample variance formula from n to n-1 to ensure an unbiased estimator of the population variance. This paper provides rigorous algebraic derivations geometric interpretations and…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…