arXiv research

Quantum algorithm estimates mean with sub-Gaussian error.

Optimal Gaussian noise mechanisms achieve nearly optimal error in unbiased mean estimation.

New winsorized mean improves robustness to up to 50% contamination.

Study on estimating Gaussian mean from coarse data, resolving identifiability and computational efficiency questions.

New estimator accurately estimates mean of real-valued distributions without variance knowledge.

New study shows mean estimation algorithms can't beat sub-Gaussian rate in general.

Improved median of means estimator with tighter bounds.

New algorithm estimates Gaussian means and covariances efficiently and privately.

Algorithm estimates common mean from Gaussian variables with unknown variances.

Robust estimators for Gaussian sparse tasks with optimal error under contamination.

Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.

New kriging method improves mean estimation and uncertainty.

Study on estimating Gaussian mean with missing data in high dimensions.

We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of $X$ exists. The estimator is based on a novel concept of a…

New measure of robustness for estimators, with tight bounds for Gaussian mean estimation.

We consider the problem of estimating the mean and covariance of a distribution from iid samples in $\mathbb{R}^n$, in the presence of an $η$ fraction of malicious noise; this is in contrast to much recent work where the noise itself is assumed to be from a distribution of known type. The agnostic problem includes many…

Optimizes sliding window approach for tracking Gaussian densities.

We propose an estimator for the mean of a random vector in $\mathbb{R}^d$ that can be computed in time $O(n^4+n^2d)$ for $n$ i.i.d.~samples and that has error bounds matching the sub-Gaussian case. The only assumptions we make about the data distribution are that it has finite mean and covariance; in particular, we mak…

This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, wit…

A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.

We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus on estimators based on median-of-means techniques but other methods such as the t…

Lower bound shows super-polynomial gap for estimating truncated Gaussian means.

Enhances deep neural networks with fixed-mean Gaussian processes for uncertainty estimation.

Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adaptation to combination MCC and combination to adaptation MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distri…

Study non-asymptotic estimation bounds for LTI models with Gaussian noise.

Proposes a convex method to estimate GGMs with covariates.

Study robust estimation under varying corruption probabilities in data.

This paper improves Gaussian process predictions by integrating prior knowledge.

Paper extends multi-task Gaussian Cox processes for heterogeneous tasks.

The stochastic multi-armed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper we examine the bandit problem under the weaker assumption that the distributions have moments of order 1+ε, for some $ε\in (0,1]$. Surprisingly, moments of order 2 (i.e., finite variance) are suffi…

Efficiently estimates mean in contaminated Gaussian data with near-optimal sample complexity.

New method for robust linear regression in nearly linear time.

The paper estimates common mean of entangled Gaussians with bounded variances.

A new method for uncertainty estimation in neural networks using Gaussian-softmax integration.

We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy, are established in both the univariate and multivariate settings. Communication-…

We tackle the problem of estimating a location parameter with differential privacy guarantees and sub-Gaussian deviations. Recent work in statistics has focused on the study of estimators that achieve sub-Gaussian type deviations even for heavy tailed data. We revisit some of these estimators through the lens of differ…

We develop time-uniform confidence spheres for estimating means of random vectors.

Simple private estimators for mean and covariance outperform existing methods.

Gradient boosting can be seen as Gaussian process inference.

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian processes. The proposed method can also achieve high generalization performance fo…

Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical covariance estimator (and its modifications) is very sensitive to outliers in the da…

New algorithms reduce communication for sparse mean estimation in noisy distributed systems.

Method estimates multiple related Gaussian distributions using Laplacian regularization.

This paper investigates a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the drift arriving at the jump times of a homogeneous Poisson process. Dr…

Paper improves SDR estimation speed and conditions.

The mixture of Gaussian distributions, a soft version of k-means , is considered a state-of-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color, texture, and shapes. In this algorithm, each class is described by a Gaussian distribution, defined by its mean and covarianc…

Corrected whitening restores orthogonality in high-dimensional spherical Gaussian mixtures.

Proposes variational Gaussian approximations for solving the Kushner equation.