arXiv research

This work extends Ledoit-Wolf shrinkage to unknown mean covariance estimation.

Sharp inequalities for matrix means with unknown variance.

Algorithm estimates common mean from Gaussian variables with unknown variances.

New algorithm detects changes in Markov kernels with unknown post-change kernel.

This paper introduces the first asymptotically optimal strategy for a multi armed bandit (MAB) model under side constraints. The side constraints model situations in which bandit activations are limited by the availability of certain resources that are replenished at a constant rate. The main result involves the deriva…

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

Proposes Causal k-Means Clustering to identify subgroup effects.

New algorithms learn graphons in GMFGs without knowing them.

Optimal nonparametric regression estimator adapts to unknown smoothness.

Markowitz's celebrated mean--variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the estimates into the efficient frontier that assumes known parameters has led to p…

New method estimates mean from noisy data with few outliers.

The paper tackles resource allocation for arms with unknown and random rewards, achieving optimal regret bounds.

Safe learning in uncertain systems with state measurements and optimization.

Consider the problem of sampling sequentially from a finite number of $N \geq 2$ populations, specified by random variables $X^i_k$, $i = 1,\ldots , N,$ and $k = 1, 2, \ldots$; where $X^i_k$ denotes the outcome from population $i$ the $k^{th}$ time it is sampled. It is assumed that for each fixed $i$, $\{ X^i_k \}_{k …

Develops new e-processes and confidence sequences for Gaussian means with unknown variance.

Efficiently learns MFC systems with unknown dynamics.

Paper improves CI and CS for bounded means using betting and mixtures.

It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated high-dimensional data with unknown mean and dependence structures. Matrix-variate appr…

We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process $X(t)$ and a \emph{predictive mean-field} backward SDE (BSDE) in the unknowns $Y(t), Z(t), K(t,\cdot)$. The driver of …

Improved mean estimation for symmetric distributions with finite-sample guarantees.

Paper proposes a 1-bit mean estimation method with near-optimal sample complexity.

Identification of patterns from discrete data time-series for statistical inference, threat detection, social opinion dynamics, brain activity prediction has received recent momentum. In addition to the huge data size, the associated challenges are, for example, (i) missing data to construct a closed time-varying compl…

Expands causal clustering framework with hierarchical and density-based methods.

Transformers solve Poisson means estimation via empirical Bayes.

The original k-means clustering method works only if the exact vectors representing the data points are known. Therefore calculating the distances from the centroids needs vector operations, since the average of abstract data points is undefined. Existing algorithms can be extended for those cases when the sole input i…

Optimal B-robust estimate is constructed for multidimensional parameter in drift coefficient of diffusion type process with small noise. Optimal mean-variance robust (optimal V -robust) trading strategy is find to hedge in mean-variance sense the contingent claim in incomplete financial market with arbitrary informatio…

In numerical modeling of the Earth System, many processes remain unknown or ill represented (let us quote sub-grid processes, the dependence to unknown latent variables or the non-inclusion of complex dynamics in numerical models) but sometimes can be observed. This paper proposes a methodology to produce a hybrid mode…

Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance), with numerous successful applications. The representation is constructed as the e…

We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably dominates its conventional counterpart in terms of mean square deviations. We es…

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve estimation error $O(\varepsilon)$ in the total variation distance, which is optimal up…

New collaborative algorithm improves personalized mean estimation in online settings.

The paper develops tests for comparing means in high dimensions with unknown covariance.

New method tracks time-varying parameters in data.

A new algorithm optimizes unknown functions with noisy data and unmatched features.

We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a generalization of the maximum mean discrepancy tests described in Gretton et al. [2006], …

The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, like the mean vector and the covariance matrix are unknown and have to be estimated by using historical data of the asset returns. The new approach employs the Bayesian posterior predictive distribution which…

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

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with dimension-independent error guarantees for several families of structured distributions…

Existing strategies for finite-armed stochastic bandits mostly depend on a parameter of scale that must be known in advance. Sometimes this is in the form of a bound on the payoffs, or the knowledge of a variance or subgaussian parameter. The notable exceptions are the analysis of Gaussian bandits with unknown mean and…

A simple algorithm for Gaussian mean testing with optimal sample complexity.

In this paper we consider a Lagrange Multiplier-type test (LM) to detect change in the mean of time series with heteroskedasticity of unknown form. We derive the limiting distribution under the null, and prove the consistency of the test against the alternative of either an abrupt or smooth changes in the mean. We perf…

Method improves treatment effect prediction robust to unknown covariate shifts.

Paper estimates GMMs with unknown covariances using sparse regularization.

New algorithm clusters Gaussian mixtures with unknown covariance efficiently.

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

Variational Bayes (VB) is a recent approximate method for Bayesian inference. It has the merit of being a fast and scalable alternative to Markov Chain Monte Carlo (MCMC) but its approximation error is often unknown. In this paper, we derive the approximation error of VB in terms of mean, mode, variance, predictive den…

Paper develops an efficient mean estimator for 1-bit communication constraints.

Bayesian investor learns unknown asset drift, trades mean-variance optimal portfolio, but policy is robust to observation model distortion.