arXiv research

New method splits unknown covariance Gaussians into independent parts.

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

Safety filter for unknown discrete-time systems with learned models and noise covariance.

Paper estimates GMMs with unknown covariances using sparse regularization.

New method predicts sets under unknown covariate shift with high confidence.

Method improves treatment effect prediction robust to unknown covariate shifts.

New algorithm clusters Gaussian mixtures with unknown covariance efficiently.

Estimation of the intensity of a point process is considered within a nonparametric framework. The intensity measure is unknown and depends on covariates, possibly many more than the observed number of jumps. Only a single trajectory of the counting process is observed. Interest lies in estimating the intensity conditi…

Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, time and other factors, relatively little has been done in the multivariate case. Our focus is on developing a class of nonparametric covariance regression models, which allow an unknown p …

New method reduces regret in nonparametric bandits with unknown covariate shifts.

Safe learning in uncertain systems with state measurements and optimization.

We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span a low dimensional linear subspace in the space of symmetric matrices, our aim i…

Paper tackles moment estimation under covariate shift with a two-stage algorithm.

Robustly estimates linear regression coefficients with adversarial and noisy data.

Two new covariance estimators for ROOT-SGD improve statistical inference.

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…

Robust covariance testing requires significantly more samples in contaminated data.

Algorithm estimates covariance from noisy data efficiently.

New method for valid prediction sets in high-dimensional covariate shifts.

Optimizes clustering in Gaussian mixtures with varying covariance matrices.

New method for estimating covariance with robustness to outliers.

In this paper, we present a simple non-parametric method for learning the structure of undirected graphs from data that drawn from an underlying unknown distribution. We propose to use Brownian distance covariance to estimate the conditional independences between the random variables and encodes pairwise Markov graph. …

Markowitz' celebrated optimal portfolio theory generally fails to deliver out-of-sample diversification. In this note, we propose a new portfolio construction strategy based on symmetry arguments only, leading to "Eigenrisk Parity" portfolios that achieve equal realized risk on all the principal components of the covar…

New bounds quantify estimation error in kernel-based system identification with unknown hyperparameters.

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

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse parameters with sub-linear sample complexity, in the presence of a constant fractio…

Bayesian method adapts to unknown distribution shifts in online learning.

Over the past decades, researchers and ML practitioners have come up with better and better ways to build, understand and improve the quality of ML models, but mostly under the key assumption that the training data is distributed identically to the testing data. In many real-world applications, however, some potential …

A new method estimates parameters in heavy-tailed corrupted regression with unknown covariance and heterogeneous noise.

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…

This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least squares optimization problem in any constant dimension. Next, in an average-case…

Optimal strategy proposed for maximizing cumulative reward in continuum-armed bandits.

Kalman filtering and smoothing algorithms are used in many areas, including tracking and navigation, medical applications, and financial trend filtering. One of the basic assumptions required to apply the Kalman smoothing framework is that error covariance matrices are known and given. In this paper, we study a general…

Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters are estimated by least squares. This paper analyzes forward regression in high-…

Paper tackles transfer learning for contextual multi-armed bandits under covariate shift.

Bayesian optimization improves with nonstationary covariance functions.

New method estimates covariance in deep heteroscedastic regression without labels.

NICE learns a representation to avoid bad controls in causal inference.

Bayesian methods estimate regression functions on submanifolds using graph Laplacian eigenbasis.

The paper proves a new method to improve generalization in covariate-shift scenarios.

Performing statistical inference in high-dimension is an outstanding challenge. A major source of difficulty is the absence of precise information on the distribution of high-dimensional estimators. Here, we consider linear regression in the high-dimensional regime $p\gg n$. In this context, we would like to perform in…

This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The resulting latent force models (LFMs) can be seen as hybrid models that contain a first…

Improved Kalman filtering with hierarchical variational approach.

New algorithm reduces semi-bandit regret using covariance estimates.

Nyström subsampling with Tikhonov regularization for covariate shift adaptation under misspecified case

The paper tackles high-dimensional mixed linear regression with unknown parameters and proposes methods for estimation, confidence intervals, and hypothesis testing.

We study the problem of detecting an abrupt change to the signal covariance matrix. In particular, the covariance changes from a "white" identity matrix to an unknown spiked or low-rank matrix. Two sequential change-point detection procedures are presented, based on the largest and the smallest eigenvalues of the sampl…

Kernel $ε$-Greedy optimizes multi-armed bandits with covariates for sub-linear regret.