Related papers: The Sample Complexity of Robust Covariance Testing

We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too…

Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…

Identification-robust hypothesis tests are commonly based on the continuous updating GMM objective function. When the number of moment conditions grows proportionally with the sample size, the large-dimensional weighting matrix prohibits…

This paper studies the problem of robust signal detection in Gaussian noise under quadratically convex orthosymmetric (QCO) constraints. We consider a minimax testing framework where the signal belongs to a QCO set and is separated from…

Large datasets are often affected by cell-wise outliers in the form of missing or erroneous data. However, discarding any samples containing outliers may result in a dataset that is too small to accurately estimate the covariance matrix.…

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…

We study the problem of robustly estimating the posterior distribution for the setting where observed data can be contaminated with potentially adversarial outliers. We propose Rob-ULA, a robust variant of the Unadjusted Langevin Algorithm…

We propose a general method for constructing robust permutation tests under data corruption. The proposed tests effectively control the non-asymptotic type I error under data corruption, and we prove their consistency in power under minimal…

This paper studies quantum supervised learning for classical inference from quantum states. In this model, a learner has access to a set of labeled quantum samples as the training set. The objective is to find a quantum measurement that…

Hypothesis testing for small-sample scenarios is a practically important problem. In this paper, we investigate the robust hypothesis testing problem in a data-driven manner, where we seek the worst-case detector over distributional…

Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important problem in signal processing. Motivated by these applications, we study in this…

Robust Bayesian linear regression is a classical but essential statistical tool. Although novel robustness properties of posterior distributions have been proved recently under a certain class of error distributions, their sufficient…

Hypothesis testing of structure in covariance matrices is of significant importance, but faces great challenges in high-dimensional settings. Although consistent frequentist one-sample covariance tests have been proposed, there is a lack of…

Several recent results provide theoretical insights into the phenomena of adversarial examples. Existing results, however, are often limited due to a gap between the simplicity of the models studied and the complexity of those deployed in…

Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance $\Sigma$, we propose a test for $\Sigma$ being banded with possible diverging bandwidth. The test is adaptive to the "large $p$, small $n$"…

We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…

Estimating the clutter-plus-noise covariance matrix in high-dimensional STAP is challenging in the presence of Internal Clutter Motion (ICM) and a high noise floor. The problem becomes more difficult in low-sample regimes, where the Sample…

A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…

We study the problem of learning nonparametric distributions in a finite mixture, and establish tight bounds on the sample complexity for learning the component distributions in such models. Namely, we are given i.i.d. samples from a pdf…