Related papers: Robust Testing in High-Dimensional Sparse Models

Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…

One of the most common machine learning setups is logistic regression. In many classification models, including neural networks, the final prediction is obtained by applying a logistic link function to a linear score. In binary logistic…

We study the detection of a change in the covariance matrix of $n$ independent sub-Gaussian random variables of dimension $p$. Our first contribution is to show that $\log\log(8n)$ is the exact minimax testing rate for a change in variance…

Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…

We study combinatorial group testing schemes for learning $d$-sparse Boolean vectors using highly unreliable disjunctive measurements. We consider an adversarial noise model that only limits the number of false observations, and show that…

It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…

This paper is motivated by the comparison of genetic networks based on microarray samples. The aim is to test whether the differences observed between two inferred Gaussian graphical models come from real differences or arise from…

In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…

We consider the problem of sparsity-constrained $M$-estimation when both explanatory and response variables have heavy tails (bounded 4-th moments), or a fraction of arbitrary corruptions. We focus on the $k$-sparse, high-dimensional regime…

We propose a weak-identification-robust test for linear instrumental variable (IV) regressions with high-dimensional instruments, whose number is allowed to exceed the sample size. In addition, our test is robust to general error…

We consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single…

We consider a Gaussian sequence space model $X_{\lambda}=f_{\lambda} + \xi_{\lambda},$ where $\xi $ has a diagonal covariance matrix $\Sigma=\diag(\sigma_\lambda ^2)$. We consider the situation where the parameter vector $(f_{\lambda})$ is…

This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…

We proposed a weighted l1 minimization to recover a sparse signal vector and the corrupted noise vector from a linear measurement when the sensing matrix A is an m by n row i.i.d subgaussian matrix. We obtain both uniform and nonuniform…

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…

The robustness and anomaly detection capability of neural networks are crucial topics for their safe adoption in the real-world. Moreover, the over-parameterization of recent networks comes with high computational costs and raises questions…

Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…

We propose a novel bootstrap test of a dense model, namely factor regression, against a sparse plus dense alternative augmenting model with sparse idiosyncratic components. The asymptotic properties of the test are established under time…

The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for…

This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the…