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High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…
Blockwise missing data occurs frequently when we integrate multisource or multimodality data where different sources or modalities contain complementary information. In this paper, we consider a high-dimensional linear regression model with…
High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based…
Feature selection is important for modeling high-dimensional data, where the number of variables can be much larger than the sample size. In this paper, we develop a support detection and root finding procedure to learn the high dimensional…
The problem of learning structural equation models (SEMs) from data is a fundamental problem in causal inference. We develop a new algorithm --- which is computationally and statistically efficient and works in the high-dimensional regime…
We consider a robust linear regression model $y=X\beta^* + \eta$, where an adversary oblivious to the design $X\in \mathbb{R}^{n\times d}$ may choose $\eta$ to corrupt all but an $\alpha$ fraction of the observations $y$ in an arbitrary…
In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response,…
This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work on robust…
We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex…
Clustering is a fundamental primitive in unsupervised learning which gives rise to a rich class of computationally-challenging inference tasks. In this work, we focus on the canonical task of clustering d-dimensional Gaussian mixtures with…
We consider an uncertain linear inverse problem as follows. Given observation $\omega=Ax_*+\zeta$ where $A\in {\bf R}^{m\times p}$ and $\zeta\in {\bf R}^{m}$ is observation noise, we want to recover unknown signal $x_*$, known to belong to…
We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
We consider the problem of linear regression with self-selection bias in the unknown-index setting, as introduced in recent work by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [STOC 2023]. In this model, one observes $m$ i.i.d.…
This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector $\beta^0$ which is identified through instrumental variables. We allow for eigenvalues of the expected outer product of included…
Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic…
We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called…
We propose statistically robust and computationally efficient linear learning methods in the high-dimensional batch setting, where the number of features $d$ may exceed the sample size $n$. We employ, in a generic learning setting, two…