Related papers: Outlier-robust sparse/low-rank least-squares regre…
We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being…
This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…
In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions for the success of any statistical procedure in…
Missing values in datasets are common in applied statistics. For regression problems, theoretical work thus far has largely considered the issue of missing covariates as distinct from missing responses. However, in practice, many datasets…
The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…
We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…
We explore the connection between outlier-robust high-dimensional statistics and non-convex optimization in the presence of sparsity constraints, with a focus on the fundamental tasks of robust sparse mean estimation and robust sparse PCA.…
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…
We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on…
The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the_representation_ problem of how to best approximate a noisy measurement matrix using a low-rank matrix. Here, we consider the…
The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…
Empirical research in economics increasingly relies on restricted-access data held by multiple firms or agencies, making it impossible to construct the estimator of interest on the pooled sample. At the same time, heavy-tailed distributions…
Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…
We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model y = X beta + z, then we suggest estimating the regression…
Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods. To provide a better theoretical understanding of the reasons for its success, we…
Challenges with data in the big-data era include (i) the dimension $p$ is often larger than the sample size $n$ (ii) outliers or contaminated points are frequently hidden and more difficult to detect. Challenge (i) renders most conventional…
Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…
Given a full rank matrix $X$ with more columns than rows, consider the task of estimating the pseudo inverse $X^+$ based on the pseudo inverse of a sampled subset of columns (of size at least the number of rows). We show that this is…
Latest least squares regression (LSR) methods mainly try to learn slack regression targets to replace strict zero-one labels. However, the difference of intra-class targets can also be highlighted when enlarging the distance between…