Related papers: Sparse Regression Learning by Aggregation and Lang…

Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity…

We prove an L2 recovery bound for a family of sparse estimators defined as minimizers of some empirical loss functions -- which include hinge loss and logistic loss. More precisely, we achieve an upper-bound for coefficients estimation…

When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…

We present a novel algorithm for parameter learning in generic deep generative models that builds upon the predictive coding (PC) framework of computational neuroscience. Our approach modifies the standard PC algorithm to bring performance…

We study the problem of testing $H_0: \xi^\top\beta=t_0$ in high-dimensional sparse linear regression with Gaussian random design and unknown design covariance. The loading vector $\xi$ is arbitrary, and the exact sparsity level $k$ is…

For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…

Many state-of-the-art machine learning models such as deep neural networks have recently shown to be vulnerable to adversarial perturbations, especially in classification tasks. Motivated by adversarial machine learning, in this paper we…

Given a training sample of size $m$ from a $d$-dimensional population, we wish to allocate a new observation $Z\in \R^d$ to this population or to the noise. We suppose that the difference between the distribution of the population and that…

Incorporating sparsity priors in learning tasks can give rise to simple, and interpretable models for complex high dimensional data. Sparse models have found widespread use in structure discovery, recovering data from corruptions, and a…

Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…

Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds…

While distributed training is often viewed as a solution to optimizing linear models on increasingly large datasets, inter-machine communication costs of popular distributed approaches can dominate as data dimensionality increases. Recent…

This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in $\mathbb{R}^d$ under noise. Though recent works have established attribute-efficient learning algorithms under various types of label noise…

We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…

In this paper we initiate the study of whether or not sparse estimation tasks can be performed efficiently in high dimensions, in the robust setting where an $\eps$-fraction of samples are corrupted adversarially. We study the natural…

Motivated by the problem of determining the atomic structure of macromolecules using single-particle cryo-electron microscopy (cryo-EM), we study the sample and computational complexities of the sparse multi-reference alignment (MRA) model:…

We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…

We study the Gibbs posterior distribution for sparse deep neural nets in a nonparametric regression setting. The posterior can be accessed via Metropolis-adjusted Langevin algorithms. Using a mixture over uniform priors on sparse sets of…

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…

In the high-dimensional sparse modeling literature, it has been crucially assumed that the sparsity structure of the model is homogeneous over the entire population. That is, the identities of important regressors are invariant across the…