Related papers: Support estimation in high-dimensional heterosceda…
In Compressed Sensing and high dimensional estimation, signal recovery often relies on sparsity assumptions and estimation is performed via $\ell_1$-penalized least-squares optimization, a.k.a. LASSO. The $\ell_1$ penalisation is usually…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
Traditional and modern machine learning-based path loss models typically assume a constant prediction variance. We propose a neural network that jointly predicts the mean and link-specific variance by minimizing a Gaussian negative…
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…
Expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. Expected shortfall regression provides powerful tools for learning the relationship between a response variable…
The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. In this work, we study tuning regimes under which the Lasso exhibits suboptimal prediction performance, in the…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty,…
We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior…
The nested error regression model is a useful tool for analyzing clustered (grouped) data, and is especially used in small area estimation. The classical nested error regression model assumes normality of random effects and error terms, and…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the "lower tail" of such a matrix, and prove that it is subgaussian under a simple fourth moment assumption on the…
We consider the problem of heteroscedastic linear regression, where, given $n$ samples $(\mathbf{x}_i, y_i)$ from $y_i = \langle \mathbf{w}^{*}, \mathbf{x}_i \rangle + \epsilon_i \cdot \langle \mathbf{f}^{*}, \mathbf{x}_i \rangle$ with…
We study the problem of heavy-tailed mean estimation in settings where the variance of the data-generating distribution does not exist. Concretely, given a sample $\mathbf{X} = \{X_i\}_{i = 1}^n$ from a distribution $\mathcal{D}$ over…
For regularized estimation, the upper tail behavior of the random Lipschitz coefficient associated with empirical loss functions is known to play an important role in the error bound of Lasso for high dimensional generalized linear models.…
We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…
We study the algorithmic problem of estimating the mean of heavy-tailed random vector in $\mathbb{R}^d$, given $n$ i.i.d. samples. The goal is to design an efficient estimator that attains the optimal sub-gaussian error bound, only assuming…
In this work, we consider the algorithm to the (nonlinear) regression problems with $\ell_0$ penalty. The existing algorithms for $\ell_0$ based optimization problem are often carried out with a fixed step size, and the selection of an…
Sparse learning is ubiquitous in many machine learning tasks. It aims to regularize the goodness-of-fit objective by adding a penalty term to encode structural constraints on the model parameters. In this paper, we develop a flexible sparse…
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…