Related papers: Learning from MOM's principles: Le Cam's approach

We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order terms dominated by the prediction…

We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…

We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers. The guarantees of our algorithms improve in many cases significantly over the best previous ones, obtained…

The lasso has become an important practical tool for high dimensional regression as well as the object of intense theoretical investigation. But despite the availability of efficient algorithms, the lasso remains computationally demanding…

We generalize the notion of minimax convergence rate. In contrast to the standard definition, we do not assume that the sample size is fixed in advance. Allowing for varying sample size results in time-robust minimax rates and estimators.…

Although there exist plentiful theories of empirical risk minimization (ERM) for supervised learning, current theoretical understandings of ERM for a related problem---stochastic convex optimization (SCO), are limited. In this work, we…

We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…

We propose a new inference framework, named MOSAIC, for change-point detection in dynamic networks with the simultaneous low-rank and sparse-change structure. We establish the minimax rate of detection boundary, which relies on the sparsity…

We consider minimax signal detection in the sequence model. Working with certain ellipsoids in the space of square-summable sequences of real numbers, with a ball of positive radius removed, we obtain upper and lower bounds for the minimax…

A Bayesian method of moments/instrumental variable (BMOM/IV) approach is developed and applied in the analysis of the important mean and multiple regression models. Given a single set of data, it is shown how to obtain posterior and…

Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…

There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…

We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…

In this work, we show, for the well-studied problem of learning parity under noise, where a learner tries to learn $x=(x_1,\ldots,x_n) \in \{0,1\}^n$ from a stream of random linear equations over $\mathrm{F}_2$ that are correct with…

In this paper, we consider the problem of recovering a sparse signal from noisy linear measurements using the so called LASSO formulation. We assume a correlated Gaussian design matrix with additive Gaussian noise. We precisely analyze the…

In this paper we revisit the risk bounds of the lasso estimator in the context of transductive and semi-supervised learning. In other terms, the setting under consideration is that of regression with random design under partial labeling.…

We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…

This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm…

This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain…