32 citations · 88 across the 15 of their papers we have counts for
16 papers
Ratio Covers of Convex Sets and Optimal Mixture Density Estimation
Spencer Compton, Gábor Lugosi, Jaouad Mourtada +2
We study density estimation in Kullback-Leibler divergence: given an i.i.d. sample from an unknown density , the goal is to construct an estimator such that…
Estimation of discrete distributions in relative entropy, and the deviations of the missing mass
Jaouad Mourtada
We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While opti…
Finite-sample performance of the maximum likelihood estimator in logistic regression
Hugo Chardon, Matthieu Lerasle, Jaouad Mourtada
Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the m…
Local Risk Bounds for Statistical Aggregation
Jaouad Mourtada, Tomas Vaškevičius, Nikita Zhivotovskiy
In the problem of aggregation, the aim is to combine a given class of base predictors to achieve predictions nearly as accurate as the best one. In this flexible framework, no assu…
Universal coding, intrinsic volumes, and metric complexity
Jaouad Mourtada
We study sequential probability assignment in the Gaussian setting, where the goal is to predict, or equivalently compress, a sequence of real-valued observations almost as well as…
An elementary analysis of ridge regression with random design
Jaouad Mourtada, Lorenzo Rosasco
In this note, we provide an elementary analysis of the prediction error of ridge regression with random design. The proof is short and self-contained. In particular, it bypasses th…
Distribution-Free Robust Linear Regression
Jaouad Mourtada, Tomas Vaškevičius, Nikita Zhivotovskiy
We study random design linear regression with no assumptions on the distribution of the covariates and with a heavy-tailed response variable. In this distribution-free regression s…
The Nyström method for convex loss functions
Andrea Della Vecchia, Ernesto De Vito, Jaouad Mourtada +1
We investigate an extension of classical empirical risk minimization, where the hypothesis space consists of a random subspace within a given Hilbert space. Specifically, we examin…
Asymptotics of Ridge (less) Regression under General Source Condition
Dominic Richards, Jaouad Mourtada, Lorenzo Rosasco
We analyze the prediction error of ridge regression in an asymptotic regime where the sample size and dimension go to infinity at a proportional rate. In particular, we consider th…
An improper estimator with optimal excess risk in misspecified density estimation and logistic regression
Jaouad Mourtada, Stéphane Gaïffas
We introduce a procedure for conditional density estimation under logarithmic loss, which we call SMP (Sample Minmax Predictor). This estimator minimizes a new general excess risk…
Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices
Jaouad Mourtada
We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of orde…
AMF: Aggregated Mondrian Forests for Online Learning
Jaouad Mourtada, Stéphane Gaïffas, Erwan Scornet
Random Forests (RF) is one of the algorithms of choice in many supervised learning applications, be it classification or regression. The appeal of such tree-ensemble methods comes…
On the optimality of the Hedge algorithm in the stochastic regime
Jaouad Mourtada, Stéphane Gaïffas
In this paper, we study the behavior of the Hedge algorithm in the online stochastic setting. We prove that anytime Hedge with decreasing learning rate, which is one of the simples…
Minimax optimal rates for Mondrian trees and forests
Jaouad Mourtada, Stéphane Gaïffas, Erwan Scornet
Introduced by Breiman, Random Forests are widely used classification and regression algorithms. While being initially designed as batch algorithms, several variants have been propo…
Universal consistency and minimax rates for online Mondrian Forests
Jaouad Mourtada, Stéphane Gaïffas, Erwan Scornet
We establish the consistency of an algorithm of Mondrian Forests, a randomized classification algorithm that can be implemented online. First, we amend the original Mondrian Forest…
Efficient tracking of a growing number of experts
Jaouad Mourtada, Odalric-Ambrym Maillard
We consider a variation on the problem of prediction with expert advice, where new forecasters that were unknown until then may appear at each round. As often in prediction with ex…