5 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…
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…
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…
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…
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…