192 citations · 1.1k across the 46 of their papers we have counts for
4 papers · 2 filters
Minimax estimation of a p-dimensional linear functional in sparse Gaussian models and robust estimation of the mean
Olivier Collier, Arnak S. Dalalyan
We consider two problems of estimation in high-dimensional Gaussian models. The first problem is that of estimating a linear functional of the means of independent -dimensio…
User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
Arnak S. Dalalyan, Avetik G. Karagulyan
In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approxi…
Further and stronger analogy between sampling and optimization: Langevin Monte Carlo and gradient descent
Arnak S. Dalalyan
In this paper, we revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-con…
Optimal Kullback-Leibler Aggregation in Mixture Density Estimation by Maximum Likelihood
Arnak S. Dalalyan, Mehdi Sebbar
We study the maximum likelihood estimator of density of independent observations, under the assumption that it is well approximated by a mixture with a large number of componen…