192 citations · 1.1k across the 46 of their papers we have counts for
44 papers · 1 filter
Improved Guarantees for Langevin Monte Carlo with Average Smoothness
Arnak S. Dalalyan, Avetik Karagulyan
We establish improved nonasymptotic bounds for Langevin Monte Carlo in the strongly log-concave setting, when the error is measured by the Wasserstein distance. The main result sho…
Parallelized Midpoint Randomization for Langevin Monte Carlo
Lu Yu, Arnak Dalalyan
We study the problem of sampling from a target probability density function in frameworks where parallel evaluations of the log-density gradient are feasible. Focusing on smooth an…
Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution
Elen Vardanyan, Sona Hunanyan, Tigran Galstyan +2
This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focus…
Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisited
Lu Yu, Avetik Karagulyan, Arnak Dalalyan
We revisit the problem of sampling from a target distribution that has a smooth strongly log-concave density everywhere in . In this context, if no additional density…
Graphon Estimation in bipartite graphs with observable edge labels and unobservable node labels
Etienne Donier-Meroz, Arnak S. Dalalyan, Francis Kramarz +2
Many real-world data sets can be presented in the form of a matrix whose entries correspond to the interaction between two entities of different natures (number of times a web user…
Simple proof of the risk bound for denoising by exponential weights for asymmetric noise distributions
Arnak S. Dalalyan
In this note, we consider the problem of aggregation of estimators in order to denoise a signal. The main contribution is a short proof of the fact that the exponentially weighted…
Matching Map Recovery with an Unknown Number of Outliers
Arshak Minasyan, Tigran Galstyan, Sona Hunanyan +1
We consider the problem of finding the matching map between two sets of -dimensional noisy feature-vectors. The distinctive feature of our setting is that we do not assume that…
Nearly minimax robust estimator of the mean vector by iterative spectral dimension reduction
Amir-Hossein Bateni, Arshak Minasyan, Arnak S. Dalalyan
We study the problem of robust estimation of the mean vector of a sub-Gaussian distribution. We introduce an estimator based on spectral dimension reduction (SDR) and establish a f…
Optimal detection of the feature matching map in presence of noise and outliers
Tigran Galstyan, Arshak Minasyan, Arnak Dalalyan
We consider the problem of finding the matching map between two sets of dimensional vectors from noisy observations, where the second set contains outliers. The matching map is…
Statistical guarantees for generative models without domination
Nicolas Schreuder, Victor-Emmanuel Brunel, Arnak Dalalyan
In this paper, we introduce a convenient framework for studying (adversarial) generative models from a statistical perspective. It consists in modeling the generative device as a s…
Penalized Langevin dynamics with vanishing penalty for smooth and log-concave targets
Avetik Karagulyan, Arnak S. Dalalyan
We study the problem of sampling from a probability distribution on defined via a convex and smooth potential function. We consider a continuous-time diffusion-type p…
All-In-One Robust Estimator of the Gaussian Mean
Arnak S. Dalalyan, Arshak Minasyan
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computational…
Bounding the error of discretized Langevin algorithms for non-strongly log-concave targets
Arnak S. Dalalyan, Avetik Karagulyan, Lionel Riou-Durand
In this paper, we provide non-asymptotic upper bounds on the error of sampling from a target density using three schemes of discretized Langevin diffusions. The first scheme is the…
Outlier-robust estimation of a sparse linear model using -penalized Huber's -estimator
Arnak S. Dalalyan, Philip Thompson
We study the problem of estimating a -dimensional -sparse vector in a linear model with Gaussian design and additive noise. In the case where the labels are contaminated by a…
A nonasymptotic law of iterated logarithm for general M-estimators
Victor-Emmanuel Brunel, Arnak S. Dalalyan, Nicolas Schreuder
M-estimators are ubiquitous in machine learning and statistical learning theory. They are used both for defining prediction strategies and for evaluating their precision. In this p…
Confidence regions and minimax rates in outlier-robust estimation on the probability simplex
Amir-Hossein Bateni, Arnak S. Dalalyan
We consider the problem of estimating the mean of a distribution supported by the -dimensional probability simplex in the setting where an fraction of observations…
Exponential weights in multivariate regression and a low-rankness favoring prior
Arnak S. Dalalyan
We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is…
Restricted eigenvalue property for corrupted Gaussian designs
Philip Thompson, Arnak S. Dalalyan
Motivated by the construction of tractable robust estimators via convex relaxations, we present conditions on the sample size which guarantee an augmented notion of Restricted Eige…
Estimating linear functionals of a sparse family of Poisson means
Olivier Collier, Arnak Dalalyan
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensi…
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…
On the Exponentially Weighted Aggregate with the Laplace Prior
Arnak S. Dalalyan, Edwin Grappin, Quentin Paris
In this paper, we study the statistical behaviour of the Exponentially Weighted Aggregate (EWA) in the problem of high-dimensional regression with fixed design. Under the assumptio…