18 citations · 112 across the 31 of their papers we have counts for
36 papers
Geometry and barycenters in large $\CAT(κ)$ spaces
Yassine Boukhateb, Victor-Emmanuel Brunel, Austin J. Stromme
We study the geometry and resulting properties of Fréchet functions and barycenters in metric spaces with curvature bounded above by a positive constant in the sense of Alexandrov.…
Functional Central Limit Theorem for Stochastic Gradient Descent
Kessang Flamand, Victor-Emmanuel Brunel
We study the asymptotic shape of the trajectory of the stochastic gradient descent algorithm applied to a convex objective function. Under mild regularity assumptions, we prove a f…
Bernstein-von Mises theorem for log-concave posteriors
Victor-Emmanuel Brunel
We prove new, general versions of Bernstein-von Mises theorem for both well-specified and misspecified models when the log-likelihood is concave in the parameter and the prior dist…
On the continuity of geodesically convex functions on Riemannian manifolds
Victor-Emmanuel Brunel, Pierre Pansu
In this short note, we prove that all geodesically convex functions defined on a Riemannian manifold are continuous in the interior of their domain. This is a folklore result, but…
Asymptotics of constrained -estimation under convexity
Victor-Emmanuel Brunel
M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well u…
Finite sample bounds for barycenter estimation in geodesic spaces
Victor-Emmanuel Brunel, Jordan Serres
We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support con…
A generalization of Grünbaum's inequality in RCD-spaces
Victor-Emmanuel Brunel, Shin-ichi Ohta, Jordan Serres
We generalize Grünbaum's classical inequality in convex geometry to curved spaces with nonnegative Ricci curvature, precisely, to -spaces with …
Unified PAC-Bayesian Study of Pessimism for Offline Policy Learning with Regularized Importance Sampling
Imad Aouali, Victor-Emmanuel Brunel, David Rohde +1
Off-policy learning (OPL) often involves minimizing a risk estimator based on importance weighting to correct bias from the logging policy used to collect data. However, this metho…
Recovering a Magnitude-Symmetric Matrix from its Principal Minors
Victor-Emmanuel Brunel, John Urschel
We consider the inverse problem of finding a magnitude-symmetric matrix (matrix with opposing off-diagonal entries equal in magnitude) with a prescribed set of principal minors. Th…
Bayesian Off-Policy Evaluation and Learning for Large Action Spaces
Imad Aouali, Victor-Emmanuel Brunel, David Rohde +1
In interactive systems, actions are often correlated, presenting an opportunity for more sample-efficient off-policy evaluation (OPE) and learning (OPL) in large action spaces. We…
Convex generalized Fréchet means in a metric tree
Gabriel Romon, Victor-Emmanuel Brunel
We are interested in measures of central tendency for a population on a network, which is modeled by a metric tree. The location parameters that we study are generalized Fréche…
Exponential Smoothing for Off-Policy Learning
Imad Aouali, Victor-Emmanuel Brunel, David Rohde +1
Off-policy learning (OPL) aims at finding improved policies from logged bandit data, often by minimizing the inverse propensity scoring (IPS) estimator of the risk. In this work, w…
Geodesically convex -estimation in metric spaces
Victor-Emmanuel Brunel
We study the asymptotic properties of geodesically convex -estimation on non-linear spaces. Namely, we prove that under very minimal assumptions besides geodesic convexity of th…
Concentration of empirical barycenters in metric spaces
Victor-Emmanuel Brunel, Jordan Serres
Barycenters (aka Fréchet means) were introduced in statistics in the 1940's and popularized in the fields of shape statistics and, later, in optimal transport and matrix analysis.…
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…
Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes
Mike Gartrell, Insu Han, Elvis Dohmatob +2
Determinantal point processes (DPPs) have attracted significant attention in machine learning for their ability to model subsets drawn from a large item collection. Recent work sho…
Propose, Test, Release: Differentially private estimation with high probability
Victor-Emmanuel Brunel, Marco Avella-Medina
We derive concentration inequalities for differentially private median and mean estimators building on the "Propose, Test, Release" (PTR) mechanism introduced by Dwork and Lei (200…
Differentially private sub-Gaussian location estimators
Marco Avella-Medina, Victor-Emmanuel Brunel
We tackle the problem of estimating a location parameter with differential privacy guarantees and sub-Gaussian deviations. Recent work in statistics has focused on the study of est…
Learning Nonsymmetric Determinantal Point Processes
Mike Gartrell, Victor-Emmanuel Brunel, Elvis Dohmatob +1
Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPP…
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…
Learning rates for Gaussian mixtures under group invariance
Victor-Emmanuel Brunel
We study the pointwise maximum likelihood estimation rates for a class of Gaussian mixtures that are invariant under the action of some isometry group. This model is also known as…
Learning Signed Determinantal Point Processes through the Principal Minor Assignment Problem
Victor-Emmanuel Brunel
Symmetric determinantal point processes (DPP's) are a class of probabilistic models that encode the random selection of items that exhibit a repulsive behavior. They have attracted…
A change-point problem and inference for segment signals
Victor-Emmanuel Brunel
We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: To…
Estimation of convex supports from noisy measurements
Victor-Emmanuel Brunel, Jason M. Klusowski, Dana Yang
A popular class of problem in statistics deals with estimating the support of a density from observations drawn at random from a -dimensional distribution. The one-dimension…