Related papers: Minimax Rate-Optimal Estimation of Divergences bet…
We consider the minimax estimation problem of a discrete distribution with support size $k$ under locally differential privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the…
This paper is concerned with the detection of multiple change-points in the joint distribution of independent categorical variables. The procedures introduced rely on model selection and are based on a penalized least-squares criterion.…
We consider model selection in generalized linear models (GLM) for high-dimensional data and propose a wide class of model selection criteria based on penalized maximum likelihood with a complexity penalty on the model size. We derive a…
For the nonparametric estimation of multivariate finite mixture models with the conditional independence assumption, we propose a new formulation of the objective function in terms of penalized smoothed Kullback-Leibler distance. The…
The main purpose of this paper is to introduce and study the behavior of minimum {\phi}-divergence estimators as an alternative to the maximum likelihood estimator in latent class models for binary items. As it will become clear below,…
We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…
We derive the optimal measurement for quantum state discrimination without a priori probabilities, i.e. in a minimax strategy instead of the usually considered Bayesian one. We consider both minimal-error and unambiguous discrimination…
We introduce a mini-batch stochastic variance-reduced algorithm to solve finite-sum scale invariant problems which cover several examples in machine learning and statistics such as principal component analysis (PCA) and estimation of…
We address the problem of Schr\"odinger potential estimation, which plays a crucial role in modern generative modelling approaches based on Schr\"odinger bridges and stochastic optimal control for SDEs. Given a simple prior diffusion…
Derivative based optimization methods are efficient at solving optimal control problems near local optima. However, their ability to converge halts when derivative information vanishes. The inference approach to optimal control does not…
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…
We construct optimal low-rank approximations for the Gaussian posterior distribution in linear Gaussian inverse problems with possibly infinite-dimensional separable Hilbert parameter spaces and finite-dimensional data spaces. We first…
We propose a closed-form spectral framework for relative log-density estimation in linearly parameterized probabilistic models, including unnormalized and conditional models. This is achieved by representing the Kullback-Leibler (KL)…
In this work, we introduce a novel estimator of the predictive risk with Poisson data, when the loss function is the Kullback-Leibler divergence, in order to define a regularization parameter's choice rule for the Expectation Maximization…
In this paper, we derive minimax rates for estimating both parametric and nonparametric components in partially linear additive models with high dimensional sparse vectors and smooth functional components. The minimax lower bound for…
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. We obtain closed formulas for the expected model approximation errors,…
We study the rates of estimation of finite mixing distributions, that is, the parameters of the mixture. We prove that under some regularity and strong identifiability conditions, around a given mixing distribution with $m_0$ components,…
We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for approximating optimal couplings. We prove convergence of the…
This paper presents how to perform minimax optimal classification, regression, and density estimation based on fixed-$k$ nearest neighbor (NN) searches. We consider a distributed learning scenario, in which a massive dataset is split into…
In this paper we investigate the performance of a variety of estimation techniques for the scale and shape parameter of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the…