Related papers: Optimal rates of estimation for multi-reference al…

Estimation of extreme-value parameters from observations in the max-domain of attraction (MDA) of a multivariate max-stable distribution commonly uses aggregated data such as block maxima. Since we expect that additional information is…

This article concerns the performance limits of strictly causal state estimation for linear systems with fixed, but uncertain, parameters belonging to a finite set. In particular, we provide upper and lower bounds on the smallest achievable…

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…

The maximum correntropy criterion (MCC) has recently been successfully applied in robust regression, classification and adaptive filtering, where the correntropy is maximized instead of minimizing the well-known mean square error (MSE) to…

We study an extension of the classic stochastic multi-armed bandit problem which involves multiple plays and Markovian rewards in the rested bandits setting. In order to tackle this problem we consider an adaptive allocation rule which at…

Interpreting the decisions of complex computer vision models is crucial to establish trust and accountability, especially in safety-critical domains. An established approach to interpretability is generating visual attribution maps that…

The increment ratio (IR) statistic was first defined and studied in Surgailis {\it et al.} (2007) for estimating the memory parameter either of a stationary or an increment stationary Gaussian process. Here three extensions are proposed in…

The multi-index model is a simple yet powerful high-dimensional regression model which circumvents the curse of dimensionality assuming $ \mathbb{E} [ Y | X ] = g(A^\top X) $ for some unknown index space $A$ and link function $g$. In this…

Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to…

Predictive recursion (PR) is a fast stochastic algorithm for nonparametric estimation of mixing distributions in mixture models. It is known that the PR estimates of both the mixing and mixture densities are consistent under fairly mild…

This paper applies the recently axiomatized Optimum Information Principle (minimize the Kullback-Leibler information subject to all relevant information) to nonparametric density estimation, which provides a theoretical foundation as well…

We derive improved regression and classification rates for support vector machines using Gaussian kernels under the assumption that the data has some low-dimensional intrinsic structure that is described by the box-counting dimension. Under…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

We study the estimation error of constrained M-estimators, and derive explicit upper bounds on the expected estimation error determined by the Gaussian width of the constraint set. Both of the cases where the true parameter is on the…

We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are…

This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…

Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…

Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

We consider the question of estimating multi-dimensional Gaussian mixtures (GM) with compactly supported or subgaussian mixing distributions. Minimax estimation rate for this class (under Hellinger, TV and KL divergences) is a long-standing…