Related papers: Adaptive density estimation: a curse of support?

Nonsmoothness is often a curse for optimization; but it is sometimes a blessing, in particular for applications in machine learning. In this paper, we present the specific structure of nonsmooth optimization problems appearing in machine…

This is the second part of the research project initiated in Cleanthous et al (2024). We deal with the problem of the adaptive estimation of the $\mathbb{L}_2$-norm of a probability density on $\mathbb{R}^d$, $d\geq 1$, from independent…

We study a non-parametric approach to multivariate density estimation. The estimators are piecewise constant density functions supported by binary partitions. The partition of the sample space is learned by maximizing the likelihood of the…

Online Convex Optimization plays a key role in large scale machine learning. Early approaches to this problem were conservative, in which the main focus was protection against the worst case scenario. But recently several algorithms have…

This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Cand\`es and Tao's approach, we propose an $\ell_1$-minimization…

We investigate online convex optimization in changing environments, and choose the adaptive regret as the performance measure. The goal is to achieve a small regret over every interval so that the comparator is allowed to change over time.…

We investigate the problem of center estimation in the high dimensional binary sub-Gaussian Mixture Model with Hidden Markov structure on the labels. We first study the limitations of existing results in the high dimensional setting and…

Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with…

We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…

We study the problem of sequential prediction and online minimax regret with stochastically generated features under a general loss function. We introduce a notion of expected worst case minimax regret that generalizes and encompasses prior…

This paper considers the design of a minimax test for two hypotheses where the actual probability densities of the observations are located in neighborhoods obtained by placing a bound on the relative entropy between actual and nominal…

The purpose of this paper is to pursue our study of rho-estimators built from i.i.d. observations that we defined in Baraud et al. (2014). For a \rho-estimator based on some model S (which means that the estimator belongs to S) and a true…

We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…

This paper deals with minimax rates of convergence for estimation of density functions on the real line. The densities are assumed to be location mixtures of normals, a global regularity requirement that creates subtle difficulties for the…

Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…

Shape restriction, like monotonicity or convexity, imposed on a function of interest, such as a regression or density function, allows for its estimation without smoothness assumptions. The concept of $k$-monotonicity encompasses a family…

Estimating the transition dynamics of controlled Markov chains is crucial in fields such as time series analysis, reinforcement learning, and system exploration. Traditional non-parametric density estimation methods often assume independent…

Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, which in principle suffers from the curse of dimensionality. It is therefore important…

Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical…

Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…