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Most of the classical denoising methods restore clear results by selecting and averaging pixels in the noisy input. Instead of relying on hand-crafted selecting and averaging strategies, we propose to explicitly learn this process with deep…
Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semi-parametric context: estimating the…
Understanding generalization and estimation error of estimators for simple models such as linear and generalized linear models has attracted a lot of attention recently. This is in part due to an interesting observation made in machine…
The finite sample properties of estimators are usually understood or approximated using asymptotic theories. Two main asymptotic constructions have been used to characterize the presence of many instruments. The first assumes that the…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, with simpler models exhibiting high bias and more complex models exhibiting high…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is…
This paper investigates the behavior of the Min-Sum decoder running on noisy devices. The aim is to evaluate the robustness of the decoder in the presence of computation noise, e.g. due to faulty logic in the processing units, which…
We study local asymptotic properties of likelihood ratios of certain Heston models. We distinguish three cases: subcritical, critical and supercritical models. For the drift parameters, local asymptotic normality is proved in the…
Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are nonstochastic. In practice, however, in order to improve finite…
We study nonparametric estimation of density functions for undirected dyadic random variables (i.e., random variables defined for all n\overset{def}{\equiv}\tbinom{N}{2} unordered pairs of agents/nodes in a weighted network of order N).…
We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric…
This tutorial provides a gentle introduction to kernel density estimation (KDE) and recent advances regarding confidence bands and geometric/topological features. We begin with a discussion of basic properties of KDE: the convergence rate…
The authors consider the problem of estimating the density $g$ of independent and identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$, $\epsilon$ is a noise…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
We study kernel estimation of highest-density regions (HDR). Our main contributions are two-fold. First, we derive a uniform-in-bandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then…
We present a new non-parametric estimator of the conditional density of the kernel type. It is based on an efficient transformation of the data by quantile transform. By use of the copula representation, it turns out to have a remarkable…
We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the…
We study the semiparametric efficient estimation of a class of linear functionals in settings where a complete multivariate dataset is supplemented by additional datasets recording subsets of the variables of interest. These datasets are…