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We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…

We elaborate on a deconvolution method, used to estimate the empirical distribution of unknown parameters, as suggested recently by Efron (2013). It is applied to estimating the empirical distribution of the 'sampling probabilities' of m…

Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…

Given samples (x_1,...,x_m) and (z_1,...,z_n) which we believe are independent realizations of random variables X and Z respectively, where we further believe that Z=X+Y with Y independent of X, the problem is to estimate the distribution…

Existing approaches to model uncertainty typically either compare models using a quantitative model selection criterion or evaluate posterior model probabilities having set a prior. In this paper, we propose an alternative strategy which…

Standard machine learning is unable to accommodate inputs which do not belong to the training distribution. The resulting models often give rise to confident incorrect predictions which may lead to devastating consequences. This problem is…

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…

We study the non-parametric estimation of an unknown stationary density fV of an unobserved strictly stationary volatility process $(\bm V_t)_{t\geq 0}$ on $\IRp^2 := (0,\infty)^2$ based on discrete-time observations in a stochastic…

Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution…

This paper studies the non-parametric estimation and uniform inference for the conditional quantile regression function (CQRF) with covariates exposed to measurement errors. We consider the case that the distribution of the measurement…

Thanks to the tractability of their likelihood, several deep generative models show promise for seemingly straightforward but important applications like anomaly detection, uncertainty estimation, and active learning. However, the…

We study how the training data distribution affects confidence and performance in image classification models. We introduce Embedding Density, a model-agnostic framework that estimates prediction confidence by measuring the distance of test…

A basic issue in both teaching of and practice of statistics is the interplay between modelling assumptions and inference performance. The general message conveyed is that stronger assumptions lead to better statistical performance of the…

Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…

Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…

Causal inference from observational data often assumes "ignorability," that all confounders are observed. This assumption is standard yet untestable. However, many scientific studies involve multiple causes, different variables whose…

We derive estimators of the density of the event times of current status data. The estimators are derived for the situations where the distribution of the observation times is known and where this distribution is unknown. The density…

This paper deals with the nonparametric density estimation of the regression error term assuming its independence with the covariate. The difference between the feasible estimator which uses the estimated residuals and the unfeasible one…

The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…