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We propose a scalable divergence estimation method based on hashing. Consider two continuous random variables $X$ and $Y$ whose densities have bounded support. We consider a particular locality sensitive random hashing, and consider the…
Semicontinuous outcomes occur frequently in health services, insurance, and cost studies. Standard nonparametric density estimators are not well suited to such data because they do not naturally accommodate the mixed structure, the…
Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…
Orthogonal group synchronization aims to recover orthogonal group elements from their noisy pairwise measurements. It has found numerous applications including computer vision, imaging science, and community detection. Due to the orthogonal…
We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For…
Averaging predictions of a deep ensemble of networks is apopular and effective method to improve predictive performance andcalibration in various benchmarks and Kaggle competitions. However, theruntime and training cost of deep ensembles…
Aggregating estimators using exponential weights depending on their risk appears optimal in expectation but not in probability. We use here a slight overpenalization to obtain oracle inequality in probability for such an explicit…
This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…
We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…
We consider the problem of aggregating a general collection of affine estimators for fixed design regression. Relevant examples include some commonly used statistical estimators such as least squares, ridge and robust least squares…
The kernel smoothing with large bandwidth values causes oversmoothing or underfitting in general. However, when irrelevant variables are included, the corresponding large bandwidth values are known to have an effect of shrinking them. This…
We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
We design the weights in consensus algorithms with spatially correlated random topologies. These arise with: 1) networks with spatially correlated random link failures and 2) networks with randomized averaging protocols. We show that the…
In this paper we propose a convolution estimator for estimating the density of a response variable that employs an underlying multiple regression framework to enhance the accuracy of density estimates through the incorporation of auxiliary…
Propensity score weighting is a common method for estimating treatment effects with survey data. The method is applied to minimize confounding using measured covariates that are often different between individuals in treatment and control.…
The parameter estimation of unnormalized models is a challenging problem. The maximum likelihood estimation (MLE) is computationally infeasible for these models since normalizing constants are not explicitly calculated. Although some…
In this paper, we study estimation of certain integral functionals of one or two densities with samples from stationary m-dependent sequences. We consider two types of U-statistic estimators for these functionals that are functions of the…
We construct a density estimator in the bivariate uniform deconvolution model. For this model we derive four inversion formulas to express the bivariate density that we want to estimate in terms of the bivariate density of the observations.…
We consider the sparse regression model where the number of parameters $p$ is larger than the sample size $n$. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between…