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We propose a novel use of a broadcasting operation, which distributes univariate functions to all entries of the tensor covariate, to model the nonlinearity in tensor regression nonparametrically. A penalized estimation and the…
Considering the issue of estimating small probabilities p, ie. measuring a rare domain F = {x | g(x) > q} with respect to the distribution of a random vector X, Multilevel Splitting strategies (also called Subset Simulation) aim at writing…
We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…
Factor models are widely applied to the analysis of multivariate data across disparate fields of research. However, modern scientific data are often incomplete, and estimating a factor model from partially observed data can be very…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
Conditional density estimation (CDE) is a fundamental task in machine learning that aims to model the full conditional law $\mathbb{P}(\mathbf{y} \mid \mathbf{x})$, beyond mere point prediction (e.g., mean, mode). A core challenge is…
Composite likelihood estimation has an important role in the analysis of multivariate data for which the full likelihood function is intractable. An important issue in composite likelihood inference is the choice of the weights associated…
We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable when the event time is subject to interval censoring case 1 and the continuous mark variable is only observed in case the…
We derive a fully analytical, one-line closed-form expression for the cumulative distribution function (CDF) of the product of two correlated zero-mean normal random variables, avoiding any series representation. This result complements the…
Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…
Joint probability mass function (PMF) estimation is a fundamental machine learning problem. The number of free parameters scales exponentially with respect to the number of random variables. Hence, most work on nonparametric PMF estimation…
Covariance estimation is essential yet underdeveloped for analyzing multivariate functional data. We propose a fast covariance estimation method for multivariate sparse functional data using bivariate penalized splines. The tensor-product…
We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian…
We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and…
There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender…
Given an i.i.d. sample from a distribution $F$ on $\mathbb{R}$ with uniformly continuous density $p_0$, purely data-driven estimators are constructed that efficiently estimate $F$ in sup-norm loss and simultaneously estimate $p_0$ at the…
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
We introduce an optimization model for maximum likelihood-type estimation (M-estimation) that generalizes a large class of existing statistical models, including Huber's concomitant M-estimator, Owen's Huber/Berhu concomitant estimator, the…
This paper considers nonconvex distributed constrained optimization over networks, modeled as directed (possibly time-varying) graphs. We introduce the first algorithmic framework for the minimization of the sum of a smooth nonconvex…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…