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We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable based on censored data. More specifically, the event time is subject to current status censoring and the continuous mark…
One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function…
Human microbiome studies based on genetic sequencing techniques produce compositional longitudinal data of the relative abundances of microbial taxa over time, allowing to understand, through mixed-effects modeling, how microbial…
We consider the estimation of Dirichlet Process Mixture Models (DPMMs) in distributed environments, where data are distributed across multiple computing nodes. A key advantage of Bayesian nonparametric models such as DPMMs is that they…
In this note, we explore a simple approach to composition estimation, using penalized likelihood density estimation on a nominal discrete domain. Practical issues such as smoothing parameter selection and the use of prior information are…
Microscopy research often requires recovering particle-size distributions in three dimensions from only a few (10 - 200) profile measurements in the section. This problem is especially relevant for petrographic and mineralogical studies,…
Maximum likelihood estimation in logistic regression with mixed effects is known to often result in estimates on the boundary of the parameter space. Such estimates, which include infinite values for fixed effects and singular or infinite…
We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…
The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…
Mixture proportion estimation (MPE) is the problem of estimating the weight of a component distribution in a mixture, given samples from the mixture and component. This problem constitutes a key part in many "weakly supervised learning"…
The traditional maximum likelihood estimator (MLE) is often of limited use in complex high-dimensional data due to the intractability of the underlying likelihood function. Maximum composite likelihood estimation (McLE) avoids full…
In recent years, log-concave density estimation via maximum likelihood estimation has emerged as a fascinating alternative to traditional nonparametric smoothing techniques, such as kernel density estimation, which require the choice of one…
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…
This article proposes a mixture modeling approach to estimating cluster-wise conditional distributions in clustered (grouped) data. We adapt the mixture-of-experts model to the latent distributions, and propose a model in which each…
Mixtures of generalized normal distributions (MGND) have gained popularity for modelling datasets with complex statistical behaviours. However, the estimation of the shape parameter within the maximum likelihood framework is quite complex,…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
Simple exponential smoothing is widely used in forecasting economic time series. This is because it is quick to compute and it generally delivers accurate forecasts. On the other hand, its multivariate version has received little attention…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
Maximum pseudolikelihood method has been among the most important methods for learning parameters of statistical physics models, such as Ising models. In this paper, we study how pseudolikelihood can be derived for learning parameters of a…