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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…
Consider the communication-constrained estimation of discrete distributions under $\ell^p$ losses, where each distributed terminal holds multiple independent samples and uses limited number of bits to describe the samples. We obtain the…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
The multinomial and related distributions have long been used to model categorical, count-based data in fields ranging from bioinformatics to natural language processing. Commonly utilized variants include the standard multinomial and the…
The Weibull distribution, with shape parameter $k>0$ and scale parameter $\lambda>0$, is one of the most popular parametric distributions in survival analysis with complete or censored data. Although inference of the parameters of the…
Analysis of experimental data must sometimes deal with abrupt changes in the distribution of measured values. Setting upper limits on signals usually involves a veto procedure that excludes data not described by an assumed statistical…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
This paper presents a unified and novel estimation framework for the Weibull, Gamma, and Log-normal distributions based on arbitrary-order moment pairs. Traditional estimation techniques, such as Maximum Likelihood Estimation (MLE) and the…
Rough set theory is one of the most widely used and significant approaches for handling incomplete information. It divides the universe in the beginning and uses equivalency relations to produce blocks. Numerous generalized rough set models…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…
As the maximum likelihood method is the most commonly used method for parameters estimation being unbiased, consistent, efficient, and asymptotically normal, MLE is used to fit the new distribution (MBUW). But in small to moderate sample…
Weibull distribution is widely used in modelling health data. However, its lack of sufficient tail flexibility often results in poor fit in extreme events. We proposed another three-parameter extension of the Weibull distribution with…
Training models that perform well under distribution shifts is a central challenge in machine learning. In this paper, we introduce a modeling framework where, in addition to training data, we have partial structural knowledge of the…
Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…
For estimating area-specific parameters (quantities) in a finite population, a mixed model prediction approach is attractive. However, this approach strongly depends on the normality assumption of the response values although we often…
Human feedback is increasingly used across diverse applications like training AI models, developing recommender systems, and measuring public opinion -- with granular feedback often being preferred over binary feedback for its greater…
This paper studies the partial estimation of Gaussian graphical models from high-dimensional empirical observations. We derive a convex formulation for this problem using $\ell_1$-regularized maximum-likelihood estimation, which can be…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
Peak counts have been shown to be an excellent tool to extract the non-Gaussian part of the weak lensing signal. Recently, we developped a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct…