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In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…

Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score…

The nonparametric formulation of density-based clustering, known as modal clustering, draws a correspondence between groups and the attraction domains of the modes of the density function underlying the data. Its probabilistic foundation…

Statistical tasks such as density estimation and approximate Bayesian inference often involve densities with unknown normalising constants. Score-based methods, including score matching, are popular techniques as they are free of…

Score matching estimators have gained widespread attention in recent years partly because they are free from calculating the integral of normalizing constant, thereby addressing the computational challenges in maximum likelihood estimation…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…

The popular generalized additive model framework is extended to allow both the mean curves and the response distribution to be nonparametric. The approach is demonstrated to be a flexible yet parsimonious tool for data analysis in its own…

We study the generalized trace regression with a near low-rank regression coefficient matrix, which extends notion of sparsity for regression coefficient vectors. Specifically, given a matrix covariate $X$, the probability density function…

Given a collection of observed signals corrupted with Gaussian noise, how can we learn to optimally denoise them? This fundamental problem arises in both empirical Bayes and generative modeling. In empirical Bayes, the predominant approach…

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…

The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…

In this paper we consider the problem of collectively classifying entities where relational information is available across the entities. In practice inaccurate class distribution for each entity is often available from another (external)…

Score-based generative models have demonstrated significant practical success in data-generating tasks. The models establish a diffusion process that perturbs the ground truth data to Gaussian noise and then learn the reverse process to…

Conformal prediction (CP) provides model-agnostic uncertainty quantification with guaranteed coverage, but conventional methods often produce overly conservative uncertainty sets, especially in multi-dimensional settings. This limitation…

In this paper we propose a new sequential data assimilation method for non-linear ordinary differential equations with compact state space. The method is designed so that the Lyapunov exponents of the corresponding estimation error dynamics…

Supervised and unsupervised homography estimation methods depend on image pairs tailored to specific modalities to achieve high accuracy. However, their performance deteriorates substantially when applied to unseen modalities. To address…

This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical…

Non-random sample selection is a commonplace amongst many empirical studies and it appears when an output variable of interest is available only for a restricted non-random sub-sample of data. We introduce an extension of the generalized…

Recovering the random graph model from an observed collection of networks is known to present significant challenges in the setting, where the networks do not share a common node set and have different sizes. More specifically, the goal is…