Related papers: A universal framework for learning the elliptical …

The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…

The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

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…

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly…

Mini-batch algorithms have become increasingly popular due to the requirement for solving optimization problems, based on large-scale data sets. Using an existing online expectation-{}-maximization (EM) algorithm framework, we demonstrate…

This paper provides a mixture modeling framework using the bivariate generalized exponential distribution. We study different properties of this mixture distribution. Hierarchical EM algorithm is developed for finding the estimates of the…

Parallelization framework has become a necessity to speed up the training of deep neural networks (DNN) recently. Such framework typically employs the Model Average approach, denoted as MA-DNN, in which parallel workers conduct respective…

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare…

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…

Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM)…

A fundamental problem in statistics is estimating the shape matrix of an Elliptical distribution. This generalizes the familiar problem of Gaussian covariance estimation, for which the sample covariance achieves optimal estimation error.…

Hyperspectral imagery collected from airborne or satellite sources inevitably suffers from spectral variability, making it difficult for spectral unmixing to accurately estimate abundance maps. The classical unmixing model, the linear…

Multimodal large language models (MLLMs) have shown promising capabilities but struggle under distribution shifts, where evaluation data differ from instruction tuning distributions. Although previous works have provided empirical…

We present a generalized framework, renormalized density matrix downfolding (RDMD), to derive systematically improvable, highly accurate, and nonperturbative effective models from ab initio calculations. This framework moves beyond the…

Machine learning models have exhibited exceptional results in various domains. The most prevalent approach for learning is the empirical risk minimizer (ERM), which adapts the model's weights to reduce the loss on a training set and…

Exploring the free-energy landscape along reaction coordinates or system parameters $\lambda$ is central to many studies of high-dimensional model systems in physics, e.g. large molecules or spin glasses. In simulations this usually…

A universal and rigorous ensemble framework for nonequilibrium system remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using matrix-based approach. By introducing…

Gaussian Mixture Models (GMMs) are one of the most potent parametric density models used extensively in many applications. Flexibly-tied factorization of the covariance matrices in GMMs is a powerful approach for coping with the challenges…

Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…