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Many physical systems evolve on matrix Lie groups and mixture filtering designed for such manifolds represent an inevitable tool for challenging estimation problems. However, mixture filtering faces the issue of a constantly growing number…
Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…
Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available, introducing a…
Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social…
Metabolic Syndrome (MetS) is a cluster of interrelated risk factors that significantly increases the risk of cardiovascular diseases and type 2 diabetes. Despite its global prevalence, accurate prediction of MetS remains challenging due to…
Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…
In systems biology, it is becoming increasingly common to measure biochemical entities at different levels of the same biological system. Hence, data fusion problems are abundant in the life sciences. With the availability of a multitude of…
Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…
Recent advances in stochastic gradient techniques have made it possible to estimate posterior distributions from large datasets via Markov Chain Monte Carlo (MCMC). However, when the target posterior is multimodal, mixing performance is…
Growth mixture models are an important tool for detecting group structure in repeated measures data. Unlike traditional clustering methods, they explicitly model the repeat measurements on observations, and the statistical framework they…
We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…
LocalSGD and SCAFFOLD are widely used methods in distributed stochastic optimization, with numerous applications in machine learning, large-scale data processing, and federated learning. However, rigorously establishing their theoretical…
Generalized Hydrodynamics (GHD) has recently been devised as a method to solve the dynamics of integrable quantum many-body systems beyond the mean-field approximation. In its original form, a major limitation is the inability to predict…
There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…
Extended magnetohydrodynamics (XMHD) is a fluid plasma model generalizing ideal MHD by taking into account the impact of Hall drift effects and the influence of electron inertial effects. XMHD has a Hamiltonian structure which has received…
Linear mixed models are widely used for clustered data, but their reliance on parametric forms limits flexibility in complex and high-dimensional settings. In contrast, gradient boosting methods achieve high predictive accuracy through…
Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression model with a standard improper prior distribution yields an…
This article introduces a nonlinear generalized matrix factor model (GMFM) that allows for mixed-type variables, extending the scope of linear matrix factor models (LMFM) that are so far limited to handling continuous variables. We…
A scale mixture of normals is a distribution formed by mixing a collection of normal distributions with fixed mean but different variances. A generalized gamma scale mixture draws the variances from a generalized gamma distribution.…
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…