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(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…
Large-scale biobanks are being collected around the world in efforts to better understand human health and risk factors for disease. They often survey hundreds of thousands of individuals, combining questionnaires with clinical, genetic,…
Complex dynamic systems can be investigated by fitting mechanistic stochastic dynamic models to time series data. In this context, commonly used Monte Carlo inference procedures for model selection and parameter estimation quickly become…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing maximum likelihood estimate when dealing with Gaussian Mixture Model (GMM). When the sample size is smaller than the data dimension, this could lead…
The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP)…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
The analysis of longitudinal categorical data can be complex and unfeasible due to the number of parameters involved, characterised by overparameterisation leading to model non-convergence, in addition to problems related to sample size and…
Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested…
Immersed boundary-lattice Boltzmann method (IB-LBM) has been widely used for simulation of particle-laden flows recently. However, it was limited to small-scale simulations with no more than O(103) particles. Here, we expand IB-LBM for…
We consider the analysis of continuous repeated measurement outcomes that are collected through time, also known as longitudinal data. A standard framework for analysing data of this kind is a linear Gaussian mixed-effects model within…
This paper represents a preliminary (pre-reviewing) version of a sublinear variational algorithm for isotropic Gaussian mixture models (GMMs). Further developments of the algorithm for GMMs with diagonal covariance matrices (instead of…
The Expectation-Maximization (EM) algorithm has been predominantly used to approximate the maximum likelihood estimation of the location-scale Gaussian mixtures. However, when the models are over-specified, namely, the chosen number of…
Transformer-based large language models (LLMs) are comprised of billions of parameters arranged in deep and wide computational graphs. Several studies on LLM efficiency optimization argue that it is possible to prune a significant portion…
Physical simulations based on partial differential equations typically generate spatial fields results, which are utilized to calculate specific properties of a system for engineering design and optimization. Due to the intensive…
In electronic health records (EHRs), latent subgroups of patients may exhibit distinctive patterning in their longitudinal health trajectories. For such data, growth mixture models (GMMs) enable classifying patients into different latent…
We tackle the problem of multiscale regression for predictors that are spatially or temporally indexed, or with a pre-specified multiscale structure, with a Bayesian modular approach. The regression function at the finest scale is expressed…
Large language models (LLMs) have become a popular approach for simulating human behaviors, yet it remains unclear if LLMs are necessary for all simulation tasks. We study a broad family of close-ended simulation tasks, with applications…
Hidden Markov models (HMMs) are powerful tools for analysing time series data that depend on discrete underlying but unobserved states. As such, they have gained prominence across numerous empirical disciplines, in particular ecology,…
In statistics, generalized linear models (GLMs) are widely used for modeling data and can expressively capture potential nonlinear dependence of the model's outcomes on its covariates. Within the broad family of GLMs, those with binary…
Multilevel models (MLMs) are a central building block of the Bayesian workflow. They enable joint, interpretable modeling of data across hierarchical levels and provide a fully probabilistic quantification of uncertainty. Despite their…