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This report works out the details of a closed-form, fully Bayesian, multiclass, openset, generative pattern classifier using multivariate Gaussian likelihoods, with conjugate priors. The generative model has a common within-class…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
Factor graphs have recently gained increasing attention as a unified framework for representing and constructing algorithms for signal processing, estimation, and control. One capability that does not seem to be well explored within the…
A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the…
Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…
The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing…
In this paper, I present three closed-form approximations of the two-sample Pearson Bayes factor, a recently developed index of evidential value for data in two-group designs. The techniques rely on some classical asymptotic results about…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes…
Graph transformers are the state-of-the-art for learning from graph-structured data and are empirically known to avoid several pitfalls of message-passing architectures. However, there is limited theoretical analysis on why these models…
Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for…
A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdiagrams of certain combinatorial types. In this paper we…
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…
Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…
To build recommender systems that not only consider user-item interactions represented as ordinal variables, but also exploit the social network describing the relationships between the users, we develop a hierarchical Bayesian model termed…
Structural knowledge graph foundation models aim to generalize reasoning to completely new graphs with unseen entities and relations. A key limitation of existing approaches like Ultra is their reliance on a single relational transformation…
Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…
Vector autoregression has been widely used for modeling and analysis of multivariate time series data. In high-dimensional settings, model parameter regularization schemes inducing sparsity yield interpretable models and achieved good…
Ancestral graph models, introduced by Richardson and Spirtes (2002), generalize both Markov random fields and Bayesian networks to a class of graphs with a global Markov property that is closed under conditioning and marginalization. By…
A key goal of unsupervised learning is to go beyond density estimation and sample generation to reveal the structure inherent within observed data. Such structure can be expressed in the pattern of interactions between explanatory latent…