Related papers: A Direct Sampler for G-Wishart Variates
In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…
In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…
We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing…
The joint problem of reconstruction / feature extraction is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of its features. In this work, we firstly…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based…
Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms…
Incorporating information about the target distribution in proposal mechanisms generally produces efficient Markov chain Monte Carlo algorithms (or at least, algorithms that are more efficient than uninformed counterparts). For instance, it…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…
We consider large-dimensional Hermitian or symmetric random matrices of the form $W=M+\vartheta V$ where $M$ is a Wigner matrix and $V$ is a real diagonal matrix whose entries are independent of $M$. For a large class of diagonal matrices…
Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI…
This article develops a general-purpose adaptive sampler that approximates the target density by a mixture of multivariate t densities. The adaptive sampler is based on reversible proposal distributions each of which has the mixture of…
Symbolic regression discovers explicit, interpretable equations without assuming a functional form in advance. A Bayesian approach strengthens this through probability distributions over candidate expressions, thus quantifying uncertainty…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
The invariance to permutations of the adjacency matrix, i.e., graph isomorphism, is an overarching requirement for Graph Neural Networks (GNNs). Conventionally, this prerequisite can be satisfied by the invariant operations over node…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
Our article considers a Gaussian variational approximation of the posterior density in a high-dimensional state space model. The variational parameters to be optimized are the mean vector and the covariance matrix of the approximation. The…
Many methods for machine learning rely on approximate inference from intractable probability distributions. Variational inference approximates such distributions by tractable models that can be subsequently used for approximate inference.…