Related papers: Bayesian Structure Learning for Markov Random Fiel…

In this work, we propose a scalable Bayesian procedure for learning the local dependence structure in a high-dimensional model where the variables possess a natural ordering. The ordering of variables can be indexed by time, the vicinities…

To incorporate prior knowledge as well as measurement uncertainties in the traditional long short term memory (LSTM) neural networks, an efficient sparse Bayesian training algorithm is introduced to the network architecture. The proposed…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…

Sparse recovery in linear systems underpins applications from signal processing to high-dimensional regression. Sparse Bayesian Learning, grounded in the principle of automatic relevance determination (ARD), offers a practical Bayesian…

Dealing with uncertainty in Bayesian Network structures using maximum a posteriori (MAP) estimation or Bayesian Model Averaging (BMA) is often intractable due to the superexponential number of possible directed, acyclic graphs. When the…

The iterations of many first-order algorithms, when applied to minimizing common regularized regression functions, often resemble neural network layers with pre-specified weights. This observation has prompted the development of…

In this paper, we propose a new estimation procedure for discovering the structure of Gaussian Markov random fields (MRFs) with false discovery rate (FDR) control, making use of the sorted l1-norm (SL1) regularization. A Gaussian MRF is an…

In many domains, we are interested in analyzing the structure of the underlying distribution, e.g., whether one variable is a direct parent of the other. Bayesian model-selection attempts to find the MAP model and use its structure to…

In the literature on deep neural networks, there is considerable interest in developing activation functions that can enhance neural network performance. In recent years, there has been renewed scientific interest in proposing activation…

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…

Designing predictive controllers towards optimal closed-loop performance while maintaining safety and stability is challenging. This work explores closed-loop learning for predictive control parameters under imperfect information while…

This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With…

Markov networks are widely used in many Machine Learning applications including natural language processing, computer vision, and bioinformatics . Learning Markov networks have many complications ranging from intractable computations…

Recent years have seen an increasing popularity of learning the sparse \emph{changes} in Markov Networks. Changes in the structure of Markov Networks reflect alternations of interactions between random variables under different regimes and…

Markov random fields are common prior distributions used in Bayesian inverse imaging problems. In particular, difference priors assign probability distributions to differences between neighbouring pixels, such as Gaussian, Laplace, or…

Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold standard method for Bayesian sparse linear regression [CPS09,…

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…

The advances in variational inference are providing promising paths in Bayesian estimation problems. These advances make variational phylogenetic inference an alternative approach to Markov Chain Monte Carlo methods for approximating the…

Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. Among others, supervised sparsity-aware learning comprises two major paths paved by: a) discriminative methods and…