Related papers: Bayesian Model Selection with Graph Structured Spa…
Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods…
Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…
Modern approaches to perform Bayesian variable selection rely mostly on the use of shrinkage priors. That said, an ideal shrinkage prior should be adaptive to different signal levels, ensuring that small effects are ruled out, while keeping…
Sparse Bayesian learning (SBL) has been extensively utilized in data-driven modeling to combat the issue of overfitting. While SBL excels in linear-in-parameter models, its direct applicability is limited in models where observations…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
This article describes a full Bayesian treatment for simultaneous fixed-effect selection and parameter estimation in high-dimensional generalized linear mixed models. The approach consists of using a Bayesian adaptive Lasso penalty for…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
The goal of Bayesian deep learning is to provide uncertainty quantification via the posterior distribution. However, exact inference over the weight space is computationally intractable due to the ultra-high dimensions of the neural…
This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their…
We present a novel Bayesian approach for high-dimensional grouped regression under sparsity. We leverage a sparse projection method that uses a sparsity-inducing map to derive an induced posterior on a lower-dimensional parameter space. Our…
Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…
We consider Bayesian logistic regression models with group-structured covariates. In high-dimensional settings, it is often assumed that only small portion of groups are significant, thus consistent group selection is of significant…
Latent space models (LSMs) are often used to analyze dynamic (time-varying) networks that evolve in continuous time. Existing approaches to Bayesian inference for these models rely on Markov chain Monte Carlo algorithms, which cannot handle…
We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…
Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This…
Variational Bayes (VB) is a popular scalable alternative to Markov chain Monte Carlo for Bayesian inference. We study a mean-field spike and slab VB approximation of widely used Bayesian model selection priors in sparse high-dimensional…
Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
We define and discuss the first sparse coding algorithm based on closed-form EM updates and continuous latent variables. The underlying generative model consists of a standard `spike-and-slab' prior and a Gaussian noise model. Closed-form…
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…