Goto

Collaborating Authors

Bayesian Inference for Structured Spike and Slab Priors

Neural Information Processing Systems

Sparse signal recovery addresses the problem of solving underdetermined linear inverse problems subject to a sparsity constraint. We propose a novel prior formulation, the structured spike and slab prior, which allows to incorporate a priori knowledge of the sparsity pattern by imposing a spatial Gaussian process on the spike and slab probabilities. Thus, prior information on the structure of the sparsity pattern can be encoded using generic covariance functions. Furthermore, we provide a Bayesian inference scheme for the proposed model based on the expectation propagation framework. Using numerical experiments on synthetic data, we demonstrate the benefits of the model.


Simultaneous Block-Sparse Signal Recovery Using Pattern-Coupled Sparse Bayesian Learning

arXiv.org Machine Learning

In this paper, we consider the block-sparse signals recovery problem in the context of multiple measurement vectors (MMV) with common row sparsity patterns. We develop a new method for recovery of common row sparsity MMV signals, where a pattern-coupled hierarchical Gaussian prior model is introduced to characterize both the block-sparsity of the coefficients and the statistical dependency between neighboring coefficients of the common row sparsity MMV signals. Unlike many other methods, the proposed method is able to automatically capture the block sparse structure of the unknown signal. Our method is developed using an expectation-maximization (EM) framework. Simulation results show that our proposed method offers competitive performance in recovering block-sparse common row sparsity pattern MMV signals.


Sparse Bayesian Multi-Task Learning

Neural Information Processing Systems

We propose a new sparse Bayesian model for multi-task regression and classification. The model is able to capture correlations between tasks, or more specifically a low-rank approximation of the covariance matrix, while being sparse in the features. We introduce a general family of group sparsity inducing priors based on matrix-variate Gaussian scale mixtures. We show the amount of sparsity can be learnt from the data by combining an approximate inference approach with type II maximum likelihood estimation of the hyperparameters. Empirical evaluations on data sets from biology and vision demonstrate the applicability of the model, where on both regression and classification tasks it achieves competitive predictive performance compared to previously proposed methods.


Bayesian Sparse Factor Models and DAGs Inference and Comparison

Neural Information Processing Systems

In this paper we present a novel approach to learn directed acyclic graphs (DAG) and factor models within the same framework while also allowing for model comparison between them. For this purpose, we exploit the connection between factor models and DAGs to propose Bayesian hierarchies based on spike and slab priors to promote sparsity, heavy-tailed priors to ensure identifiability and predictive densities to perform the model comparison. We require identifiability to be able to produce variable orderings leading to valid DAGs and sparsity to learn the structures. The effectiveness of our approach is demonstrated through extensive experiments on artificial and biological data showing that our approach outperform a number of state of the art methods. Papers published at the Neural Information Processing Systems Conference.


Bayesian Sparse Factor Models and DAGs Inference and Comparison

Neural Information Processing Systems

In this paper we present a novel approach to learn directed acyclic graphs (DAG) and factor models within the same framework while also allowing for model comparison between them. For this purpose, we exploit the connection between factor models and DAGs to propose Bayesian hierarchies based on spike and slab priors to promote sparsity, heavy-tailed priors to ensure identifiability and predictive densities to perform the model comparison. We require identifiability to be able to produce variable orderings leading to valid DAGs and sparsity to learn the structures. The effectiveness of our approach is demonstrated through extensive experiments on artificial and biological data showing that our approach outperform a number of state of the art methods.