Related papers: Computationally Efficient Sparse Bayesian Learning…

Approximate message passing (AMP) methods have gained recent traction in sparse signal recovery. Additional information about the signal, or \emph{side information} (SI), is commonly available and can aid in efficient signal recovery. This…

Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the…

We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically…

Approximate message passing (AMP) refers to a class of efficient algorithms for statistical estimation in high-dimensional problems such as compressed sensing and low-rank matrix estimation. This paper analyzes the performance of AMP in the…

Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…

There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…

In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty…

A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…

Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

There is significant interest in learning and optimizing a complex system composed of multiple sub-components, where these components may be agents or autonomous sensors. Among the rich literature on this topic, agent-based and…

In this paper, we present a communication-efficient federated learning framework inspired by quantized compressed sensing. The presented framework consists of gradient compression for wireless devices and gradient reconstruction for a…

We discuss a method for sparse signal approximation, which is based on the correlation of the target signal with a pseudo-random signal, and uses a modification of the greedy matching pursuit algorithm. We show that this approach provides…

We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same…

Approximate message passing (AMP) algorithms are devised under the Gaussianity assumption of the measurement noise vector. In this work, we relax this assumption within the vector AMP (VAMP) framework to arbitrary independent and…

Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

Sparse Bayesian learning has promoted many effective frameworks for brain activity decoding, especially for the reconstruction of muscle activity. However, existing sparse Bayesian learning mainly employs Gaussian distribution as error…

Approximate Message Passing (AMP) algorithms are a class of iterative procedures for computationally-efficient estimation in high-dimensional inference and estimation tasks. Due to the presence of an 'Onsager' correction term in its…

The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…