相关论文: Equation Discovery with Bayesian Spike-and-Slab Pr…

Ransomware attacks are increasing at an alarming rate, leading to large financial losses, unrecoverable encrypted data, data leakage, and privacy concerns. The prompt detection of ransomware attacks is required to minimize further damage,…

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…

Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…

In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is…

High-dimensional data sets have become ubiquitous in the past few decades, often with many more covariates than observations. In the frequentist setting, penalized likelihood methods are the most popular approach for variable selection and…

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…

Deep kernel learning is a promising combination of deep neural networks and nonparametric function learning. However, as a data driven approach, the performance of deep kernel learning can still be restricted by scarce or insufficient data,…

Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution…

This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…

Sparsity of the solution of a linear regression model is a common requirement, and many prior distributions have been designed for this purpose. A combination of the sparsity requirement with smoothness of the solution is also common in…

Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample…

In this paper we show that the classical problem of frequency estimation can be formulated and solved efficiently in an empirical Bayesian framework by assigning a uniform a priori probability distribution to the unknown frequency. We…

We propose a novel Bayesian methodology for inference in functional linear and logistic regression models based on the theory of reproducing kernel Hilbert spaces (RKHS's). We introduce general models that build upon the RKHS generated by…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

Over the past decade and a half, adoption of Bayesian inference in pulsar timing analysis has led to increasingly sophisticated models. The recent announcement of evidence for a stochastic background of gravitational waves by various pulsar…

We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional…

We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional…

We study the use of spike and slab priors for consistent estimation of the number of change points and their locations. Leveraging recent results in the variable selection literature, we show that an estimator based on spike and slab priors…

Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…

In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem…