Related papers: Maximum a Posteriori Estimation for Linear Structu…
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…
The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…
There are several challenges associated with inverse problems in which we seek to reconstruct a piecewise constant field, and which we model using multiple level sets. Adopting a Bayesian viewpoint, we impose prior distributions on both the…
The sparse Beyesian learning (also referred to as Bayesian compressed sensing) algorithm is one of the most popular approaches for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless,…
In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this…
Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution. Many kinds of priors have been explored in the…
Polynomial Chaos Expansions (PCEs) are widely recognized for their efficient computational performance in surrogate modeling. Yet, a robust framework to quantify local model errors is still lacking. While the local uncertainty of PCE…
In Bayesian inference, the maximum a posteriori (MAP) problem combines the most probable explanation (MPE) and marginalization (MAR) problems. The counterpart in propositional logic is the exist-random stochastic satisfiability (ER-SSAT)…
This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. The advantage of adaptivity in this context is the ability to focus more resources on regions of space where signal…
For wideband spectrum sensing, compressive sensing has been proposed as a solution to speed up the high dimensional signals sensing and reduce the computational complexity. Compressive sensing consists of acquiring the essential information…
Purpose: To achieve automatic hyperparameter estimation for the joint recovery of quantitative MR images, we propose a Bayesian formulation of the reconstruction problem that incorporates the signal model. Additionally, we investigate the…
Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties, is unavoidable. Polynomial Chaos Expansion (PCE) is widely…
This paper proposes an adaptive sparse polynomial chaos expansion(PCE)-based method to quantify the impacts of uncertainties on critical clearing time (CCT) that is an important index in transient stability analysis. The proposed method can…
We propose a new procedure named PASOA, for Bayesian experimental design, that performs sequential design optimization by simultaneously providing accurate estimates of successive posterior distributions for parameter inference. The…
Consider the problem of estimating parameters $X^n \in \mathbb{R}^n $, generated by a stationary process, from $m$ response variables $Y^m = AX^n+Z^m$, under the assumption that the distribution of $X^n$ is known. This is the most general…
Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…
Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…
The pretrained diffusion model as a strong prior has been leveraged to address inverse problems in a zero-shot manner without task-specific retraining. Different from the unconditional generation, the measurement-guided generation requires…
We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…
Numerical integration and emulation are fundamental topics across scientific fields. We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate…