Related papers: Hierarchical Bayesian Level Set Inversion

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…

An inverse problem of identifying inhomogeneity or crack in the workpiece made of nonlinear magnetic material is investigated. To recover the shape from the local measurements, a piecewise constant level set algorithm is proposed. By means…

Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…

Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…

Hierarchical inference in (generalized) regression problems is powerful for finding significant groups or even single covariates, especially in high-dimensional settings where identifiability of the entire regression parameter vector may be…

Variational inference methods have been shown to lead to significant improvements in the computational efficiency of approximate Bayesian inference in mixed multinomial logit models when compared to standard Markov-chain Monte Carlo (MCMC)…

Leaving posterior sensitivity concerns aside, non-identifiability of the parameters does not raise a difficulty for Bayesian inference as far as the posterior is proper, but multi-modality or flat regions of the posterior induced by the…

The choice of tuning parameters in Bayesian variable selection is a critical problem in modern statistics. In particular, for Bayesian linear regression with non-local priors, the scale parameter in the non-local prior density is an…

Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again…

Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…

In this work, we present, analyze, and implement a class of Multi-Level Markov chain Monte Carlo (ML-MCMC) algorithms based on independent Metropolis-Hastings proposals for Bayesian inverse problems. In this context, the likelihood function…

Hierarchical categorical variables often exhibit many levels (high granularity) and many classes within each level (high dimensionality). This may cause overfitting and estimation issues when including such covariates in a predictive model.…

Meta-learning allows an intelligent agent to leverage prior learning episodes as a basis for quickly improving performance on a novel task. Bayesian hierarchical modeling provides a theoretical framework for formalizing meta-learning as…

Prior sensitivity examination plays an important role in applied Bayesian analyses. This is especially true for Bayesian hierarchical models, where interpretability of the parameters within deeper layers in the hierarchy becomes…

Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for both Newton solution of deterministic inverse problems, as…

We generalize the approach of Liu and Lawrence (1999) for multiple changepoint problems where the number of changepoints is unknown. The approach is based on dynamic programming recursion for efficient calculation of the marginal…

We propose a new splitting criterion for a meta-learning approach to multiclass classifier design that adaptively merges the classes into a tree-structured hierarchy of increasingly difficult binary classification problems. The…

This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and…

Previous work on sensitivity analysis in Bayesian networks has focused on single parameters, where the goal is to understand the sensitivity of queries to single parameter changes, and to identify single parameter changes that would enforce…