Related papers: A Bayesian approach with persistent homology prior…

Balancing performance and interpretability in multivariate time series classification is a significant challenge due to data complexity and high dimensionality. This paper introduces PHeatPruner, a method integrating persistent homology and…

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine…

Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…

Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…

Persistent homology (PH) characterizes the shape of brain networks through the persistence features. Group comparison of persistence features from brain networks can be challenging as they are inherently heterogeneous. A recent scale-space…

Variational inference often struggles with the posterior geometry exhibited by complex hierarchical Bayesian models. Recent advances in flow-based variational families and Variationally Inferred Parameters (VIP) each address aspects of this…

We present a Bayesian hierarchical modeling approach to paleoclimate reconstruction using borehole temperature profiles. The approach relies on modeling heat conduction in solids via the heat equation with step function, surface boundary…

This paper presents a hierarchical Bayesian modeling framework for the uncertainty quantification in modal identification of linear dynamical systems using multiple vibration data sets. This novel framework integrates the state-of-the-art…

We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from…

Time-lapse images carry out important information about dynamic changes in Earth's interior which can be inferred using different Full Waveform Inversion (FWI) schemes. The estimation process is performed by manipulating more than one…

This paper investigates asset allocation problems when returns are predictable. We introduce a market-timing Bayesian hierarchical (BH) approach that adopts heterogeneous time-varying coefficients driven by lagged fundamental…

In this paper, we propose a Bayesian approach for multiscale problems with the availability of dynamic observational data. Our method selects important degrees of freedom probabilistically in a Generalized multiscale finite element method…

We consider the problem of simultaneously inferring the heterogeneous coefficient field for a Robin boundary condition on an inaccessible part of the boundary along with the shape of the boundary for the Poisson problem. Such a problem…

We provide a complete framework for performing infinite-dimensional Bayesian inference and uncertainty quantification for image reconstruction with Poisson data. In particular, we address the following issues to make the Bayesian framework…

Stochastic variational inference allows for fast posterior inference in complex Bayesian models. However, the algorithm is prone to local optima which can make the quality of the posterior approximation sensitive to the choice of…

Inverse Uncertainty Quantification (IUQ) method has been widely used to quantify the uncertainty of Physical Model Parameters (PMPs) in nuclear Thermal Hydraulics (TH) systems. This paper introduces a novel hierarchical Bayesian model which…

Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…

Solving high-dimensional PDE-governed inverse problems is often challenging due to complex non-Gaussian posterior distributions, expensive forward model evaluations, and misspecified prior information. To address these issues, we propose a…

The level set approach has proven widely successful in the study of inverse problems for interfaces, since its systematic development in the 1990s. Recently it has been employed in the context of Bayesian inversion, allowing for the…

In this work, we propose a Bayesian thinning algorithm for recovering weighted point source functions in the heat equation from boundary flux observations. The major challenge in the classical Bayesian framework lies in constructing…