Related papers: Invariant Priors for Bayesian Quadrature
Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…
Quadratic Unconstrained Binary Optimization (QUBO) is a general-purpose modeling framework for combinatorial optimization problems and is a requirement for quantum annealers. This paper utilizes the eigenvalue decomposition of the…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…
In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation…
Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…
We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian…
We consider the problem of Bayesian regression with trustworthy uncertainty quantification. We define that the uncertainty quantification is trustworthy if the ground truth can be captured by intervals dependent on the predictive…
Bayesian experimental design is a technique that allows to efficiently select measurements to characterize a physical system by maximizing the expected information gain. Recent developments in deep neural networks and normalizing flows…
Next-generation radio interferometers like the Square Kilometer Array have the potential to unlock scientific discoveries thanks to their unprecedented angular resolution and sensitivity. One key to unlocking their potential resides in…
Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…
There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…
In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…
Before the availability of large scale fault-tolerant quantum devices, one has to find ways to make the most of current noisy intermediate-scale quantum devices. One possibility is to seek smaller repetitive hybrid quantum-classical tasks…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…
Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a…
The framework of quantum invariants is an elegant generalization of adiabatic quantum control to control fields that do not need to change slowly. Due to the unavailability of invariants for systems with more than one spatial dimension, the…