Related papers: Dynamical System Identification, Model Selection a…
We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…
We present a theoretical analysis of Maximum a Posteriori (MAP) sequence estimation for binary symmetric hidden Markov processes. We reduce the MAP estimation to the energy minimization of an appropriately defined Ising spin model, and…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…
We propose a general algorithmic framework for Bayesian model selection. A spike-and-slab Laplacian prior is introduced to model the underlying structural assumption. Using the notion of effective resistance, we derive an EM-type algorithm…
In many inverse problems such as 3D X-ray Computed Tomography (CT), the estimation of an unknown quantity, such as a volume or an image, can be greatly enhanced, compared to maximum-likelihood techniques, by incorporating a prior model on…
This paper details how to parameterize the posterior distribution of state-space systems to generate improved optimization problems for system identification using variational inference. Three different parameterizations of the assumed…
Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structure and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. Hence, severe ill-conditioning may affect the estimation problem. This is a scenario often arising…
We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large…
Being able to reliably assess not only the \emph{accuracy} but also the \emph{uncertainty} of models' predictions is an important endeavour in modern machine learning. Even if the model generating the data and labels is known, computing the…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…
This report investigates the extension of the Bayesian Subspace System Identification method proposed in our previous work to the Multiple-Input Multiple-Output (MIMO) case. We derive new equivariant priors and posterior distributions…
We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
Variational system identification is a new formulation of maximum likelihood for estimation of parameters of dynamical systems subject to process and measurement noise, such as aircraft flying in turbulence. This formulation is an…
A Bayesian framework is proposed to define flexible coupling models for joint tensor decompositions of multiple data sets. Under this framework, a natural formulation of the data fusion problem is to cast it in terms of a joint maximum a…
This paper addresses the adaptive radar target detection problem in the presence of Gaussian interference with unknown statistical properties. To this end, the problem is first formulated as a binary hypothesis test, and then we derive a…