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We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and…

Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…

We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…

Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…

Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly…

Distributed inference/estimation in Bayesian framework in the context of sensor networks has recently received much attention due to its broad applicability. The variational Bayesian (VB) algorithm is a technique for approximating…

Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…

Despite the risk of misspecification they are tied to, parametric models continue to be used in statistical practice because they are accessible to all. In particular, efficient estimation procedures in parametric models are simple to…

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

Indirect inference requires simulating realisations of endogenous variables from the model under study. When the endogenous variables are discontinuous functions of the model parameters, the resulting indirect inference criterion function…

Replication of experimental results has been a challenge faced by many scientific disciplines, including the field of machine learning. Recent work on the theory of machine learning has formalized replicability as the demand that an…

The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Bayesian modelling allows for the quantification of predictive uncertainty which is crucial in safety-critical applications. Yet for many machine learning (ML) algorithms, it is difficult to construct or implement their Bayesian…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…