Related papers: Improved Pseudolikelihood Regularization and Decim…
This work proposes new estimators for discrete optimal transport plans that enjoy Gaussian limits centered at the true solution. This behavior stands in stark contrast with the performance of existing estimators, including those based on…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
Calibration is nowadays one of the most important processes involved in the extraction of valuable data from measurements. The current availability of an optimum data cube measured from a heterogeneous set of instruments and surveys relies…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
Statistical inference with nonresponse is quite challenging, especially when the response mechanism is nonignorable. In this case, the validity of statistical inference depends on untestable correct specification of the response model. To…
Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov…
This paper addresses the estimation of signals with sublinear sparsity sent over the additive white Gaussian noise channel. This fundamental problem arises in designing denoisers used in message-passing algorithms for sublinear sparsity.…
Most image deblurring methods assume an over-simplistic image formation model and as a result are sensitive to more realistic image degradations. We propose a novel variational framework, that explicitly handles pixel saturation, noise,…
We explore anisotropic regularisation methods in the spirit of [Holler & Kunisch, 14]. Based on ground truth data, we propose a bilevel optimisation strategy to compute the optimal regularisation parameters of such a model for the…
The pseudo-likelihood method is one of the most popular algorithms for learning sparse binary pairwise Markov networks. In this paper, we formulate the $L_1$ regularized pseudo-likelihood problem as a sparse multiple logistic regression…
This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational…
Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a…
These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
Uncertainty in state or model parameters is common in robotics and typically handled by acquiring system measurements that yield information about the uncertain quantities of interest. Inputs to a nonlinear dynamical system yield outcomes…
Doubly-intractable posterior distributions arise in many applications of statistics concerned with discrete and dependent data, including physics, spatial statistics, machine learning, the social sciences, and other fields. A specific…
We consider an on-line system identification setting, in which new data become available at given time steps. In order to meet real-time estimation requirements, we propose a tailored Bayesian system identification procedure, in which the…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…