Variational Bayesian Approximation (VBA): Implementation and Comparison of Different Optimization Algorithms.

In any Bayesian computations, the first step is to derive the joint distribution of all the unknown variables given the observed data. Then, we have to do the computations. There are four general methods for performing computations: Joint MAP optimization; Posterior expectation computations that require integration methods; Sampling-based methods, such as MCMC, slice sampling, nested sampling, etc.

Dynamical system identification, model selection, and model uncertainty quantification by Bayesian inference.

This study presents a Bayesian maximum 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 justification for the choice of the residual and regularization terms, respectively, from the negative logarithms of the likelihood and prior distributions. In addition to the estimation of model coefficients, the Bayesian interpretation gives access to the full apparatus for Bayesian inference, including the ranking of models, the quantification of model uncertainties, and the estimation of unknown (nuisance) hyperparameters.

An interpretable machine learning approach to study the relationship beetwen retrognathia and skull anatomy.

Mandibular retrognathia (C2Rm) is one of the most common oral pathologies. Acquiring a better understanding of the points of impact of C2Rm on the entire skull is of major interest in the diagnosis, treatment, and management of this dysmorphism, but also permits us to contribute to the debate on the changes undergone by the shape of the skull during human evolution. However, conventional methods have some limits in meeting these challenges, insofar as they require defining in advance the structures to be studied, and identifying them using landmarks.

Regularization, Bayesian Inference, and Machine Learning Methods for Inverse Problems.

Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond to the likelihood and prior-probability models, respectively.

Bayesian 3D X-ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain.

In this paper, a hierarchical prior model based on the Haar transformation and an appropriate Bayesian computational method for X-ray CT reconstruction are presented. Given the piece-wise continuous property of the object, a multilevel Haar transformation is used to associate a sparse representation for the object. The sparse structure is enforced via a generalized Student- distribution ( S t g ), expressed as the marginal of a normal-inverse Gamma distribution.

Clinical Relevance of the First Domomedicine Platform Securing Multidrug Chronotherapy Delivery in Metastatic Cancer Patients at Home: The inCASA European Project.

Background: Telehealth solutions can improve the safety of ambulatory chemotherapy, contributing to the maintenance of patients at their home, hence improving their well-being, all the while reducing health care costs. There is, however, need for a practicable multilevel monitoring solution, encompassing relevant outputs involved in the pathophysiology of chemotherapy-induced toxicity. Domomedicine embraces the delivery of complex care and medical procedures at the patient's home based on modern technologies, and thus it offers an integrated approach for increasing the safety of cancer patients on chemotherapy.

Precise periodic components estimation for chronobiological signals through Bayesian Inference with sparsity enforcing prior.

The toxicity and efficacy of more than 30 anticancer agents present very high variations, depending on the dosing time. Therefore, the biologists studying the circadian rhythm require a very precise method for estimating the periodic component (PC) vector of chronobiological signals. Moreover, in recent developments, not only the dominant period or the PC vector present a crucial interest but also their stability or variability.

A circadian clock transcription model for the personalization of cancer chronotherapy.

Circadian timing of anticancer medications has improved treatment tolerability and efficacy several fold, yet with intersubject variability. Using three C57BL/6-based mouse strains of both sexes, we identified three chronotoxicity classes with distinct circadian toxicity patterns of irinotecan, a topoisomerase I inhibitor active against colorectal cancer. Liver and colon circadian 24-hour expression patterns of clock genes Rev-erbα and Bmal1 best discriminated these chronotoxicity classes, among 27 transcriptional 24-hour time series, according to sparse linear discriminant analysis.

Joint NDT image restoration and segmentation using Gauss-Markov-Potts prior models and variational Bayesian computation.

In this paper, we propose a method to simultaneously restore and to segment piecewise homogeneous images degraded by a known point spread function (PSF) and additive noise. For this purpose, we propose a family of nonhomogeneous Gauss-Markov fields with Potts region labels model for images to be used in a Bayesian estimation framework. The joint posterior law of all the unknowns (the unknown image, its segmentation (hidden variable) and all the hyperparameters) is approximated by a separable probability law via the variational Bayes technique.

Bayesian approach with hidden Markov modeling and mean field approximation for hyperspectral data analysis.

The main problems in hyperspectral image analysis are spectral classification, segmentation, and data reduction. In this paper, we propose a Bayesian estimation approach which gives a joint solution for these problems. The problem is modeled as a blind sources separation (BSS).

Hidden Markov models for wavelet-based blind source separation.

In this paper, we consider the problem of blind source separation in the wavelet domain. We propose a Bayesian estimation framework for the problem where different models of the wavelet coefficients are considered: the independent Gaussian mixture model, the hidden Markov tree model, and the contextual hidden Markov field model. For each of the three models, we give expressions of the posterior laws and propose appropriate Markov chain Monte Carlo algorithms in order to perform unsupervised joint blind separation of the sources and estimation of the mixing matrix and hyper parameters of the problem.

Polygonal and polyhedral contour reconstruction in computed tomography.

This paper is about three-dimensional (3-D) reconstruction of a binary image from its X-ray tomographic data. We study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation. We formulate this problem as a nonlinear inverse problem using the Bayesian framework.