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# Documents  65C60 | enregistrements trouvés : 29

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## Bayesian inference and mathematical imaging - Part 3: probability and convex optimisation Pereyra, Marcelo | CIRM H

Post-edited

Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

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## Inexact gradient projection and fast data driven compressed sensing: theory and application Davies, Michael E. | CIRM H

Post-edited

Research schools

We consider the convergence of the iterative projected gradient (IPG) algorithm for arbitrary (typically nonconvex) sets and when both the gradient and projection oracles are only computed approximately. We consider different notions of approximation of which we show that the Progressive Fixed Precision (PFP) and (1+epsilon) optimal oracles can achieve the same accuracy as for the exact IPG algorithm. We also show that the former scheme is also able to maintain the (linear) rate of convergence of the exact algorithm, under the same embedding assumption, while the latter requires a stronger embedding condition, moderate compression ratios and typically exhibits slower convergence. We apply our results to accelerate solving a class of data driven compressed sensing problems, where we replace iterative exhaustive searches over large datasets by fast approximate nearest neighbour search strategies based on the cover tree data structure. Finally, if there is time we will give examples of this theory applied in practice for rapid enhanced solutions to an emerging MRI protocol called magnetic resonance fingerprinting for quantitative MRI. We consider the convergence of the iterative projected gradient (IPG) algorithm for arbitrary (typically nonconvex) sets and when both the gradient and projection oracles are only computed approximately. We consider different notions of approximation of which we show that the Progressive Fixed Precision (PFP) and (1+epsilon) optimal oracles can achieve the same accuracy as for the exact IPG algorithm. We also show that the former scheme is also ...

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## Monte Carlo and quasi-Monte Carlo methods 2010.Selected papers based on the presentations at the 9th international conference on Monte Carlo and quasi Monte Carlo in scientific computing (MCQMC 2010)Warsaw # august 15-20, 2010 Plaskota, Leszek ; Wozniakowski, Henryk | Springer 2012

Congrès

- xii; 732 p.
ISBN 978-3-642-27439-8

Springer proceedings in mathematics & statistics

Localisation : Colloque 1er étage (WARS)

méthode de Monte Carlo # méthode de quasi-Monte Carlo # statistique en grande dimension # finance # analyse numérique # probabilités # chaîne de Markov

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## Algebraic and geometric methods in discrete mathematics.AMS special session on algebraic and geometric methods in applied discrete mathematicsSan Antonio # January 11, 2015 Harrington, Heather A. ; Omar, Mohamed ; Wright, Matthew | American Mathematical Society 2017

Congrès

- vii; 277 p.
ISBN 978-1-4704-2321-6

Contemporary mathematics , 0685

Localisation : Collection 1er étage

géométrie algébrique # algèbre commutative # théorie des groupes # représentation de groupes # analyse fonctionnelle # géométrie discrète et convexe # polytope # polyhèdre # analyse numérique # théorie des jeux

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## Model assessment, selection and averaging Vehtari, Aki | CIRM H

Multi angle

Research School

The tutorial covers cross-validation, and projection predictive approaches for model assessment, selection and inference after model selection and Bayesian stacking for model averaging. The talk is accompanied with R notebooks using rstanarm, bayesplot, loo, and projpred packages.

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## Bayesian computation with INLA Rue, Havard | CIRM H

Multi angle

Research School

This talk focuses on the estimation of the distribution of unobserved nodes in large random graphs from the observation of very few edges. These graphs naturally model tournaments involving a large number of players (the nodes) where the ability to win of each player is unknown. The players are only partially observed through discrete valued scores (edges) describing the results of contests between players. In this very sparse setting, we present the first nonasymptotic risk bounds for maximum likelihood estimators (MLE) of the unknown distribution of the nodes. The proof relies on the construction of a graphical model encoding conditional dependencies that is extremely efficient to study n-regular graphs obtained using a round-robin scheduling. This graphical model allows to prove geometric loss of memory properties and deduce the asymptotic behavior of the likelihood function. Following a classical construction in learning theory, the asymptotic likelihood is used to define a measure of performance for the MLE. Risk bounds for the MLE are finally obtained by subgaussian deviation results derived from concentration inequalities for Markov chains applied to our graphical model. This talk focuses on the estimation of the distribution of unobserved nodes in large random graphs from the observation of very few edges. These graphs naturally model tournaments involving a large number of players (the nodes) where the ability to win of each player is unknown. The players are only partially observed through discrete valued scores (edges) describing the results of contests between players. In this very sparse setting, we ...

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## Bayesian computational methods Robert, Christian P. | CIRM H

Multi angle

Research School

This is a short introduction to the many directions of current research in Bayesian computational statistics, from accelerating MCMC algorithms, to using partly deterministic Markov processes like the bouncy particle and the zigzag samplers, to approximating the target or the proposal distributions in such methods. The main illustration focuses on the evaluation of normalising constants and ratios of normalising constants.

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## Bayesian inference and mathematical imaging - Part 2: Markov chain Monte Carlo Pereyra, Marcelo | CIRM H

Multi angle

Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

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## Bayesian inference and mathematical imaging - Part 4: mixture, random fields and hierarchical models Pereyra, Marcelo | CIRM H

Multi angle

Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

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## Bayesian inference and mathematical imaging - Part 1: Bayesian analysis and decision theory Pereyra, Marcelo | CIRM H

Multi angle

Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

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## Approximate Bayesian Computation methods for model choice a machine learning point of view - Part 1 Marin, Jean-Michel | CIRM H

Multi angle

Research talks;Probability and Statistics

Approximate Bayesian computation (ABC) techniques, also known as likelihood-free methods, have become a standard tool for the analysis of complex models, primarily in population genetics. The development of new ABC methodologies is undergoing a rapid increase in the past years, as shown by multiple publications, conferences and softwares. In this lecture, we introduce some recent advances on ABC techniques, notably for model choice problems.

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## Overlapping community detection by spectral methods Levina, Elizaveta | CIRM

Multi angle

Research talks;Computer Science;Probability and Statistics

Community detection is a fundamental problem in network analysis which is made more challenging by overlaps between communities which often occur in practice. Here we propose a general, flexible, and interpretable generative model for overlapping communities, which can be thought of as a generalization of the degree-corrected stochastic block model. We develop an efficient spectral algorithm for estimating the community memberships, which deals with the overlaps by employing the $K$-medians algorithm rather than the usual $K$-means for clustering in the spectral domain. We show that the algorithm is asymptotically consistent when networks are not too sparse and the overlaps between communities not too large. Numerical experiments on both simulated networks and many real social networks demonstrate that our method performs very well compared to a number of benchmark methods for overlapping community detection. This is joint work with Yuan Zhang and Ji Zhu.

community detection - networks - pseudo-likelihood
Community detection is a fundamental problem in network analysis which is made more challenging by overlaps between communities which often occur in practice. Here we propose a general, flexible, and interpretable generative model for overlapping communities, which can be thought of as a generalization of the degree-corrected stochastic block model. We develop an efficient spectral algorithm for estimating the community memberships, which deals ...

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## Numerical studies of space filling designs: optimization algorithm and subprojection properties Iooss, Bertrand | CIRM H

Multi angle

Research talks;Probability and Statistics

discrepancy, optimal design, Latin Hypercube Sampling, computer experiment

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## Rare event simulation for molecular dynamics Guyader, Arnaud | CIRM H

Multi angle

Research talks

This talk is devoted to the presentation of algorithms for simulating rare events in a molecular dynamics context, e.g., the simulation of reactive paths. We will consider $\mathbb{R}^d$ as the space of configurations for a given system, where the probability of a specific configuration is given by a Gibbs measure depending on a temperature parameter. The dynamics of the system is given by an overdamped Langevin (or gradient) equation. The problem is to find how the system can evolve from a local minimum of the potential to another, following the above dynamics. After a brief overview of classical Monte Carlo methods, we will expose recent results on adaptive multilevel splitting techniques. This talk is devoted to the presentation of algorithms for simulating rare events in a molecular dynamics context, e.g., the simulation of reactive paths. We will consider $\mathbb{R}^d$ as the space of configurations for a given system, where the probability of a specific configuration is given by a Gibbs measure depending on a temperature parameter. The dynamics of the system is given by an overdamped Langevin (or gradient) equation. The ...

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## An introduction to statistical computing:a simulation-based approach Voss, Jochen | Wiley 2014

Ouvrage

- xii; 382 p.
ISBN 978-1-118-35772-9

Wiley series in computational statistics

Localisation : Ouvrage RdC (VOSS)

générateur de nombres aléatoires # modèles de simulation statistique # méthode de Monte Carlo # chaîne de Markov # logiciel R # programmation

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## La simulation de Monte Carlo Tuffin, Bruno | Hermes;Lavoisier 2010

Ouvrage

- 270 p.
ISBN 978-2-7462-2521-3

Méthodes stochastiques appliquées

Localisation : Ouvrage RdC (TUFF)

méthode de Monte Carlo # méthode de simulation # quadrature # programmation mathématique # quadrature # optimization # équation linéaire # équation intégrale # application statistique

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## Correlated data analysis:modeling, analytics, and applications Song, Peter X.-K. | Springer 2007

Ouvrage

- xv; 346 p.
ISBN 978-0-387-71392-2

Springer series in statistics

Localisation : Ouvrage RdC (SONG)

corrélation # équation d'estimation généralisée # méthode longitudinale # analyse de données # inférence paramétrique

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## Méthodes de Monte-Carlo avec R Robert, Christian P. ; Casella, George ; Robert, Joachim ; Ryder, Robin ; Arbel, Julyan ; Jacob, Pierre ; Plessis, Brigitte | Springer 2011

Ouvrage

- xv; 256 p.
ISBN 978-2-8178-0180-3

Pratique R

Localisation : Ouvrage RdC (ROBE)

méthode de Monte-Carlo # langage de programmation R # simulation statistique # analyse bayésienne

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## The Bayesan choice :from decision-theoretic foundations to computational implementation Robert, Christian P. | Springer 2001

Ouvrage

- 602 p.
ISBN 978-0-387-71598-8

Springer texts in statistics

Localisation : Ouvrage RdC (ROBE)

statistiques # problème de Bayes # théorie de la décision en statistiques # inférence de Bayes # loi à priori # estimation ponctuelle # modèle de choix # admissibilité # invarience

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## Computational statistics with R Rao, Marepalli B. ; Rao, C.R. | Elsevier;North-Holland 2014

Ouvrage

- xvii; 394 p.
ISBN 978-0-444-63431-3

Handbook of statistics , 0032

Localisation : Ouvrage RdC (COMP)

statistiques computationnelles # logiciel R # environnement R # graphique R # calcul de la taille d'un échantillon # régression binômiale # réseau Bayesien # tolérance

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