Information détaillée concernant le cours
École d’été 2019
1-4 septembre 2019
M. Yves Tillé, UNINE (Président); Mme Caroline Gillardin, UNINE (coordinatrice)
Prof. Finn Lindgren, University of Edinburgh
Prof. Finn Lindgren (University of Edinburgh)
Title : Numerical computation for statistics
Traditionally, geostatistical computations for spatial and spatio-temporal data centred around expressions for conditional expectations and covariances that explicitly use the covariance matrix for the whole data set. With the ever larger data sets in modern applications, naive applications of these equations leads to intractable storage and computation. Many alternative models and methods have been designed to handle this issue. In these lectures I will focus on Gaussian spatial Markov models, and how these lead to efficient numerical algebra through sparse matrices, while also providing direct links to the traditional models, so that the discrete models are consistently interpretable for continuous domains. Practical Bayesian inference is now largely focused around making MCMC methods that are efficient for broader ranges of models. However, for large models, making direct use of the model structure can provide computational methods that produce deterministic approximations to the posterior distributions, instead of MCMC approximations that generate finite sets of dependent samples. For latent Gaussian Markov models this bias-variance tradeoff is substantially in favour of deterministic approximations. I will discuss the basic principles of Integrated Nested Laplace Approximations (INLA), and how they are a natural method for spatial and spatio-temporal geostatistics. For very large problems (e.g. billions of observations or more) direct storage of and equation solves with the needed sparse matrices is again intractable. One can then delve even deeper into methods numerical linear algebra and apply iterative methods that take advantage of the strong structure provided by multiscale spatio-temporal models. I will illustrate how some of these techniques were combined to estimate daily mean temperatures on a 20 km global resolution across 165 years in the Prof. Finn Lindgren (University of Edinburgh)
Prof. Ryan Tibshirani (Carnegie Mellon University)
Title : Convex Optimization for Statistics and Machine Learning
Nearly every problem in computational statistics and machine learning can be formulated in terms of the optimization of some function, possibly under some set of constraints. As we obviously cannot solve every problem in statistics and machine learning, this means that we cannot generically solve every optimization problem (at least not efficiently). Fortunately, many problems of interest can be posed as optimization tasks that have special properties---such as convexity, smoothness, sparsity, separability, etc.---permitting standardized, efficient solution techniques.
These lectures are designed to give a graduate-level student a thorough grounding in these properties and their role in optimization, and a broad comprehension of algorithms tailored to exploit such properties. The focus will be on convex optimization problems, and we will visit several important applications in machine learning and statistics.
The first two lectures will be a rapid-paced advanced-level review comprising four parts: Part I: basic convex analysis, Part II: first-order methods, Part III: optimality and duality, Part IV: second-order methods. The third lecture will either be on a survey of advanced methods, or focused on one specific advanced method: (parallel) coordinate descent.
Prof. Darren Wilkinson (Newcastle University)
Title : Statistical computing for systems biology
This course will advocate a computational Bayesian approach to modelling and inference for dynamic stochastic models of biological systems. An introduction will be given to the theory of Markov processes in continuous time, and their application to biological modelling. Examples will include simple models of populations and epidemics, Lotka-Volterra predator-prey systems, and biochemical network dynamics. Discrete state jump processes and associated diffusion approximations described by stochastic differential equations will be considered, with a strong emphasis on algorithms and computer simulation. Observation models and time course data will be introduced, leading to hierarchical Bayesian dynamic state-space models with intractable transition kernels. Bayesian inference for models of this type will be considered, and several different algorithms will be illustrated. Particular emphasis will be placed on "likelihood free" methods of inference, including approximate Bayesian computation (ABC) and particle MCMC algorithms. Full use will be made of samples from the posterior distribution, which will be used to investigate convergence, parameter identifiability, and confounding.
Eurotel Victoria Villars
Doctorant CUSO chambre double: 200 CHF
Doctorant CUSO chambre simple: 350 CHF
Post-doctorant CUSO chambre double: 300 CHF
Post-doctorant CUSO chambre simple: 450 CHF
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Professeur CUSO chambre simple: 550 CHF
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