In this presentation, I focus on the layered adaptive importance sampling (LAIS), a class of adaptive importance samplers where Markov chain Monte Carlo (MCMC) algorithms are employed to drive an underlying multiple importance sampling (IS) scheme. Its power lies in the simplicity of the layered framework: the upper layer locates proposal densities by means of MCMC algorithms; while the lower layer handles the multiple IS scheme, in order to compute the final estimators. The modular nature of LAIS allows for different possible choices in the upper and lower layers, that will have different performance and computational costs. I show different enhancements in order to increase the efficiency and reduce the computational cost, of both upper and lower layers. The different variants are essential if we aim to address computational challenges arising in real-world applications, such as highly concentrated posterior distributions (due to large amounts of data, etc.). Hamiltonian-driven importance samplers will be presented and. Furthermore, I will describe different strategies for designing cheaper schemes, for instance, recycling samples generated in the upper layer and using them in the final estimators in the lower layer.
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Luca Martino - I have obtained the MSc degree in Electronic Engineering at the Politecnico di Milano and my PhD inStatistical Signal Processing from Universidad Carlos III de Madrid, Spain, in 2011. I was Assistant Professor in the Department of Signal Theory and Communications at Universidad Carlos III deMadrid since then. In August 2013 I joined the Department of Mathematics and Statistics at theUniversity of Helsinki with a postdoctoral position. In March 2015, I joined the Universidade de São Paulo (USP) as postdoctoral researcher. In May 2016, I started to work as a postdoctoral researcher at the University of Valencia. Currently, I am Associate Professor in URJC ("Profesor Titular" in Spain, permanent position). My research interests focus mainly on Bayesian inference, Computational algorithms, Gaussian Processes and machine learning techniques.