This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.

Abstract Greedy importance sampling is an unbiased estimation technique that re-duces the variance of standard importance sampling by explicitly searching for modes in the estimation objective. Previous work has demon-strated the feasibility of implementing this method and proved that the technique is unbiased in both discrete and continuous domains. In thispaper we present a reformulation of greedy importance sampling that eliminates the free parameters from the original estimator, and introducesa new regularization strategy that further reduces variance without compromising unbiasedness. The resulting estimator is shown to be effectivefor difficult estimation problems arising in Markov random field inference. In particular, improvements are achieved over standard MCMCestimators when the distribution has multiple peaked modes. 1 Introduction Many inference problems in graphical models can be cast as determining the expectedvalue of a random variable of interest, f, given observations drawn according to a tar-get distribution P. That is, we are interested in computing EP (x)f (x). Unfortunately, innatural situations

This paper proposes an efficient sampling method for inference in probabilistic graphical models. The method exploits a blessing of dimensionality known as the concentration of measure phenomenon in order to derive analytic expressions for proposal distributions. The method can also...