The Expectation-Propagation algorithm was introduced by Minka in 2001, and is today still one of the most effective algorithms for approximate inference. It is relatively difficult to implement well but in certain cases it can give results that are almost exact, while being much faster than MCMC. In this course I will review EP and classical applications to Generalised Linear Models and Gaussian Process models. I will also introduce some recent developments, including applications of EP to ABC problems, and discuss how to parallelise EP effectively.[-]

In this short course, we will discuss the problem of ranking with partially observed pairwise comparisons in the setting of Bradley-Terry-Luce (BTL) model. There are two fundamental problems: 1) top-K ranking, which is to select the set of K players with top performances; 2) total ranking, which is to rank the entire set of players. Both ranking problems find important applications in web search, recommender systems and sports competition.
In the first presentation, we will consider the top-K ranking problem. The statistical properties of two popular algorithms, MLE and rank centrality (spectral ranking) will be precisely characterized. In terms of both partial and exact recovery, the MLE achieves optimality with matching lower bounds. The spectral method is shown to be generally sub-optimal, though it has the same order of sample complexity as the MLE. Our theory also reveals the essentially only situation when the spectral method is optimal. This turns out to be the most favorable choice of skill parameter given the separation of the two groups.
The second presentation will be focused on total ranking. The problem is to find a permutation vector to rank the entire set of players. We will show that the minimax rate of the problem with respect to the Kendall's tau loss exhibits a transition between an exponential rate and a polynomial rate depending on the signal to noise ratio of the problem. The optimal algorithm consists of two stages. In the first stage, games with very high or low scores are used to partition the entire set of players into different leagues. In the second stage, games that are very close are used to rank the players within each league. We will give intuition and some analysis to show why the algorithm works optimally.[-]

In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its derivatives as a "non-smooth + non-smooth'' optimization problem.
Modern techniques to solve these include smoothing the datafitting term, to benefit from fast efficient proximal algorithms.
In this work we focus on minimax sup-norm convergence rates for non smoothed and smoothed, single task and multitask square-root Lasso-type estimators. We also provide some guidelines on how to set the smoothing hyperparameter, and illustrate on synthetic data the interest of such guidelines.
This is joint work with Quentin Bertrand (INRIA), Mathurin Massias, Olivier Fercoq and Alexandre Gramfort.[-]

In this short course, we will discuss the problem of ranking with partially observed pairwise comparisons in the setting of Bradley-Terry-Luce (BTL) model. There are two fundamental problems: 1) top-K ranking, which is to select the set of K players with top performances; 2) total ranking, which is to rank the entire set of players. Both ranking problems find important applications in web search, recommender systems and sports competition.
In the first presentation, we will consider the top-K ranking problem. The statistical properties of two popular algorithms, MLE and rank centrality (spectral ranking) will be precisely characterized. In terms of both partial and exact recovery, the MLE achieves optimality with matching lower bounds. The spectral method is shown to be generally sub-optimal, though it has the same order of sample complexity as the MLE. Our theory also reveals the essentially only situation when the spectral method is optimal. This turns out to be the most favorable choice of skill parameter given the separation of the two groups.
The second presentation will be focused on total ranking. The problem is to find a permutation vector to rank the entire set of players. We will show that the minimax rate of the problem with respect to the Kendall's tau loss exhibits a transition between an exponential rate and a polynomial rate depending on the signal to noise ratio of the problem. The optimal algorithm consists of two stages. In the first stage, games with very high or low scores are used to partition the entire set of players into different leagues. In the second stage, games that are very close are used to rank the players within each league. We will give intuition and some analysis to show why the algorithm works optimally.[-]