EPFL Statistics Seminar

Prof. Marloes Maathuis

Title: High-dimensional consistency in score-based and hybrid structure learning

Abstract

The main approaches for learning Bayesian networks can be classified as constraint-based, score-based or hybrid methods. Although high-dimensional consistency results are available for the constraint-based PC algorithm, such results have been lacking for score-based and hybrid methods, and most hybrid methods are not even proved to be consistent in the classical setting where the number of variables remains fixed. We study the score-based Greedy Equivalence Search (GES) algorithm, as well as hybrid algorithms that are based on GES. We show that such hybrid algorithms can be made consistent in the classical setting by using an adaptive restriction on the search space. Moreover, we prove consistency of GES and adaptively restricted GES (ARGES) for certain sparse high-dimensional scenarios. ARGES scales well to large graphs with thousands of variables, and our simulation studies indicate that both ARGES and GES generally outperform the PC algorithm.

Joint work with Preetam Nandy and Alain Hauser

Prof. Philip B. Stark

Title: Simple Random Sampling: Not So Simple

Abstract

A simple random sample (SRS) of size $k$ from a population of size $n$ is a sample drawn at random in such a way that every subset of $k$ of the $n$ items is equally likely to be selected. The theory of inference from SRSs is fundamental in statistics; many statistical techniques and formulae assume that the data are an SRS. True SRSs are rare; in practice, people tend to draw samples by using pseudo-random number generators (PRNGs) and algorithms that map a set of pseudo-random numbers into a subset of the population. Most statisticians take for granted that the software they use "does the right thing," producing samples that can be treated as if they are SRSs. In fact, the PRNG algorithm and the algorithm for drawing samples using the PRNG matter enormously. Some widely used methods are particularly bad. They cannot generate all subsets of size $k$; the subsets they do generate may not have equal frequencies; and they are numerically inefficient. Using such methods introduces bias and makes standard uncertainty calculations meaningless.

Joint work with Kellie Ottoboni, Department of Statistics, University of California, Berkeley

Prof. Jonathan Rougier

Title: Ensemble averaging and mean squared error

Abstract

In fields such as climate science, it is common to compile an ensemble of different simulators for the same underlying process. It is an interesting observation that the ensemble mean often out-performs at least half of the ensemble members in mean squared error (measured with respect to observations). This despite the fact that the ensemble mean is typically 'less physical' than the individual ensemble members (the state space not being convex). In fact, as demonstrated in the most recent IPCC report, the ensemble mean often out-performs all or almost all of the ensemble members. It turns out that that this is likely to be a mathematical result based on convexity and asymptotic averaging, rather than a deep insight about climate simulators. I will outline the result and discuss its implications.