 anglais uniquement
EPFL Statistics Seminar

Statistics seminar organised by UNIL
Jonas Peters University of Copenhagen
Tuesday, February 20, 2018
Time 12:15 to 13:15  Internef  237
Title: Invariant Causal Prediction
Abstract
Why are we interested in the causal structure of a process? In classical prediction tasks as regression, for example, it seems that no causal knowledge is required. In many situations, however, we want to understand how a system reacts under interventions, e.g., in gene knockout experiments. Here, causal models become important because they are usually considered invariant under those changes. A causal prediction uses only direct causes of the target variable as predictors; it remains valid even if we intervene on predictor variables or change the whole experimental setting. In this talk, we show how we can exploit this invariance principle to estimate causal structure from data. We apply the methodology to data sets from biology, epidemiology, and finance.
The talk does not require any knowledge about causal concepts. 
Dr. Łukasz Kidziński
Stanford University
Friday, February 23, 2018
Time 15:15  Room MA10
Title: Sparse longitudinal modeling using matrix factorization
Abstract
A common problem in clinical practice is to predict disease progression from sparse observations of individual patients. The classical approach to modeling this kind of data relies on a mixedeffect model where time is considered as both a fixed effect (a population trajectory) and a random effect (an individual trajectory). In our work, we map the problem to a matrix completion framework and solve it using matrix factorization techniques. The proposed approach does not require assumptions of the mixedeffect model and it can be naturally extended to multivariate measurements

Dr. Giacomo Zanella
Università Bocconi, Milano
Friday, March 16, 2018
Time 15:15  Room MA10
Title: Optimization and complexity of the Gibbs Sampler for multilevel Gaussian models
Abstract
We study the convergence properties of the Gibbs Sampler in the context of Bayesian hierarchical linear models with nested and crossedeffects structures. We develop a novel methodology based on multigrid decompositions to derive analytic expressions for the convergence rates of the algorithm. In the nested context, our work gives a rather complete understanding of the Gibbs Sampler behavior for models with arbitrary depth, leading to simple and easytoimplement guidelines to optimize algorithmic implementations. In the context of crossedeffect models, where classical strategies to speedup convergence are not applicable, we show that the convergence of commonly implemented Gibbs Sampler strategies deteriorates as the datasize increases. This results in superlinear computational complexity (potentially even quadratic) in the number of datapoints. Leveraging the insight provided by the multigrid analysis, we design a simple collapsed Gibbs Sampler whose complexity matches the one of nested scenarios. The implications for scalable Bayesian inferences on large multilevel models are discussed.
Joint work with Omiros Papaspiliopoulos and Gareth Roberts 
Ass. Prof. Ben Shaby
Penn State University
Friday, March 23, 2018
Time 15:15  Room MA10
Title: MaxInfinitely Divisible Models for Spatial Extremes Using Random Effects
Abstract
Rare events can have crippling effects on economies, infrastructure, and human health and wellbeing. Their outsized impacts make extreme events critical to understand, yet their defining characteristic, rareness, means that precious little information is available to study them. Extremes of environmental processes are inherently spatial in structure, as a given event necessarily occurs over a particular spatial extent at a particular collection of locations. Characterizing their probabilistic structure therefore requires moving well beyond the wellunderstood models that describe marginal extremal behavior at a single location. Rather, stochastic process models are needed to describe joint tail event across space. Distinguishing between the subtly different dependence characteristics implied by current families of stochastic process models for spatial extremes is difficult or impossible based on exploratory analysis of data that is by definition scarce. Furthermore, different choices of extremal dependence classes have large consequences in the analysis they produce. We present stochastic models for extreme events in space that are 1) flexible enough to transition across different classes of extremal dependence, and 2) permit inference through likelihood functions that can be computed for large datasets. It will accomplish these modeling goals by representing stochastic dependence relationships conditionally, which will induce desirable tail dependence properties and allow efficient inference through Markov chain Monte Carlo. We develop models for spatial extremes using maxinfinitely divisible processes, a generalization of the limiting maxstable class of processes which has received a great deal of attention. This work extends previous family of maxstable models based on a conditional hierarchical representation to the more flexible maxid class, thus accommodating a wider variety of extremal dependence characteristics while retaining the structure that makes it computationally attractive.

Dr. Quentin Berthet
University of Cambridge
Friday, April 13, 2018
Time 15:15  Room MA10
Title: Optimal Link Prediction with Matrix Logistic Regression
Abstract
We consider the problem of link prediction, based on partial observation of a large network and on covariates associated to its vertices. The generative model is formulated as matrix logistic regression. The performance of the model is analysed in a highdimensional regime under structural assumption. The minimax rate for the Frobenius norm risk is established and a combinatorial estimator based on the penalised maximum likelihood approach is shown to achieve it. Furthermore, it is shown that this rate cannot be attained by any algorithm computable in polynomial time, under a computational complexity assumption, and we will present the tools needed to establish these fundamental limits, and other problems where they appear. Joint work with Nicolai Baldin

Ass. Prof. David Bolin
Chalmers University of Technology
Friday, April 27, 2018
Time 15:15  Room MA10
Title: A Bayesian General Linear Modeling Approach to Cortical Surface fMRI Data Analysis
Abstract
Cortical surface fMRI (csfMRI) has recently grown in popularity versus traditional volumetric fMRI, as it allows for more meaningful spatial smoothing and is more compatible with the common assumptions of isotropy and stationarity in Bayesian spatial models. However, as no Bayesian spatial model has been proposed for csfMRI data, most analyses continue to employ the classical, voxelwise general linear model (GLM). Here, we propose a Bayesian GLM for csfMRI, which employs a class of spatial processes based on stochastic partial differential equations to model latent activation fields. Bayesian inference is performed using integrated nested Laplacian approximations (INLA), which is a computationally efficient alternative to Markov Chain Monte Carlo. To identify regions of activation, we propose an excursions set method based on the joint posterior distribution of the latent fields, which eliminates the need for multiple comparisons correction. Finally, we address a gap in the existing literature by proposing a Bayesian approach for multisubject analysis. The methods are validated and compared to the classical GLM through simulation studies and a motor task fMRI study from the Human Connectome Project. The proposed Bayesian approach results in smoother activation estimates, more accurate false positive control, and increased power to detect truly active regions.

Prof. Philippe Rigollet
MIT
Thursday, May 24, 2018
Time 15:15  Room MA10
Title: Learning determinantal point processes
Abstract
Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning (such as recommendation systems) where returning a diverse set of objects is important. While there are fast algorithms for sampling, marginalization and conditioning, much less is known about learning the parameters of a DPP. In this talk, I will present recent results related to this problem, specifically:
 Rates of convergence for the maximum likelihood estimator: by studying the local and global geometry of the expected loglikelihood function we are able to establish rates of convergence for the MLE and give a complete characterization of the cases where these are parametric. We also give a partial description of the critical points for the expected loglikelihood.
 Optimal rates of convergence for this problem: these are achievable by the method of moments and are governed by a combinatorial parameter, which we call the cycle sparsity.
 A fast combinatorial algorithm to implement the method of moments efficiently.
Coauthors: VictorEmmanuel Brunel (MIT), Ankur Moitra (MIT), John Urschel (MIT) 
Ass. Prof. Patrick RubinDelanchy
University of Bristol
Friday, June 1st, 2018
Time 15:15  Room MA10
Title: The generalised random dot product graph: a statistical model underpinning spectral embedding
Abstract
Finding a statistical framework under which to perform inference about graphvalued data has proved to be surprisingly challenging, considering the wealth of prior work in the fields of (broader) Mathematics and Computer Science. In this talk, a probabilistic model is presented that allows more refined analysis of spectral embedding and clustering as statistical estimation procedures, and which has several other advantages including generality (e.g. the mixed membership and standard stochastic block models are special cases), scalability (e.g. by some arguments requiring computation of only the first few singular vectors of the adjacency matrix), and interpretability (e.g. mixtures of connectivity behaviours are represented as convex combinations in latent space). Corresponding to this canonical statistical interpretation of spectral embedding is an indefinite orthogonal group that describes the identifiability limitations on the latent positions defined by the model. This group, which is most famously relevant to the theory of special relativity, can consist of transformations that affect interpoint distances, with worrying implications for spectral clustering. All such issues are resolved by simple statistical insights on the effect of linear transformations on volumes and Gaussian mixture models, confirming a more generally recognised ruleofthumb in data science: Gaussian clustering should be preferred over Kmeans. Methodology and ideas are illustrated with cybersecurity applications.
Seminar Speakers
Past Statistics Seminars
 Statistics Seminar
 Seminars held during 2017
 Seminars held during 2016
 Seminars held during 2015
 Seminars held during 2014
 Seminars held during 2013
 Seminars held during 2012
 Seminars held during 2011
 Seminars held during 2010
 Seminars held during 2009
 Seminars held during 2008
 Seminars held during 2007
 Seminars held from 1995 through 2006
Visitor Information
Directions for visitorsMailing List
Please email Ms. Schaffner if you would like to be added to the seminar mailing list.