EPFL Statistics Seminar

Prof. Po-Ling Loh

Title: From information to estimation in stochastic differential equations

Abstract

We study the relationship between information- and estimation-theoretic quantities in time-evolving systems. Our starting point is a stochastic differential equation and its associated partial differential equation, known as the Fokker-Planck equation. We show that the time derivatives of entropy, KL divergence, and mutual information are characterized by estimation-theoretic quantities involving an appropriate generalization of the Fisher information. Our results vastly extend relationships known as De Bruijn's identity and the I-MMSE relation, which have generated recent interest in the information theory community for the special case of Brownian motion. We also develop connections to a generalized version of the Bayesian Cramer-Rao bound. This is joint work with Andre Wibisono and Varun Jog

Prof. Jonas Peters

Title: Invariances and Causality

Abstract

Why are we interested in the causal structure of a data-generating process? In a classical regression problem, for example, we include a variable into the model if it improves the prediction; it seems that no causal knowledge is required. In many situations, however, we are interested in the system's behavior under a change of environment. Here, causal models become important because they are usually considered invariant under those changes. In this talk, we briefly introduce the formalism of structural causal models, which can be used to compute intervention distributions when the causal structure is known. We also discuss ideas that can be used to estimate causal structures from data. No prior knowledge is required.

Prof. Andrea Rinaldo

Title: Covariations in Ecological Scaling Laws

Abstract

Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and theoreticians. In fact, broad -- if disconnected -- empirical evidence exists for scaling laws in ecology associated with the number of species inhabiting an ecosystem, their abundances an traits. Although their power-law functional form appears to be ubiquitous, perhaps reflecting a self-organized inevitability whose origins are yet to be convincingly described, empirical scaling exponents can be shown to depend on ecosystem type and resource supply – thus far from universal. Although the idea that ecological and evolutionary scaling laws are linked had been entertained before, the full extent of macroecological pattern covariations, the role of the constraints imposed by finite resource supply and a comprehensive empirical verification are still largely unexplored to date. In this Seminar, I shall analyze a recently proposed theoretical scaling framework that predicts the linkages of several macroecological patterns related to species' abundances and body sizes. I plan to show that such framework is consistent with the stationary state statistics of a broad class of resource-limited community dynamics models, regardless of parametrization and model assumptions. I shall then proceed to show the verification of predicted theoretical covariations by contrasting empirical data collected from a number of sources and contexts and to provide testable hypotheses for yet unexplored patterns. The work thus is aimed at placing the observed variability of ecological scaling exponents in a coherent statistical framework where patterns in ecology embed constrained fluctuations.

Dr. Emeric Thibaud

Title: Exploration and inference in spatial extremes using empirical basis functions

Abstract

Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to explore and model spatial extremal dependence. Based on a low-rank max-stable model we propose a data-driven approach to estimate meaningful basis functions using empirical pairwise extremal coefficients. These spatial empirical basis functions can be used to visualize the main trends in extremal dependence. In addition to exploratory analysis, we show how these functions can be used in a Bayesian hierarchical model to model spatial extremes of large datasets. We illustrate our method with an application to extreme precipitations in eastern U.S.

This is joint work with Samuel Morris and Brian Reich (North Carolina State University).

Dr. Shahin Tavakoli

Title: A Spatial Modeling Approach for Linguistic Object Data: Analysing dialect sound variations across Great Britain

Abstract

Dialect variation is of considerable interest in linguistics and other social sciences. However, traditionally it has been studied using proxies (transcriptions) rather than acoustic recordings directly. We introduce novel statistical techniques to analyse geolocalised speech recordings and to explore the spatial variation of pronunciations continuously over the region of interest, as opposed to traditional isoglosses, which provide a discrete partition of the region. Data of this type require an explicit modeling of the variation in the mean and the covariance. Usual Euclidean metrics are not appropriate, and we therefore introduce the concept of d-covariance, which allows consistent estimation both in space and at individual locations. We then propose spatial smoothing for these objects which accounts for the possibly non convex geometry of the domain of interest. We apply the proposed method to data from the spoken part of the British National Corpus, deposited at the British Library, London, and we produce maps of the dialect variation over Great Britain. In addition, the methods allow for acoustic reconstruction across the domain of interest, allowing researchers to listen to the statistical analysis.

This is joint work with Davide Pigoli and John Aston (Cambridge), and John Coleman (Oxford).

Dr. Guillaume Dehaene

Title: A Bayesian model of binaural localization in the owl

Abstract

In order to act efficiently, animals must fit and continually update a model of their environment, i.e: they must perform some form of statistics. In particular, Bayesian statistics have been a popular model for a number of sensory tasks (see Knill and Richards, 2008, for an extensive review).

In this talk, I will present a Bayesian model of how owls are able to locate the position of a sound source using the slight delay between the sound arriving at the left ear and sound arriving at the right ear. With such cues, owls are able to locate and catch their prey. With co-authors R. Coen-Cagli and A. Pouget, we derived a principled model of how a Bayesian observer would process the sound reaching the ears of the animal. With no tuning, this model accounts for the existing behavioral and neuronal data and makes falsifiable prediction that differentiate it from existing phenomenological models.

Mr. Brendan Patch

Title: Detecting Markov Chain Instability: A Monte Carlo Approach

Abstract

We devise a Monte Carlo based method for detecting whether a non-negative Markov chain is stable for a given set of potential parameterizations. More precisely, for a given set in parameter space, we develop an algorithm that is capable of deciding whether the set has a subset of positive Lebesgue measure for which the Markov chain is unstable. The approach is based on a variant of simulated annealing, and consequently only mild assumptions are needed to obtain performance guarantees. I will illustrate the usage of our algorithm on models of communication networks.