EPFL Statistics Seminar

  • Prof. Po-Ling Loh

    University of Wisconsin
    Friday, February 24, 2017
    Time 15:15 - Room MA10

    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

    University of Copenhagen
    Friday, March 31, 2017
    Time 15:15 - Room MA10

    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

    EPFL ENAC
    Thursday, April 6, 2017
    Time 16:15 - Room GC A1 416 ---- please note the unusual day, time and room! ---

    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

    EPFL
    Friday, April 28, 2017
    Time 15:15 - Room MA10

    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. Guillaume Dehaene

    EPFL
    Friday, June 2, 2017
    Time 15:15 - Room MA10

    Title: TBA

    Abstract

    TBA

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