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.

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