Главная

Johannes Rauh

  1. Optimally approximating exponential families.

    Чт, 11/03/2011 - 15:01 — SomNambul
    Authors: Johannes Rauh
    Subjects: Statistics
    Abstract

    This article studies exponential families $\mathcal{E}$ on finite sets such
    that the information divergence $D(P\|\mathcal{E})$ of an arbitrary probability
    distribution from $\mathcal{E}$ is bounded by some constant $D>0$. A particular
    class of low-dimensional exponential families that have low values of $D$ can
    be obtained from partitions of the state space. The main results concern
    optimality properties of these partition exponential families. Exponential
    families where $D=\log(2)$ are studied in detail.

  2. Robustness and Conditional Independence Ideals.

    Пт, 10/07/2011 - 15:01 — SomNambul
    Authors: Nihat Ay, Johannes Rauh
    Subjects: Commutative Algebra
    Abstract

    We study notions of robustness of Markov kernels and probability distribution
    of a system that is described by $n$ input random variables and one output
    random variable. Markov kernels can be expanded in a series of potentials that
    allow to describe the system's behaviour after knockouts. Robustness imposes
    structural constraints on these potentials. Robustness of probability
    distributions is defined via conditional independence statements. These
    statements can be studied algebraically. The corresponding conditional
    independence ideals are related to binary edge ideals.

  3. Support Sets in Exponential Families and Oriented Matroid Theory.

    Пнд, 09/19/2011 - 15:01 — SomNambul
    Authors: Nihat Ay, Johannes Rauh, Thomas Kahle
    Subjects: Statistics
    Abstract

    The closure of a discrete exponential family is described by a finite set of
    equations corresponding to the circuits of an underlying oriented matroid.
    These equations are similar to the equations used in algebraic statistics,
    although they need not be polynomial in the general case. This description
    allows for a combinatorial study of the possible support sets in the closure of
    an exponential family. If two exponential families induce the same oriented
    matroid, then their closures have the same support sets.

  4. Finding the Maximizers of the Information Divergence from an Exponential Family.

    Чт, 12/24/2009 - 16:01 — SomNambul
    Authors: Johannes Rauh
    Subjects: Information Theory
    Abstract

    This paper investigates maximizers of the information divergence from an
    exponential family $E$. It is shown that the $rI$-projection of a maximizer $P$
    to $E$ is a convex combination of $P$ and a probability measure $P_-$ with
    disjoint support and the same value of the sufficient statistics $A$. This
    observation can be used to transform the original problem of maximizing
    $D(\cdot||E)$ over the set of all probability measures into the maximization of
    a function $\Dbar$ over a convex subset of $\ker A$. The global maximizers of
    both problems correspond to each other.

Math-arch

RSS-материал