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Nihat Ay

  1. Robustness and Conditional Independence Ideals.

    Fri, 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.

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

    Mon, 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.

  3. Refinements of Universal Approximation Results for Deep Belief Networks and Restricted Boltzmann Machines.

    Tue, 05/11/2010 - 15:01 — SomNambul
    Authors: Nihat Ay, Guido Montufar
    Subjects: Machine Learning
    Abstract

    We improve recently published results about resources of Restricted Boltzmann
    Machines (RBM) and Deep Belief Networks (DBN) required to make them Universal
    Approximators. We show that any distribution p on the set of binary vectors of
    length n can be arbitrarily well approximated by an RBM with k-1 hidden units,
    where k is the minimal number of pairs of binary vectors differing in only one
    entry such that their union contains the support set of p. In important cases
    this number is half of the cardinality of the support set of p.

  4. Effective complexity of stationary process realizations.

    Mon, 01/18/2010 - 16:01 — SomNambul
    Authors: Nihat Ay, Markus Mueller, Arleta Szkola
    Subjects: Information Theory
    Abstract

    The concept of effective complexity of an object as the minimal description
    length of its regularities has been initiated by Gell-Mann and Lloyd. Based on
    their work we gave a precise definition of effective complexity of finite
    binary strings in terms of algorithmic information theory in our previous
    paper. Here we study the effective complexity of strings generated by
    stationary processes. Sufficiently long typical process realizations turn out
    to be effectively simple under any linear scaling with the string's length of
    the parameter $\Delta$ which determines the minimization domain.

  5. Higher coordination with less control - A result of information maximisation in the sensori-motor loop.

    Tue, 10/13/2009 - 18:46 — SomNambul
    Authors: Keyan Zahedi, Nihat Ay, Ralf Der
    Subjects: Artificial Intelligence
    Abstract

    This work presents a novel learning method in the context of embodied
    artificial intelligence and guided self-organisation, which is free of
    assumptions about the world and restrictions on the underlying model. The
    learning rule is derived from the principle of maximising the predictive
    information in the sensori-motor loop. It is evaluated in six experiments in
    which individually controlled robots with different control paradigms are
    physically connected to chains of varying length. The robots have no form of
    direct communication.

  6. Higher coordination with less control - A result of information maximisation in the sensori-motor loop.

    Tue, 10/13/2009 - 18:46 — SomNambul
    Authors: Keyan Zahedi, Nihat Ay, Ralf Der
    Subjects: Artificial Intelligence
    Abstract

    This work presents a novel learning method in the context of embodied
    artificial intelligence and guided self-organisation, which is free of
    assumptions about the world and restrictions on the underlying model. The
    learning rule is derived from the principle of maximising the predictive
    information in the sensori-motor loop. It is evaluated in six experiments in
    which individually controlled robots with different control paradigms are
    physically connected to chains of varying length. The robots have no form of
    direct communication.

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