Mixture decompositions of exponential families using a decomposition of their sample spaces

Guido F. Montúfar

Displaying similar documents to “Mixture decompositions of exponential families using a decomposition of their sample spaces”

Equivalence of compositional expressions and independence relations in compositional models

Francesco M. Malvestuto (2014)

Kybernetika

Similarity:

We generalize Jiroušek’s (right) composition operator in such a way that it can be applied to distribution functions with values in a “semifield“, and introduce (parenthesized) compositional expressions, which in some sense generalize Jiroušek’s “generating sequences” of compositional models. We say that two compositional expressions are equivalent if their evaluations always produce the same results whenever they are defined. Our first result is that a set system $ℋ$ is star-like with...

Entropy and growth of expanding periodic orbits for one-dimensional maps

A. Katok, A. Mezhirov (1998)

Fundamenta Mathematicae

Similarity:

Let f be a continuous map of the circle $S^{1}$ or the interval I into itself, piecewise $C^{1}$ , piecewise monotone with finitely many intervals of monotonicity and having positive entropy h. For any ε > 0 we prove the existence of at least $e^{(h - ε) n_{k}}$ periodic points of period $n_{k}$ with large derivative along the period, $| {(f^{n_{k}})}^{'} | > e^{(h - ε) n_{k}}$ for some subsequence $n_{k}$ of natural numbers. For a strictly monotone map f without critical points we show the existence of at least $(1 - ε) e^{h n}$ such points.

The Dugundji extension property can fail in ωµ -metrizable spaces

Ian Stares, Jerry Vaughan (1996)

Fundamenta Mathematicae

Similarity:

We show that there exist $ω_{μ}$ -metrizable spaces which do not have the Dugundji extension property ( $2^{ω_{1}}$ with the countable box topology is such a space). This answers a question posed by the second author in 1972, and shows that certain results of van Douwen and Borges are false.

Large equilateral triangles inscribed in the unit disk of a Minkowski plane.

Fabińska, Ewa, Lassak, Marek (2004)

Beiträge zur Algebra und Geometrie

Similarity:

Optimally approximating exponential families

Johannes Rauh (2013)

Kybernetika

Similarity:

This article studies exponential families $ℰ$ on finite sets such that the information divergence $D (P ∥ ℰ)$ of an arbitrary probability distribution from $ℰ$ 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. The case where $D = log (2)$ is studied in detail. This case is special, because if $D < log (2)$ , then $ℰ$ contains...

On an algorithm for testing T4 solvability of max-plus interval systems

Helena Myšková (2012)

Kybernetika

Similarity:

In this paper, we shall deal with the solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by $\oplus$ and $\otimes$ , where $a \oplus b = max {a, b}$ , $a \otimes b = a + b$ . The notation $𝔸 \otimes x = 𝕓$ represents an interval system of linear equations, where $𝔸 = [\bar{b}, \bar{A}]$ and $𝕓 = [\underset{̲}{b}, \bar{b}]$ are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and...