6,377 research outputs found
Ensemble estimation of multivariate f-divergence
f-divergence estimation is an important problem in the fields of information
theory, machine learning, and statistics. While several divergence estimators
exist, relatively few of their convergence rates are known. We derive the MSE
convergence rate for a density plug-in estimator of f-divergence. Then by
applying the theory of optimally weighted ensemble estimation, we derive a
divergence estimator with a convergence rate of O(1/T) that is simple to
implement and performs well in high dimensions. We validate our theoretical
results with experiments.Comment: 14 pages, 6 figures, a condensed version of this paper was accepted
to ISIT 2014, Version 2: Moved the proofs of the theorems from the main body
to appendices at the en
Renormalization and quantum field theory
The aim of this paper is to describe how to use regularization and
renormalization to construct a perturbative quantum field theory from a
Lagrangian. We first define renormalizations and Feynman measures, and show
that although there need not exist a canonical Feynman measure, there is a
canonical orbit of Feynman measures under renormalization. We then construct a
perturbative quantum field theory from a Lagrangian and a Feynman measure, and
show that it satisfies perturbative analogues of the Wightman axioms, extended
to allow time-ordered composite operators over curved spacetimes.Comment: 30 pages Revised version fixes a gap in the definition of Feynman
measure, and has other minor change
Gaussian limits for generalized spacings
Nearest neighbor cells in , are used to define
coefficients of divergence (-divergences) between continuous multivariate
samples. For large sample sizes, such distances are shown to be asymptotically
normal with a variance depending on the underlying point density. In ,
this extends classical central limit theory for sum functions of spacings. The
general results yield central limit theorems for logarithmic -spacings,
information gain, log-likelihood ratios and the number of pairs of sample
points within a fixed distance of each other.Comment: Published in at http://dx.doi.org/10.1214/08-AAP537 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On the Minimization of Convex Functionals of Probability Distributions Under Band Constraints
The problem of minimizing convex functionals of probability distributions is
solved under the assumption that the density of every distribution is bounded
from above and below. A system of sufficient and necessary first-order
optimality conditions as well as a bound on the optimality gap of feasible
candidate solutions are derived. Based on these results, two numerical
algorithms are proposed that iteratively solve the system of optimality
conditions on a grid of discrete points. Both algorithms use a block coordinate
descent strategy and terminate once the optimality gap falls below the desired
tolerance. While the first algorithm is conceptually simpler and more
efficient, it is not guaranteed to converge for objective functions that are
not strictly convex. This shortcoming is overcome in the second algorithm,
which uses an additional outer proximal iteration, and, which is proven to
converge under mild assumptions. Two examples are given to demonstrate the
theoretical usefulness of the optimality conditions as well as the high
efficiency and accuracy of the proposed numerical algorithms.Comment: 13 pages, 5 figures, 2 tables, published in the IEEE Transactions on
Signal Processing. In previous versions, the example in Section VI.B
contained some mistakes and inaccuracies, which have been fixed in this
versio
Small oscillations of a chiral Gross-Neveu system
We study the small oscillations regime (RPA approximation) of the
time-dependent mean-field equations, obtained in a previous work, which
describe the time evolution of one-body dynamical variables of a uniform Chiral
Gross-Neveu system. In this approximation we obtain an analytical solution for
the time evolution of the one-body dynamical variables. The two-fermion physics
can be explored through this solution. The condition for the existence of bound
states is examined.Comment: 21pages, Latex, 1postscript figur
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