5,302 research outputs found
Estimating Mixture Entropy with Pairwise Distances
Mixture distributions arise in many parametric and non-parametric settings --
for example, in Gaussian mixture models and in non-parametric estimation. It is
often necessary to compute the entropy of a mixture, but, in most cases, this
quantity has no closed-form expression, making some form of approximation
necessary. We propose a family of estimators based on a pairwise distance
function between mixture components, and show that this estimator class has
many attractive properties. For many distributions of interest, the proposed
estimators are efficient to compute, differentiable in the mixture parameters,
and become exact when the mixture components are clustered. We prove this
family includes lower and upper bounds on the mixture entropy. The Chernoff
-divergence gives a lower bound when chosen as the distance function,
with the Bhattacharyya distance providing the tightest lower bound for
components that are symmetric and members of a location family. The
Kullback-Leibler divergence gives an upper bound when used as the distance
function. We provide closed-form expressions of these bounds for mixtures of
Gaussians, and discuss their applications to the estimation of mutual
information. We then demonstrate that our bounds are significantly tighter than
well-known existing bounds using numeric simulations. This estimator class is
very useful in optimization problems involving maximization/minimization of
entropy and mutual information, such as MaxEnt and rate distortion problems.Comment: Corrects several errata in published version, in particular in
Section V (bounds on mutual information
Nonlinear Information Bottleneck
Information bottleneck (IB) is a technique for extracting information in one
random variable that is relevant for predicting another random variable
. IB works by encoding in a compressed "bottleneck" random variable
from which can be accurately decoded. However, finding the optimal
bottleneck variable involves a difficult optimization problem, which until
recently has been considered for only two limited cases: discrete and
with small state spaces, and continuous and with a Gaussian joint
distribution (in which case optimal encoding and decoding maps are linear). We
propose a method for performing IB on arbitrarily-distributed discrete and/or
continuous and , while allowing for nonlinear encoding and decoding
maps. Our approach relies on a novel non-parametric upper bound for mutual
information. We describe how to implement our method using neural networks. We
then show that it achieves better performance than the recently-proposed
"variational IB" method on several real-world datasets
Adverse events following influenza immunization reported by healthcare personnel using active surveillance based on text messages
Studies have demonstrated that healthcare personnel (HCP) have concerns about the potential side effects of trivalent inactivate influenza vaccine (IIV3).1-3 A recent metaanalysis of reasons HCP refuse IIV3 indicates the strongest predictors of vaccine acceptance are belief that the vaccine is safe and belief the vaccine does not cause the disease it is meant to prevent.
(p -Cymene)thioglycollatoruthenium(II) dimer; a complex with an ambi-basic S,O-donor ligand
The title compound was prepared from the (p-cymene)ruthenium chloride dimer and thioglycollic acid. The structure is a centrosymmetric dimer bridged by the soft-base S atoms, with the hard-base O atoms of the carboxylate group chelating to form a five-membered twisted-ring. The coordination of the ruthenium atoms is completed by a η6-p-cymene ligand, giving an 18-electron count. The Ru–S bonds are essentially equal at 2.396(1) Å
Caveats for information bottleneck in deterministic scenarios
Information bottleneck (IB) is a method for extracting information from one
random variable that is relevant for predicting another random variable
. To do so, IB identifies an intermediate "bottleneck" variable that has
low mutual information and high mutual information . The "IB
curve" characterizes the set of bottleneck variables that achieve maximal
for a given , and is typically explored by maximizing the "IB
Lagrangian", . In some cases, is a deterministic
function of , including many classification problems in supervised learning
where the output class is a deterministic function of the input . We
demonstrate three caveats when using IB in any situation where is a
deterministic function of : (1) the IB curve cannot be recovered by
maximizing the IB Lagrangian for different values of ; (2) there are
"uninteresting" trivial solutions at all points of the IB curve; and (3) for
multi-layer classifiers that achieve low prediction error, different layers
cannot exhibit a strict trade-off between compression and prediction, contrary
to a recent proposal. We also show that when is a small perturbation away
from being a deterministic function of , these three caveats arise in an
approximate way. To address problem (1), we propose a functional that, unlike
the IB Lagrangian, can recover the IB curve in all cases. We demonstrate the
three caveats on the MNIST dataset
Pigment analysis by Raman microscopy and portable X-ray fluorescence (pXRF) of thirteenth to fourteenth century illuminations and cuttings from Bologna
Non-destructive pigment analysis by Raman microscopy (RM) and portable X-ray fluorescence (pXRF) has been carried out on some Bolognese illuminations and cuttings chosen to represent the beginnings, evolution and height of Bolognese illuminated manuscript production. Dating to the thirteenth and fourteenth centuries and held in a private collection, the study provides evidence for the pigments generally used in this period. The results, which are compared with those obtained for other north Italian artwork, show the developments in usage of artistic materials and technique. Also addressed in this study is an examination of the respective roles of RM and pXRF analysis in this area of technical art history
Recognition of asset impairment: A Comparison of Recognition Criteria
This report examines the accounting for the impairment of long-lived assets and identifiable intangibles as discussed in the Financial Accounting Standards Board Discussion Memorandum No. 098-B. This report specifically analyzes the recognition criteria to be used in determining when an impairment exists. The economic, permanence, and probability criterion are compared and contrasted to ascertain which method is the most feasible. The relevant information for this study ~came from the discussion memorandum, Big Six accounting firms, published literature, and a national student seminar on the topic. The study revealed a great deal of ambiguity in accounting for assets whose value has diminished due to corporate restructuring. This uncertainty has lead to confusion and mistrust among financial statement users. There is, however, a solution to this problem. The use of the probability criterion in recognizing and recording impairments provides adequate disclosures and timely information.B.A. (Bachelor of Arts
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