Incorporating prior knowledge induced from stochastic differential equations in the classification of stochastic observations

Amin Zollanvari, Edward R. Dougherty

Research output: Contribution to journalArticle

Abstract

In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posterior
distribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, prior
construction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In this
paper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.
Original languageEnglish
Number of pages14
JournalEurasip Journal on Bioinformatics and Systems Biology
Volume2016:2
DOIs
Publication statusPublished - 2016

Fingerprint

Prior Knowledge
Uncertainty
Stochastic Equations
Labels
Bayesian Classifier
Differential equations
Differential equation
Prior distribution
Classifiers
Misclassification Error
Integral form
Posterior distribution
History
Minimise
Experiment
Observation
Experiments
Class
Model

ASJC Scopus subject areas

  • Signal Processing
  • Applied Mathematics

Cite this

@article{cfd61b91bfe64339bf8ff19e5a850569,
title = "Incorporating prior knowledge induced from stochastic differential equations in the classification of stochastic observations",
abstract = "In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posteriordistribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, priorconstruction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In thispaper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.",
author = "Amin Zollanvari and Dougherty, {Edward R.}",
year = "2016",
doi = "10.1186/s13637-016-0036-y",
language = "English",
volume = "2016:2",
journal = "Eurasip Journal on Bioinformatics and Systems Biology",
issn = "1687-4145",
publisher = "Springer Publishing Company",

}

TY - JOUR

T1 - Incorporating prior knowledge induced from stochastic differential equations in the classification of stochastic observations

AU - Zollanvari, Amin

AU - Dougherty, Edward R.

PY - 2016

Y1 - 2016

N2 - In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posteriordistribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, priorconstruction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In thispaper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.

AB - In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posteriordistribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, priorconstruction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In thispaper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.

U2 - 10.1186/s13637-016-0036-y

DO - 10.1186/s13637-016-0036-y

M3 - Article

VL - 2016:2

JO - Eurasip Journal on Bioinformatics and Systems Biology

JF - Eurasip Journal on Bioinformatics and Systems Biology

SN - 1687-4145

ER -