HasGP.Classification.EP.ClassificationEP

ClassificationEP is a module in the HasGP Gaussian Process library. It implements basic Gaussian Process Classification for two classes using the EP approximation. Targets should be +1/-1.

Copyright (C) 2011 Sean Holden. [e-mail].

Documentation

data EPValue

A convergence test for EP usually depends on the evidence and the number of iterations so far. This allows us to specify completely arbitrary convergence tests.

type EPConvergenceTest = EPValue -> EPValue -> Bool

By passing a function with this type we can specify arbitrary convergence tests.

data EPSiteState

When updating a single site at a time you keep track of var, tauTilde, mu, nuTilde, TauMinus, and MuMinus.

type EPState = (EPSiteState, StdGen, Int)

We hide the state used in performing EP using the state monad. We need to include a random number generator and the number of iterations.

type SiteOrder = State EPState [Int]

If we're updating sites in a random order then we need access to the random number generator.

generateRandomSiteOrder :: SiteOrder

We're often going to want to update sites in a random order. So we need a state transformer that takes the current state (which includes a random number generator) and produces a random permutation.

generateFixedSiteOrder :: SiteOrder

For completeness: just in case you want to update sites in a non-random manner, this state transformer does exactly that.

gpClassifierEPEvidence

Arguments

:: CovarianceMatrix

-> Targets

-> DMatrix

L matrix

-> EPSiteState

-> Double

log marginal likelihood.

Compute the approximation to the log marginal likelihood.

gpClassifierEPLearn :: CovarianceMatrix -> Targets -> SiteOrder -> EPConvergenceTest -> (EPValue, EPState)

The learning algorithm. Takes an arbitrary function for convergence testing.

gpClassifierEPPredict

Arguments

:: CovarianceFunction c

=> EPSiteState

-> Inputs

-> Targets

Inputs in training set

-> CovarianceMatrix

-> c

Covariance Function

-> Inputs

New inputs

-> DVector

Prediction with GP classifiers based on EP learning. Takes a matrix in which each row is an example to be classified.

gpClassifierEPLogEvidence

Arguments

:: CovarianceFunction c

=> c

Covariance

-> Inputs

-> Targets

-> SiteOrder

-> EPConvergenceTest

-> (Double, DVector)

Compute the log evidence and its first derivative for the EP approximation for GP classification. Targets should be +1/-1. Outputs the -log marginal likelihood and a vector of its derivatives.

gpClassifierEPLogEvidenceList

Arguments

:: CovarianceFunction c

=> Inputs

-> Targets

-> c

Covariance

-> SiteOrder

-> EPConvergenceTest

-> [Double]

-> (Double, DVector)

Essentially the same as gpClassifierEPLogEvidence, but makes a covariance function using the hyperparameters supplied in a list and passes it on.

gpClassifierEPLogEvidenceVec

Arguments

:: CovarianceFunction c

=> Inputs

-> Targets

-> c

Covariance

-> SiteOrder

-> EPConvergenceTest

-> DVector

-> (Double, DVector)

Essentially the same as gpClassifierEPLogEvidence, but makes a covariance function using the hyperparameters supplied in a vector and passes it on.