vbmp: Variational Bayesian Multinomial Probit Regression with Gaussian Process Priors.

Description

Used to fit a Multinomial Probit Regression model, specified by giving the matrix design X, the associated response variables t.class, kernel type and covariate scaling parameters. Covariance paramters can be inferred from the data.

Usage

vbmp(X, t.class, X.TEST, t.class.TEST, theta, control = list())

Arguments

Feature matrix for parameter 'estimation'

t.class

Target values, integer number used for class labels.

X.TEST

Feature matrix to compute out-of-sample (test) prediction errors and likelihoods

t.class.TEST

Target values for test data

theta

The covariance function parameters (e.g. scaling coefficients for each dimension)

control

A list of control parameters. See Details

Value

Kc: Number of classes
Ptest: Matrix of multinomial class predictive posterior probabilities for the test data
X: Feature matrix
invPHI: Inverse of the Kernel matrix
Y: Matrix of auxiliary variables
M: Matrix of GP random variables
theta: covariance kernel hyperparameters (estimates computed during model fitting, if inferred
sKernelType: Kernel function used in training and predicting
Test.Err: Out-of-Sample Percent Prediction error estimates computed during model fitting (0-1 error loss).
PL: Predictive Likelihood estimates computed during model fitting
LOWER.BOUND: Lower bound estimates computed during model fitting

Details

In this implementation a single covariance function is shared across all classes. Compute the predictive posteriors on the test set and the associated likelihood and test errors at each iteration.

The control argument is a list that can supply any of the following components:

InfoLevel: 0 to suppress tracing ( > 0 to print different levels of monitoring information)

sFILE.TRACE

File name where to redirect output (default NULL)

bThetaEstimate

if covariance parameter estimation switched on. Defaults to FALSE (switched off)

sKernelType

Kernel function used in training and predicting. Currently implemented kernels are Gaussian ("gauss"), Cauchy ("cauchy"), Laplace ("laplace"), Polynomial ("poly"), Homogeneous polynomial ("hpoly"), 'Thin-plate' spline ("tps"), 'linear' spline ("lsp") and Inner product("iprod"). Defaults to "gauss".

maxIts

Maximum number of variational EM steps to take. Defaults to 50.

Thresh

Convergence threshold on marginal likelihood lowerbound. Defaults to 1e-4.

method

Integral computation method: "quadrature" (Gaussian quadrature) or "classic"(simple sampler). Defaults to "quadrature".

nNodesQuad

Number of nodes used for quadrature. Defaults to 49.

nSampsTG

Number of samples used in obtaining mean of truncated Gaussian. Defaults to 1000.

nSampsIS

Number of samples used in the importance sampler. Defaults to 1000.

nSmallNo

Small number used to prevent numerical problems (ill-conditioned covariance matrix). Defaults to 1e-10.

parGammaTau,parGammaSigma

The location and scale parameters of the Gamma prior over covaraince params. Default to 1e-6.

bMonitor

TRUE to collect monitor convergence diagnostics at each iteration. Defaults to FALSE.

bPlotFitting

TRUE to plot test performance results at each iteration during model estimation (if TRUE it forces bMonitor to TRUE). Defaults to FALSE.

References

Girolami M, Rogers S, Variational Bayesian Multinomial Probit Regression with Gaussian Process Priors, Neural Computation 18, 1790-1817 (2006). Lama N, Girolami M vbmp: Variational Bayesian Multinomial Probit Regression for multi-class classification in R, Bioinformatics 24(1):135-136 (2008). http://bioinformatics.oxfordjournals.org/cgi/content/short/btm535v1

Examples

Run this code


## -----------------------------------------------------------------------------
## EXAMPLE 1 - Theta estimate with synthetic data
## -----------------------------------------------------------------------------
## Samples of 2-D data points drawn from three nonlinearly separable
## classes which take the form of two annular rings and one zero-centered
## Gaussian are used in this little illustrative example. 
genSample <- function(n, noiseVar=0) {
    ## class 1 and 2 (x ~ U(0,1))
    u <- 4. * matrix(runif(2*n), nrow=n, ncol=2) - 2.;
    i <- which(((u[, 1]^2 + u[, 2]^2) > .1) & ((u[, 1]^2 + u[, 2]^2) < .5) );
    j <- which(((u[, 1]^2 + u[, 2]^2) > .6) & ((u[, 1]^2 + u[, 2]^2) < 1) );
    X <- u[c(i, j),];
    t.class <- c(rep(1, length(i)),rep(2, length(j)));
    ## class 3 (x ~ N(0,1))
    x <- 0.1 * matrix(rnorm(2*length(i)), ncol=2, nrow=length(i) );
    k <- which((x[, 1]^2 + x[, 2]^2) < 0.1);
    X <- rbind(X, x[k, ]);
    t.class <- c(t.class, rep(3, length(k)));
    ## add random coloumns
    if (noiseVar>0) X <- cbind(X, matrix(rnorm(noiseVar*nrow(X)), ncol=noiseVar, nrow=nrow(X)));
    structure( list( t.class=t.class, X=X), class="MultiNoisyData");
}

set.seed(123); ## Init random number generator

## Generate training and test samples as an independent 
## test set to assess out-of-sample prediction error 
## and predictive likelihoods.
nNoisyInputs <- 0;       ## number of additional noisy input parameters
Ntest <- Ntrain <- 500;  ## sample sizes
dataXt.train <- genSample(Ntrain, nNoisyInputs);
dataXt.test  <- genSample(Ntest,  nNoisyInputs);

## Not run:  
#  theta <- runif(ncol(dataXt.train$X));
#  res <- vbmp( dataXt.train$X, dataXt.train$t.class,
#         dataXt.test$X, dataXt.test$t.class, theta, 
#          control=list(bThetaEstimate = T, 
#          bPlotFitting=T, maxIts=50));
# ## End(Not run)

## set theta params (previously estimated) 
theta <- c(0.09488309, 0.16141604);   
## Fit the vbmp
res <- vbmp( dataXt.train$X, dataXt.train$t.class,
        dataXt.test$X, dataXt.test$t.class, theta, 
        control=list(maxIts=5));
## print out-of-sample error estimate
predError(res);

## Not run: 
# ## ----------------------------------------------------------
# ## EXAMPLE 2 - BRCA12 genomic data
# ## ----------------------------------------------------------
# ## Leave-one-out (LOO) cross-validation prediction error of the probabilistic 
# ## Gaussian process classifier used in Zsofia Kote-Jarai et al. 
# ## Clin Cancer Res 2006;12(13);3896-3901
# 
#   if(any(installed.packages()[,1]=="Biobase")) {
#     library("Biobase");
#     data("BRCA12");
#     brca.y <- BRCA12$Target.class;
#     brca.x <- t(exprs(BRCA12));
#   } else {
#     print("Deprecated.....");
#     load(url("http://www.dcs.gla.ac.uk/people/personal/girolami/pubs_2005/VBGP/BRCA12.RData"));
#     brca.y <- as.numeric(BRCA12$y);
#     brca.x <- as.matrix(BRCA12[,-1]);
#   }
#   
#   sKernelType <- "iprod";  ## Covariance function type
#   Thresh <- 1e-8;  ## Iteration threshold
#   InfoLevel <- 1;
#   theta <- rep(1.0, ncol(brca.x));
#   ITER.THETA <- 24;
#   n     <- nrow(brca.x) ;
#   Kfold <- n; # number of folds , if equal to n then LOO
#   samps <- sample(rep(1:Kfold, length=n), n, replace=FALSE); 
#   res   <- rep(NA, n);
#   print(paste("LOO crossvalidation started...... (",n,"steps)"));
#   for (x in 1:Kfold) {
#       cat(paste(x,", ",sep="")); flush.console();
#       resX <- vbmp( brca.x[samps!=x,], brca.y[samps!=x], 
#                     brca.x[samps==x,], brca.y[samps==x], 
#                     theta,  control=list(bThetaEstimate=F, 
#                     bPlotFitting=F, maxIts=ITER.THETA, 
#                     sKernelType=sKernelType, Thresh=Thresh));    
#       res[samps==x] <- predClass(resX); 
#   }
#   print("(end)");
#   print(paste("Crossvalidated error rate", round(sum(res!=brca.y)/n,2)));
# ## End(Not run)

Run the code above in your browser using DataCamp Workspace