vbmp: Variational Bayesian Multinomial Probit Regression with...
In vbmp: Variational Bayesian Multinomial Probit Regression

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

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

`X`	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

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.

vbmp returns an object of class "VBMP.obj". An object of class "VBMP.obj" is a list containing at least the following components:

`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

N Lama nicola.lama@unina2.it, MA Girolami girolami@dcs.gla.ac.uk

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

See Also as predictCPP, covParams, lowerBound, predError, predLik, predClass

## -----------------------------------------------------------------------------
## 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)