pacbpred: pacbpred
In pacbpred: PAC-Bayesian Estimation and Prediction in Sparse Additive Models.

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

This package is intended to perform estimation and prediction in high-dimensional additive models, using a PAC-Bayesian point of view and a MCMC algorithm. The method is fully described in Guedj and Alquier (2013), 'PAC-Bayesian Estimation and Prediction in Sparse Additive Models', see http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ejs/1359041592.

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pacbpred(niter, burnin = floor(niter * 2/3), Xtrain, Xtest, Y, K = 8,
cst,
sigma2, alpha = 0.1, delta)

`niter`	Mandatory. The number of MCMC iterations.
`burnin`	Optional. How many iterations should be discarded in the beginning of the chain?
`Xtrain`	Mandatory. The design matrix of the training sample.
`Xtest`	Optional. The design matrix of the test sample.
`Y`	Mandatory. The vector of responses corresponding to `Xtrain`. `Y` is assumed to have the same number of rows as `Xtrain`.
`K`	Optional. The maximal order of the development on the trigonometric basis.
`cst`	Optional. A numerical constant bounding from above the sup norm of true regression function.
`sigma2`	Optional. The variance of the proposal density along the algorithm.
`alpha`	Optional. The penalization term over the complexity of a model.
`delta`	Optional. The inverse temperature parameter.

See Guedj and Alquier (2013), 'PAC-Bayesian Estimation and Prediction in Sparse Additive Models' on http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ejs/1359041592.

A list composed of the following items.

`predict`	If `Xtest` is provided, the predicted values of the corresponding responses.
`estimates`	The vector of estimates over the trigonometric basis.
`ratio.mcmc`	A vector of the MCMC ratio for each iteration.
`accept`	A logical vector whose length is the number of iterations. For each iteration, has the proposed move been accepted ?
`models.mcmc`	The current models all along the MCMC chain.

This is still an early stage development. Use at your own risk !

Benjamin Guedj

http://www.lsta.upmc.fr/doct/guedj/index.html

Guedj and Alquier (2013), 'PAC-Bayesian Estimation and Prediction in Sparse Additive Models'. Electronic Journal of Statistics, 7, 264–291. DOI:10.1214/13-EJS771. Available on http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ejs/1359041592.

pacbpred-package

ndata <- 100
ntrain <- 80
ntest <- ndata - ntrain
p <- 10
Y <- numeric(ndata)
X <- matrix(nr = ndata, nc = p, data = 2*runif(n = ndata*p) - 1)
for(i in 1:ndata)
  {
    Y[i] <- X[i,1]^3+sin(pi*X[i,2])
  }

Xtrain <- X[1:ntrain,]
Xtest <- X[(ntrain+1):ndata,]
Ytrain <- Y[1:ntrain]
Ytest <- Y[(ntrain+1):ndata]

niter <- 100
cst <- Inf
alpha <- .1
sigma2 <- .1
delta <- ntrain/2

res <- pacbpred(niter = niter, Xtrain = Xtrain, Xtest = Xtest, Y =
Ytrain, cst = cst,
sigma2 = sigma2, delta = delta, alpha = alpha)

print(cbind(res$predict,Ytest))