pacbpred

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Description

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.

Usage

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

Arguments

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.

Details

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.

Value

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.

Note

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

Author(s)

Benjamin Guedj

References

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.

See Also

pacbpred-package

Examples

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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))

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