Create an example data set with 4 groups, 400 train + 100 test samples and 800 features.
set.seed(123) data <- makeExampleData(n = 500, p=800, g=4, pis=c(0.05, 0.1, 0.05, 0.1), gammas=c(0.1, 0.1, 10, 10)) # training data set Xtrain <- data$X[1:400, ] ytrain <- data$y[1:400] # annotations of features to groups annot <- data$annot # test data set Xtest <- data$X[401:500, ] ytest <- data$y[401:500]
graper is the main function of this package,
which allows to fit the proposed Bayesian models with
different settings on the prior (by setting
spikeslab to FALSE or TRUE) and
the variational approximation (by setting
factoriseQ to FALSE or TRUE).
By default, the model is fit with a sparsity promoting spike-and-slab prior
and a fully-factorised mean-field assumption. The parameter
n_rep can be used
to train multiple models with different random initializations.
The best model is then chosen in terms of ELBO and returned by the function.
th defines the threshold on the ELBO for convergence
in the variational Bayes (VB) algorithm used for optimization.
fit <- graper(Xtrain, ytrain, annot, n_rep=3, verbose=FALSE, th=0.001) fit
The ELBO monitors the convergence during training.
The variational Bayes (VB) approach directly yields posterior distributions for each parameter. Note, however, that using VB these are often too concentrated and cannot be directly used for construction of confidence intervals etc. However, they can provide good point estimates.
plotPosterior(fit, "gamma", gamma0=data$gammas, range=c(0, 20)) plotPosterior(fit, "pi", pi0=data$pis)
The estimated coefficients and the intercept are contained in the result list.
# get coefficients (without the intercept) beta <- coef(fit, include_intercept=FALSE) # beta <- fit$EW_beta # plot estimated versus true beta qplot(beta, data$beta) + coord_fixed() + theme_bw()
# get intercept intercept <- fit$intercept
The estimated posterior inclusion probabilities per feature
are contained in the result list and can also be accessed
# get estimated posterior inclusion probabilities per feature pips <- getPIPs(fit) # plot pips for zero versus non-zero features df <- data.frame(pips = pips, nonzero = data$beta != 0) ggplot(df, aes(x=nonzero, y=pips, col=nonzero)) + geom_jitter(height=0, width=0.2) + theme_bw() + ylab("Posterior inclusion probability")
plotGroupPenalties can be used to plot the
penalty factors and sparsity levels inferred for each
predict can be used to make prediction on new data.
Here, we illustrate its use by predicting the response on
the test data defined above.
preds <- predict(fit, Xtest) qplot(preds, ytest) + coord_fixed() + theme_bw()
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