train_predict_mix
predicts the binary response based on
high dimemsional binary features modeled with Bayesian mixture
models. The model is trained with Gibbs sampling. A smaller number
of features can be selected based on the correlations with the
response. The bias due to the selection procedure can be corrected.
The software is written entirely with R language.
1 2 3 4 5 6 7 8  train_predict_mix(
test,train,k,
theta0=0,alpha.shape=0.5,alpha.rate=5,no.alpha=30,
common.alpha=FALSE,no.alpha0=100,
mc.iters=200,iters.labeltheta=10,
iters.theta=20,width.theta=0.1,
correction=TRUE,no.theta.adj=30,approxim=TRUE,
pred.start=100)

test 
a binary test data, a matrix, i.e. the data for which we want to predict the responses. The row stands for the cases. The first column is the binary response, which could be NA if they are missing. 
train 
a training data, of the same format as 
k 
the number of features retained 
theta0 
the prior of "theta" is uniform over ( 
alpha.shape 
the shape parameter of the Inverse Gamma, which is the prior distribution of "alpha" 
alpha.rate 
the rate parameter of the Inverse Gamma, as above 
no.alpha 
the number of "alpha"'s used in midpoint rule, which is used to approximate the integral with respect to "alpha". 
common.alpha 
Indicator whether the parameter "alpha" for the response
(i.e "alpha0" in the reference) and the parameter "alpha"
for the features are the same. By default they are two
independent paramters with the same prior distribution, i.e,

no.alpha0 
the number of "alpha0"'s used in midpoint rule, which is used to
approximate the integral with respect to "alpha0".. This parameter
takes effect only when 
mc.iters 
iterations of Gibbs sampling used to train the model. 
iters.labeltheta 
In each Gibbs iteration, the combination of updating the
“labels” once and updating the “theta” is repeated

iters.theta 
iterations of updating "theta" using MH method. 
width.theta 
the proposal distribution used to update "theta" with
MetropolisHastings method is uniform over the interval
(current "theta" + 
correction 
Indicator whether the correction method shall be applied 
no.theta.adj 
the parameter in Simpson's rule used to evaluate the integration
w.r.t. "theta", which is needed in calculating the adjustment
factor. The integrant is evaluated at 2*( 
approxim 
Indicator whether the adjustment factor is ignored in
updating the labels (laten values). In theory it should be
considered. However, it has little actual effect, but costs
much computation, since we need to recompute the adjustment
factor when updating the label of each case. By default,

pred.start 
The Markov chain iterations after 
prediction 
a matrix showing the detailed prediction result: the 1st column being the true responses, the 2nd being the predicted responses, the 3rd being the predictive probabilities of class 1 and the 4th being the indicator whether wrong prediction is made. 
aml 
the average minus log probabilities 
error.rate 
the ratio of wrong prediction 
mse 
the average square error of the predictive probabilities 
summary.pred 
tabular display of the predictive probabilities and the actual fraction of class 1. 
features.selected 
The features selected using correlation criterion 
label 
the Markov chain samples of latent values, with each column for an
iteration. The number of rows of 
I1 
the number of “1”s of features (columns) in those cases labeled by “1”, counted for each Markov chain iterations (row). 
I2 
Similar as 
N1 
a vector recording the number of cases labeled by “1” for each Markov chain iteration. 
N2 
a vector recording the number of cases labeled by “2” for each Markov chain iteration. 
theta 
Markov chain samples of “theta". Each row is an iteration. 
alpha 
a vector storing the Markov chain samples of “alpha”. 
alpha0 
a vector storing the Markov chain samples of “alpha0”. 
alpha_set 
all the possible values the “alpha” can take. The prior of “alpha” is approximated by the uniform over this set. 
alpha0_set 
all the possible values the “alpha0” can take. The prior of “alpha0” is approximated by the uniform over this set. 
http://math.usask.ca/~longhai/publication.html
gendata.mix
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  #simulating data set from a Bayesian mixture model
data < gendata.mix(20,20,50,50,101,10,c(0.9,0.1))
#training the model using Gibbs sampling, without correcting for the feature
#selection bias, then testing on predicting the responses of the test cases,
predict.uncor < train_predict_mix(
test=data$test,train=data$train,k=5,
theta0=0,alpha.shape=0.5,alpha.rate=5,no.alpha=5,
common.alpha=FALSE,no.alpha0=100,
mc.iters=30,iters.labeltheta=1,
iters.theta=10,width.theta=0.1,
correction=FALSE,no.theta.adj=5,approxim=TRUE,
pred.start=10)
#As above, but with the feature selection bias corrected
predict.cor < train_predict_mix(
test=data$test,train=data$train,k=5,
theta0=0,alpha.shape=0.5,alpha.rate=5,no.alpha=5,
common.alpha=FALSE,no.alpha0=100,
mc.iters=30,iters.labeltheta=1,
iters.theta=10,width.theta=0.1,
correction=TRUE,no.theta.adj=5,approxim=TRUE,
pred.start=10)

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