Olearning_Single: Improved single stage O-learning with cross validation
In DTRlearn: Learning Algorithms for Dynamic Treatment Regimes

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

Improved outcome weighted learning, first take residuals; and then use cross validation to choose best tuning parameter for wsvm. Return the O-learning models with best tuning parameters. Improving from Zhao 2012, the improved outcome weighted learning first take main effect out by regression; the weights are absolute value of the residual; more details can be found in Liu et al. (2015).

1 2	Olearning_Single(H,A,R2,pi=rep(1, n),pentype ="lasso",kernel="linear", sigma = c(0.03, 0.05, 0.07),clinear = 2^(-2:2), m = 4,e = 1e-05)

`H`	a n by p matrix, n is the sample size, p is the number of feature variables.
`A`	a vector of n entries coded 1 and -1 for the treatment assignments
`R2`	a vector of outcome variable, larger is more desirable.
`pi`	a vector of randomization probability P(A\|X), or the estimated observed probability.
`pentype`	the type of regression used to take residual, 'lasso' is the default (lasso regression); 'LSE' is the ordinary least square regression.
`kernel`	kernel function for weighted SVM, can be `'linear'` or `'rbf'` (radial basis kernel), default is `'linear'`. When `'rbf'` is specified, one can specify the `sigma` parameter for radial basis kernel.
`sigma`	a grid of tuning parameter sigma for 'rbf' kernel for cross validation, when kernel='rbf', the default is c(0.03, 0.05, 0.07)
`clinear`	a grid of tuning parameter C for cross validation,the default is 2^(-2:2). C is tuning parameter as defined in `wsvm`
`m`	folds of cross validation for choosing tuning parameters C and sigma. If `'lasso'` is specified for `'pentype'`, m is also the folds CV for `cv.glmnet` in the step of taking residual.
`e`	the rounding error when computing bias in `wsvm`

It returns model estimated from wsvm with the best tuning parameters picked by cross validation. If kernel 'linear' is specified, it returns an object of class 'linearcl', and it is a list include the following elements:

`alpha1`	the scaled solution for the dual problem: alpha1_i=α_i A_i wR_i
`bias`	the intercept β_0 in f(X)=β_0+Xβ.
`fit`	a vector of estimated values for \hat{f(x)} in training data, fit=bias+Xβ=bias+XX'alpha1.
`beta`	The coefficients β for linear SVM, f(X)=bias+Xβ.

If kernel 'rbf' is specified, it returns an object of class 'rbfcl', and it is a list include the following elements:

`alpha1`	the scaled solution for the dual problem: alpha1_i=α_i A_i wR_i and Xβ= K(X,X)alpha1*
`bias`	the intercept β_0 in f(X)=β_0+h(X)β.
`fit`	a vector of estimated values for \hat{f(x)} in training data, fit=β_0+h(X)β=bias+K(X,X)alpha1*.
`Sigma`	the bandwidth parameter for the rbf kernel
`X`	the matrix of training feature variable

Ying Liu

Liu et al. (2015). Under double-blinded review.

Zhao, Y., Zeng, D., Rush, A. J., & Kosorok, M. R. (2012). Estimating individualized treatment rules using outcome weighted learning. Journal of the American Statistical Association, 107(499), 1106-1118.

Olearning;wsvm

n_cluster=5
pinfo=10
pnoise=10
n_sample=50
set.seed(3)
example=make_classification(n_cluster,pinfo,pnoise,n_sample)
pi=list()
pi[[2]]=pi[[1]]=rep(1,n_sample)
modelrbf=Olearning_Single(example$X,example$A,example$R,kernel='rbf',m=3,sigma=0.05)
modellinear=Olearning_Single(example$X,example$A,example$R)