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).
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)a n by p matrix, n is the sample size, p is the number of feature variables.
a vector of n entries coded 1 and -1 for the treatment assignments
a vector of outcome variable, larger is more desirable.
a vector of randomization probability \(P(A|X)\), or the estimated observed probability.
the type of regression used to take residual, 'lasso' is the default (lasso regression); 'LSE' is the ordinary least square regression.
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.
a grid of tuning parameter sigma for 'rbf' kernel for cross validation, when kernel='rbf', the default is \(c(0.03, 0.05, 0.07)\)
a grid of tuning parameter C for cross validation,the default is \(2^(-2:2)\). C is tuning parameter as defined in wsvm
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.
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:
the scaled solution for the dual problem: \(alpha1_i=\alpha_i A_i wR_i\)
the intercept \(\beta_0\) in \(f(X)=\beta_0+X\beta\).
a vector of estimated values for \(\hat{f(x)}\) in training data, \(fit=bias+X\beta=bias+X*X'*alpha1\).
The coefficients \(\beta\) for linear SVM, \(f(X)=bias+X\beta\).
If kernel 'rbf' is specified, it returns an object of class 'rbfcl', and it is a list include the following elements:
the scaled solution for the dual problem: \(alpha1_i=\alpha_i A_i wR_i\) and \(X\beta= K(X,X)*alpha1\)
the intercept \(\beta_0\) in \(f(X)=\beta_0+h(X)\beta\).
a vector of estimated values for \(\hat{f(x)}\) in training data, \(fit=\beta_0+h(X)\beta=bias+K(X,X)*alpha1\).
the bandwidth parameter for the rbf kernel
the matrix of training feature variable
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.
# NOT RUN {
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)
# }
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