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A0628
Title: Error analysis of OWL algorithms with varying Gaussians and convex loss Authors:  Daohong Xiang - Zhejiang Normal University (China) [presenting]
Abstract: The goal of precision medicine is to determine the optimal individualized treatment rules by considering the heterogeneity of patients, so as to maximize the expected clinical outcome. Outcome weighted learning (OWL) is one of the algorithms to estimate the optimal individualized treatment rules. We mainly study the convergence theory of OWL associated with varying Gaussians and general convex loss. Fisher's consistency of OWL with convex loss is proved by making full use of the convexity of the loss function. Under some noise conditions on distributions, a quantitative relationship between weighted misclassification error and weighted generalization error is proved. The sample error is estimated by using a projection operator and a tight bound for the covering numbers of reproducing kernel Hilbert spaces generated by Gaussian kernels. Fast learning rates of OWL associated with least square loss, exponential-hinge loss and r-norm SVM loss are derived explicitly.