Learning theory of outcome weighted schemes and related topics

With the advent of data science, healthcare is booming and becoming one of the biggest and fastest-growing fields in recent years. Precision medicine aims to tailor healthcare or treatment to the individual characteristics of each patient, which has been attracting more and more attention along with the advance in diagnosis and treatment as well as the increasing adoption of electronic health records by hospitals. The data collected nowadays is usually massive, complex and high dimensional, but also contains interesting and vital information. There is a pressing need to respond to these challenges and opportunities. The goal of this project is to investigate theoretical properties and application perspectives of outcome weighted schemes for some problems that arise in precision medicine from the perspective of learning theory. We shall first consider a general framework for learning an optimal individualized treatment rule that maximizes the expected clinical outcomes from randomized trial data within the framework of reproducing kernel Hilbert spaces, where the error analysis will be conducted and fast learning rates will be derived under general convex loss functions. Outcome weighted classification algorithms with nonconvex loss or differential privacy will also be studied. We shall then propose a unified learning framework involving two types of kernels to study the generalization abilities of outcome weighted learning schemes for personalized dose finding, where the minimax optimal learning rate will be derived and gradient descent with early stopping will be employed to solve the corresponding optimization problem. The idea of online learning in reproducing kernel Hilbert spaces will be introduced to outcome weighted schemes to tackle data that arrives sequentially in a streaming way, where error analysis will be conducted and high-probability convergence rates will be derived. Finally, we will study some other topics in deep learning related to this project, such as deep neural networks for outcome weighted schemes.