Models, code, and papers for "Zhengling Qi":

Statistical Analysis of Stationary Solutions of Coupled Nonconvex Nonsmooth Empirical Risk Minimization

Oct 06, 2019
Zhengling Qi, Ying Cui, Yufeng Liu, Jong-Shi Pang

This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk minimization problems, and (b) validate these properties by a noisy amplitude-based phase retrieval problem, the latter being of much topical interest.Derived from available data via sampling, these empirical risk minimization problems are the computational workhorse of a population risk model which involves the minimization of an expected value of a random functional. When these minimization problems are nonconvex, the computation of their globally optimal solutions is elusive. Together with the fact that the expectation operator cannot be evaluated for general probability distributions, it becomes necessary to justify whether the stationary solutions of the empirical problems are practical approximations of the stationary solution of the population problem. When these two features, general distribution and nonconvexity, are coupled with nondifferentiability that often renders the problems "non-Clarke regular", the task of the justification becomes challenging. Our work aims to address such a challenge within an algorithm-free setting. The resulting analysis is therefore different from the much of the analysis in the recent literature that is based on local search algorithms. Furthermore, supplementing the classical minimizer-centric analysis, our results offer a first step to close the gap between computational optimization and asymptotic analysis of coupled nonconvex nonsmooth statistical estimation problems, expanding the former with statistical properties of the practically obtained solution and providing the latter with a more practical focus pertaining to computational tractability.


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Estimation of Individualized Decision Rules Based on an Optimized Covariate-Dependent Equivalent of Random Outcomes

Aug 27, 2019
Zhengling Qi, Ying Cui, Yufeng Liu, Jong-Shi Pang

Recent exploration of optimal individualized decision rules (IDRs) for patients in precision medicine has attracted a lot of attention due to the heterogeneous responses of patients to different treatments. In the existing literature of precision medicine, an optimal IDR is defined as a decision function mapping from the patients' covariate space into the treatment space that maximizes the expected outcome of each individual. Motivated by the concept of Optimized Certainty Equivalent (OCE) introduced originally in \cite{ben1986expected} that includes the popular conditional-value-of risk (CVaR) \cite{rockafellar2000optimization}, we propose a decision-rule based optimized covariates dependent equivalent (CDE) for individualized decision making problems. Our proposed IDR-CDE broadens the existing expected-mean outcome framework in precision medicine and enriches the previous concept of the OCE. Numerical experiments demonstrate that our overall approach outperforms existing methods in estimating optimal IDRs under heavy-tail distributions of the data.


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