Ying Cui

Le Peng, Yash Travadi, Chuan He et al.

For classification with imbalanced class frequencies, i.e., imbalanced classification (IC), standard accuracy is known to be misleading as a performance measure. While most existing methods for IC resort to optimizing balanced accuracy (i.e., the average of class-wise recalls), they fall short in scenarios where the significance of classes varies or certain metrics should reach prescribed levels. In this paper, we study two key classification metrics, precision and recall, under three practical binary IC settings: fix precision optimize recall (FPOR), fix recall optimize precision (FROP), and optimize $F_β$-score (OFBS). Unlike existing methods that rely on smooth approximations to deal with the indicator function involved, \textit{we introduce, for the first time, exact constrained reformulations for these direct metric optimization (DMO) problems}, which can be effectively solved by exact penalty methods. Experiment results on multiple benchmark datasets demonstrate the practical superiority of our approach over the state-of-the-art methods for the three DMO problems. We also expect our exact reformulation and optimization (ERO) framework to be applicable to a wide range of DMO problems for binary IC and beyond. Our code is available at https://github.com/sun-umn/DMO.

Zhengling Qi, Ying Cui, Yufeng Liu et al.

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.

Zhengling Qi, Ying Cui, Yufeng Liu et al.

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.

Shuai Wang, Tsung-Hui Chang, Ying Cui et al.

The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called the orthogonal NMF (ONMF), has been found a promising clustering model and can outperform the classical K-means. However, solving the ONMF model is a challenging optimization problem because the coupling of the orthogonality and non-negativity constraints introduces a mixed combinatorial aspect into the problem due to the determination of the correct status of the variables (positive or zero). Most of the existing methods directly deal with the orthogonality constraint in its original form via various optimization techniques, but are not scalable for large-scale problems. In this paper, we propose a new ONMF based clustering formulation that equivalently transforms the orthogonality constraint into a set of norm-based non-convex equality constraints. We then apply a non-convex penalty (NCP) approach to add them to the objective as penalty terms, leading to a problem that is efficiently solvable. One smooth penalty formulation and one non-smooth penalty formulation are respectively studied. We build theoretical conditions for the penalized problems to provide feasible stationary solutions to the ONMF based clustering problem, as well as proposing efficient algorithms for solving the penalized problems of the two NCP methods. Experimental results based on both synthetic and real datasets are presented to show that the proposed NCP methods are computationally time efficient, and either match or outperform the existing K-means and ONMF based methods in terms of the clustering performance.