Learning Markov Models Via Low-Rank Optimization

Taming high-dimensional Markov models In “Learning Markov models via low-rank optimization”, Z. Zhu, X. Li, M. Wang, and A. Zhang focus on learning a high-dimensional Markov model with low-dimensional latent structure from a single trajectory of states. To overcome the curse of high dimensions, the authors propose to equip the standard MLE (maximum-likelihood estimation) with either nuclear norm regularization or rank constraint. They show that both approaches can estimate the full transition matrix accurately using a trajectory of length that is merely proportional to the number of states. To solve the rank-constrained MLE, which is a nonconvex problem, the authors develop a new DC (difference) programming algorithm. Finally, they apply the proposed methods to analyze taxi trips on the Manhattan island and partition the island based on the destination preference of customers; this partition can help balance supply and demand of taxi service and optimize the allocation of traffic resources.

Screening Potential Drugs for COVID-19 Based on Bound Nuclear Norm Regularization

The novel coronavirus pneumonia COVID-19 infected by SARS-CoV-2 has attracted worldwide attention. It is urgent to find effective therapeutic strategies for stopping COVID-19. In this study, a Bounded Nuclear Norm Regularization (BNNR) method is developed to predict anti-SARS-CoV-2 drug candidates. First, three virus-drug association datasets are compiled. Second, a heterogeneous virus-drug network is constructed. Third, complete genomic sequences and Gaussian association profiles are integrated to compute virus similarities; chemical structures and Gaussian association profiles are integrated to calculate drug similarities. Fourth, a BNNR model based on kernel similarity (VDA-GBNNR) is proposed to predict possible anti-SARS-CoV-2 drugs. VDA-GBNNR is compared with four existing advanced methods under fivefold cross-validation. The results show that VDA-GBNNR computes better AUCs of 0.8965, 0.8562, and 0.8803 on the three datasets, respectively. There are 6 anti-SARS-CoV-2 drugs overlapping in any two datasets, that is, remdesivir, favipiravir, ribavirin, mycophenolic acid, niclosamide, and mizoribine. Molecular dockings are conducted for the 6 small molecules and the junction of SARS-CoV-2 spike protein and human angiotensin-converting enzyme 2. In particular, niclosamide and mizoribine show higher binding energy of −8.06 and −7.06 kcal/mol with the junction, respectively. G496 and K353 may be potential key residues between anti-SARS-CoV-2 drugs and the interface junction. We hope that the predicted results can contribute to the treatment of COVID-19.

The Proximal Bootstrap for Finite-Dimensional Regularized Estimators

We propose a proximal bootstrap that can consistently estimate the limiting distribution of sqrt(n)-consistent estimators with nonstandardasymptotic distributions in a computationally efficient manner by formulating the proximal bootstrap estimator as the solution to aconvex optimization problem, which can have a closed-form solution for certain designs. This paper considers the application to finite-dimensionalregularized estimators, such as the lasso, l1-norm regularized quantile regression, l1-norm support vector regression, and trace regression via nuclear norm regularization.

Background modeling from video sequences via online motion-aware RPCA

Background modeling of video frame sequences is a prerequisite for computer vision applications. Robust principal component analysis(RPCA), which aims to recover low rank matrix in applications of data mining and machine learning, has shown improved background modeling performance. Unfortunately, The traditional RPCA method considers the batch recovery of low rank matrix of all samples, which leads to higher storage cost. This paper proposes a novel online motion-aware RPCA algorithm, named OM-RPCAT, which adopt truncated nuclear norm regularization as an approximation method for of low rank constraint. And then, Two methods are employed to obtain the motion estimation matrix, the optical flow and the frame selection, which are merged into the data items to separate the foreground and background. Finally, an efficient alternating optimization algorithm is designed in an online manner. Experimental evaluations of challenging sequences demonstrate promising results over state-of-the-art methods in online application.