An Accelerated Stochastic ADMM for Nonconvex and Nonsmooth Finite-Sum Optimization

The nonconvex and nonsmooth finite-sum optimization problem with linear constraint has attracted much attention in the fields of artificial intelligence, computer, and mathematics, due to its wide applications in machine learning and the lack of efficient algorithms with convincing convergence theories. A popular approach to solve it is the stochastic Alternating Direction Method of Multipliers (ADMM), but most stochastic ADMM-type methods focus on convex models. In addition, the variance reduction (VR) and acceleration techniques are useful tools in the development of stochastic methods due to their simplicity and practicability in providing acceleration characteristics of various machine learning models. However, it remains unclear whether accelerated SVRG-ADMM algorithm (ASVRG-ADMM), which extends SVRG-ADMM by incorporating momentum techniques, exhibits a comparable acceleration characteristic or convergence rate in the nonconvex setting. To fill this gap, we consider a general nonconvex nonsmooth optimization problem and study the convergence of ASVRG-ADMM. By utilizing a well-defined potential energy function, we establish its sublinear convergence rate $O(1/T)$, where $T$ denotes the iteration number. Furthermore, under the additional Kurdyka-Lojasiewicz (KL) property which is less stringent than the frequently used conditions for showcasing linear convergence rates, such as strong convexity, we show that the ASVRG-ADMM sequence has a finite length and converges to a stationary solution with a linear convergence rate. Several experiments on solving the graph-guided fused lasso problem and regularized logistic regression problem validate that the proposed ASVRG-ADMM performs better than the state-of-the-art methods.Comment: 40 Pages, 8 figure

Sampling the spatial patterns of cancer: Optimized biopsy procedures for estimating prostate cancer volume and Gleason Score

Prostate biopsy is the current gold-standard procedure for prostate cancer diagnosis. Existing prostate biopsy procedures have been mostly focusing on detecting cancer presence. However, they often ignore the potential use of biopsy to estimate cancer volume (CV) and Gleason Score (GS, a cancer grade descriptor), the two surrogate markers for cancer aggressiveness and the two crucial factors for treatment planning. To fill up this vacancy, this paper assumes and demonstrates that, by optimally sampling the spatial patterns of cancer, biopsy procedures can be specifically designed for estimating CV and GS. Our approach combines image analysis and machine learning tools in an atlas-based population study that consists of three steps. First, the spatial distributions of cancer in a patient population are learned, by constructing statistical atlases from histological images of prostate specimens with known cancer ground truths. Then, the optimal biopsy locations are determined in a feature selection formulation, so that biopsy outcomes (either cancer presence or absence) at those locations could be used to differentiate, at the best rate, between the existing specimens having different (high vs. low) CV/GS values. Finally, the optimized biopsy locations are utilized to estimate whether a new-coming prostate cancer patient has high or low CV/GS values, based on a binary classification formulation. The estimation accuracy and the generalization ability are evaluated by the classification rates and the associated receiver-operating-characteristic (ROC) curves in cross validations. The optimized biopsy procedures are also designed to be robust to the almost inevitable needle displacement errors in clinical practice, and are found to be robust to variations in the optimization parameters as well as the training populations

Optimal Maintenance Modeling for Systems with Multiple Non-Identical Units Using Extended DSSP Method

Abstract In the optimal maintenance modeling, all possible maintenance activities and their corresponding probabilities play a key role in modeling. For a system with multiple non-identical units, its maintenance requirements are very complicated, and it is time-consuming, even omission may occur when enumerating them with various combinations of units and even with different maintenance actions for them. Deterioration state space partition (DSSP) method is an efficient approach to analyze all possible maintenance requirements at each maintenance decision point and deduce their corresponding probabilities for maintenance modeling of multi-unit systems. In this paper, an extended DSSP method is developed for systems with multiple non-identical units considering opportunistic, preventive and corrective maintenance activities for each unit. In this method, different maintenance types are distinguished in each maintenance requirement. A new representation of the possible maintenance requirements and their corresponding probabilities is derived according to the partition results based on the joint probability density function of the maintained system deterioration state. Furthermore, focusing on a two-unit system with a non-periodical inspected condition-based opportunistic preventive-maintenance strategy; a long-term average cost model is established using the proposed method to determine its optimal maintenance parameters jointly, in which "hard failure" and non-negligible maintenance time are considered. Numerical experiments indicate that the extended DSSP method is valid for opportunistic maintenance modeling of multi-unit systems

Pull-In Analysis of the Flat Circular CMUT Cell Featuring Sealed Cavity

Capacitive micromachined ultrasonic transducers (CMUTs) are one of the appealing MEMS devices. Most studies treat CMUTs as rigid plates vibrating in open air, ignoring the mechanical boundary conditions for simplification and resulting in cumulative errors in coupled fields. This paper presents a new analytical model for the pull-in characteristics of the flat circular CMUT cell featuring sealed cavity. Utilizing the plate theory coupled with Boyle’s law, the paper establishes a strong relation between the pressures inside the sealed cavity and the pull-in characteristics for the first time. Not only did we point out that the existence of the pressure inside the sealed cavity cannot be omitted, but we also quantified the direct effect of the pressure ratios on the pull-in phenomenon. The pull-in voltages increase while the pull-in ratios decrease with the pressure ratios of the pressure inside the sealed cavity to the ambient pressure. The proposed calculation process delivers a good approximation of the pull-in voltages and displacements, which are consistent with COMSOL simulation results. Particularly, the percentage error of our calculation process is 6.986% for the worst case. Therefore, our proposed analytical model accurately and efficiently predicts the pull-in characteristics and this paper offers new perspectives and reference value in designing and modeling the CMUTs

Targeted prostate biopsy using statistical image analysis

Abstract-In this paper, a method for maximizing the probability of prostate cancer detection via biopsy is presented, by combining image analysis and optimization techniques. This method consists of three major steps. First, a statistical atlas of the spatial distribution of prostate cancer is constructed from histological images obtained from radical prostatectomy specimen. Second, a probabilistic optimization framework is employed to optimize the biopsy strategy, so that the probability of cancer detection is maximized under needle placement uncertainties. Finally, the optimized biopsy strategy generated in the atlas space is mapped to a specific patient space using an automated segmentation and elastic registration method. Cross-validation experiments showed that the predictive power of the optimized biopsy strategy for cancer detection reached the 94%-96% levels for 6-7 biopsy cores, which is significantly better than standard random-systematic biopsy protocols, thereby encouraging further investigation of optimized biopsy strategies in prospective clinical studies. Index Terms-Biopsy optimization, prostate cancer, spatial normalization, statistical image analysis