High-dimensional Multi-class Classification with Presence-only Data

Classification with positive and unlabeled (PU) data frequently arises in bioinformatics, clinical data, and ecological studies, where collecting negative samples can be prohibitively expensive. While prior works on PU data focus on binary classification, in this paper we consider multiple positive labels, a practically important and common setting. We introduce a multinomial-PU model and an ordinal-PU model, suited to unordered and ordered labels respectively. We propose proximal gradient descent-based algorithms to minimize the l_{1,2}-penalized log-likelihood losses, with convergence guarantees to stationary points of the non-convex objective. Despite the challenging non-convexity induced by the presence-only data and multi-class labels, we prove statistical error bounds for the stationary points within a neighborhood around the true parameters under the high-dimensional regime. This is made possible through a careful characterization of the landscape of the log-likelihood loss in the neighborhood. In addition, simulations and two real data experiments demonstrate the empirical benefits of our algorithms compared to the baseline methods

On Control System Design for the Conventional Mode of Operation of Vibrational Gyroscopes

This paper presents a novel control circuitry design for both vibrating axes (drive and sense) of vibrational gyroscopes, and a new sensing method for time-varying rotation rates. The control design is motivated to address the challenges posed by manufacturing imperfection and environment vibrations that are particularly pronounced in microelectromechanical systems (MEMS) gyroscopes. The method of choice is active disturbance rejection control that, unlike most existing control design methods, does not depend on an accurate model of the plant. The task of control design is simplified when the internal dynamics, such as mechanical cross coupling between the drive and sense axes, and external vibrating forces are estimated and cancelled in real time. In both simulation and hardware tests on a vibrational piezoelectric beam gyroscope, the proposed controller proves to be robust against structural uncertainties; it also facilitates accurate sensing of time-varying rotation rates. The results demonstrate a simple, economic, control solution for compensating the manufacturing imperfections and improving sensing performance of the MEMS gyroscopes

A Simulation-free Group Sequential Design with Max-combo Tests in the Presence of Non-proportional Hazards

Non-proportional hazards (NPH) have been observed recently in many immuno-oncology clinical trials. Weighted log-rank tests (WLRT) with suitably chosen weights can be used to improve the power of detecting the difference of the two survival curves in the presence of NPH. However, it is not easy to choose a proper WLRT in practice when both robustness and efficiency are considered. A versatile maxcombo test was proposed to achieve the balance of robustness and efficiency and has received increasing attentions in both methodology development and application. However, survival trials often warrant interim analyses due to its high cost and long duration. The integration and application of maxcombo tests in interim analyses often require extensive simulation studies. In this paper, we propose a simulation-free approach for group sequential design with maxcombo test in survival trials. The simulation results support that the proposed approaches successfully control both the type I error rate and offer great accuracy and flexibility in estimating sample sizes, at the expense of light computation burden. Notably, our methods display a strong robustness towards various model misspecifications, and have been implemented in an R package for free access online

On Control System Design for the Conventional Mode of Operation of Vibrational Gyroscopes

This paper presents a novel control circuitry design for both vibrating axes (drive and sense) of vibrational gyroscopes, and a new sensing method for time-varying rotation rates. The control design is motivated to address the challenges posed by manufacturing imperfection and environment vibrations that are particularly pronounced in microelectromechanical systems (MEMS) gyroscopes. The method of choice is active disturbance rejection control that, unlike most existing control design methods, does not depend on an accurate model of the plant. The task of control design is simplified when the internal dynamics, such as mechanical cross coupling between the drive and sense axes, and external vibrating forces are estimated and cancelled in real time. In both simulation and hardware tests on a vibrational piezoelectric beam gyroscope, the proposed controller proves to be robust against structural uncertainties; it also facilitates accurate sensing of time-varying rotation rates. The results demonstrate a simple, economic, control solution for compensating the manufacturing imperfections and improving sensing performance of the MEMS gyroscopes

Low-Rank Covariance Completion for Graph Quilting with Applications to Functional Connectivity

As a tool for estimating networks in high dimensions, graphical models are commonly applied to calcium imaging data to estimate functional neuronal connectivity, i.e. relationships between the activities of neurons. However, in many calcium imaging data sets, the full population of neurons is not recorded simultaneously, but instead in partially overlapping blocks. This leads to the Graph Quilting problem, as first introduced by (Vinci et.al. 2019), in which the goal is to infer the structure of the full graph when only subsets of features are jointly observed. In this paper, we study a novel two-step approach to Graph Quilting, which first imputes the complete covariance matrix using low-rank covariance completion techniques before estimating the graph structure. We introduce three approaches to solve this problem: block singular value decomposition, nuclear norm penalization, and non-convex low-rank factorization. While prior works have studied low-rank matrix completion, we address the challenges brought by the block-wise missingness and are the first to investigate the problem in the context of graph learning. We discuss theoretical properties of the two-step procedure, showing graph selection consistency of one proposed approach by proving novel L infinity-norm error bounds for matrix completion with block-missingness. We then investigate the empirical performance of the proposed methods on simulations and on real-world data examples, through which we show the efficacy of these methods for estimating functional connectivity from calcium imaging data

Analytic initial relative orbit solution for angles-only space rendezvous using hybrid dynamics method

A closed-form solution to the angles-only initial relative orbit determination (IROD) problem for space rendezvous with non-cooperated target is developed, where a method of hybrid dynamics with the concept of virtual formation is introduced to analytically solve the problem. Emphasis is placed on developing the solution based on hybrid dynamics (i.e., Clohessy-Wiltshire equations and two-body dynamics), obtaining formation geometries that produce relative orbit state observability, and deriving the approximate analytic error covariance for the IROD solution. A standard Monte Carlo simulation system based on two-body dynamics is used to verify the feasibility and evaluate the performance proposed algorithms. The sensitivity of the solution accuracy to the formation geometry, observation numbers is presented and discussed