Matrix Completion via Max-Norm Constrained Optimization

Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a range of applications and the standard trace-norm relaxation can behave very poorly when the underlying sampling scheme is non-uniform. In this paper we propose and analyze a max-norm constrained empirical risk minimization method for noisy matrix completion under a general sampling model. The optimal rate of convergence is established under the Frobenius norm loss in the context of approximately low-rank matrix reconstruction. It is shown that the max-norm constrained method is minimax rate-optimal and yields a unified and robust approximate recovery guarantee, with respect to the sampling distributions. The computational effectiveness of this method is also discussed, based on first-order algorithms for solving convex optimizations involving max-norm regularization.Comment: 33 page

A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion

We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is introduced and studied. The rate of convergence for the estimate is obtained. Information-theoretical methods are used to establish a minimax lower bound under the general sampling model. The minimax upper and lower bounds together yield the optimal rate of convergence for the Frobenius norm loss. Computational algorithms and numerical performance are also discussed.Comment: 33 pages, 3 figure

A passivity based control methodology for flexible joint robots with application to a simplified shuttle RMS arm

The main goal is to develop a general theory for the control of flexible robots, including flexible joint robots, flexible link robots, rigid bodies with flexible appendages, etc. As part of the validation, the theory is applied to the control law development for a test example which consists of a three-link arm modeled after the shoulder yaw joint of the space shuttle remote manipulator system (RMS). The performance of the closed loop control system is then compared with the performance of the existing RMS controller to demonstrate the effectiveness of the proposed approach. The theoretical foundation of this new approach to the control of flexible robots is presented and its efficacy is demonstrated through simulation results on the three-link test arm

PRICE UNCERTAINTY AND AGRICULTURAL PRODUCTIVITY

This paper examines the effects of price uncertainty on agricultural productivity. Appelbaum(1991) provided an empirical framework to analyze the effects of uncertainty on firm behavior. We apply the model to the U.S. agricultural sector, using a parametric rather than a nonparametric approach to obtain the measurement of price uncertainty and risk. Keywords: risk, uncertainty, productivityrisk, uncertainty, productivity, Productivity Analysis,

Chaos-modified detrended moving average methodology for monitoring the depth of anaesthesia

This paper proposes a new method to monitor the depth of anaesthesia (DoA) based on the EEG signal. This approach firstly uses discrete wavelet transform (DWT) to to remove the spikes and the low frequency noise from raw EEG signals. After de-noising the EEG signals, the modified Hurst parameter is proposed with two new indices (CDoA and CsDoA), to estimate the anaesthesia states of the patients. To reduce the fluctuation of the new DoA index, a combination of Modified Chaos and Modifying Detrended Moving Average is used (MC-DMA). Analyses of variance (ANOVA) for C-MDMA and BIS distributions are presented The results indicate that the C-MDMA distributions at each anaesthesia state level are significantly different and the C-MDMA can distinguish five depths of anaesthesia. Compared with BIS trends, MC-DMA trend is close to BIS trend covering the whole scale from 100 to 0 with a full recording time