Accelerated Stochastic Peaceman–Rachford Method for Empirical Risk Minimization

This work is devoted to studying an accelerated stochastic Peaceman–Rachford splitting method(AS-PRSM)for solving a family of structural empirical risk minimization problems.The objective function to be optimized is the sum of a possibly nonsmooth convex function and a finite sum of smooth convex component functions.The smooth subproblem in AS-PRSM is solved by a stochastic gradient method using variance reduction technique and accelerated techniques,while the possibly nonsmooth subproblem is solved by introducing an indefinite proximal term to transform its solution into a proximity operator.By a proper choice for the involved parameters,we show that AS-PRSM converges in a sublinear convergence rate measured by the function value residual and constraint violation in the sense of expectation and ergodic.Preliminary experiments on testing the popular graph-guided fused lasso problem in machine learning and the 3D CT reconstruction problem in medical image processing show that the proposed AS-PRSM is very efficient.

The Empirical Tests on Risk in Chinese Futures Market

The Research on Market Risks has been developed abroad in all sorts of markets since 1960＇s. It＇s necessary to comprehend and consider opportunity and challenge in Chinese futures market from the viewpoint of risk management. With different ARCH models, we find heteroscedasticity does exist in Chinese market, so we adopt the Variance Ratio. We test empirically the prices of Chinese futures market from 1993 to 2002. The results show that only futures price of copper meets the random walk, thereby confirming the weak form market efficiency. It also means that the function of price discovery is weak and the risk of futures market is poor. Finally, we give much constructive policy advice.

An Empirical Study of Downstream Analysis Effects of Model Pre-Processing Choices

This study uses an empirical analysis to quantify the downstream analysis effects of data pre-processing choices. Bootstrap data simulation is used to measure the bias-variance decomposition of an empirical risk function, mean square error (MSE). Results of the risk function decomposition are used to measure the effects of model development choices on model bias, variance, and irreducible error. Measurements of bias and variance are then applied as diagnostic procedures for model pre-processing and development. Best performing model-normalization-data structure combinations were found to illustrate the downstream analysis effects of these model development choices. In additions, results found from simulations were verified and expanded to include additional data characteristics (imbalanced, sparse) by testing on benchmark datasets available from the UCI Machine Learning Library. Normalization results on benchmark data were consistent with those found using simulations, while also illustrating that more complex and/or non-linear models provide better performance on datasets with additional complexities. Finally, applying the findings from simulation experiments to previously tested applications led to equivalent or improved results with less model development overhead and processing time.

Application and Exploration of Overall Risk Management in Construction Enterprises

This paper mainly starts from the perspectives of management and economics,combined with the characteristics of the construction industry,conducts qualitative and quantitative analysis of the risks involved,studies various factors that cause construction enterprise risks from multiple angles,and uses scientific and effective methods to identify and evaluate risks,as well as determine the risk level.Through the overall risk management response strategies and empirical research of construction enterprises,this paper analyzes the general theory and main avoidance strategies of risk response of construction enterprises,and lays the foundation for follow-up risk management response in the form of cases through the implementation of technical route and innovation points.

The key theorem and the bounds on the rate of uniform convergence of learning theory on Sugeno measure space

Some properties of Sugeno measure are further discussed, which is a kind of typical nonadditive measure. The definitions and properties of gλ random variable and its distribution function, expected value, and variance are then presented. Markov inequality, Chebyshev＇s inequality and the Khinchine＇s Law of Large Numbers on Sugeno measure space are also proven. Furthermore, the concepts of empirical risk functional, expected risk functional and the strict consistency of ERM principle on Sugeno measure space are proposed. According to these properties and concepts, the key theorem of learning theory, the bounds on the rate of convergence of learning process and the relations between these bounds and capacity of the set of functions on Sugeno measure space are given.