Faster ARMA maximum likelihood estimation

A new likelihood based AR approximation is given for ARMA models. The usual algorithms for the computation of the likelihood of an ARMA model require O(n) flops per function evaluation. Using our new approximation, an algorithm is developed which requires only O(1) flops in repeated likelihood evaluations. In most cases, the new algorithm gives results identical to or very close to the exact maximum likelihood estimate (MLE). This algorithm is easily implemented in high level quantitative programming environments (QPEs) such as Mathematica, MatLab and R. In order to obtain reasonable speed, previous ARMA maximum likelihood algorithms are usually implemented in C or some other machine efficient language. With our algorithm it is easy to do maximum likelihood estimation for long time series directly in the QPE of your choice. The new algorithm is extended to obtain the MLE for the mean parameter. Simulation experiments which illustrate the effectiveness of the new algorithm are discussed. Mathematica and R packages which implement the algorithm discussed in this paper are available [McLeod, A.I., Zhang, Y., 2007. Online supplements to “Faster ARMA Maximum Likelihood Estimation”, 〈http://www.stats.uwo.ca/faculty/aim/2007/faster/〉]. Based on these package implementations, it is expected that the interested researcher would be able to implement this algorithm in other QPEs.     

A minimum Hellinger distance estimator for stochastic differential equations: An application to statistical inference for continuous time interest rate models

A minimum disparity estimator minimizes a φ-divergence between the marginal density of a parametric model and its non-parametric estimate. This principle is applied to the estimation of stochastic differential equation models, choosing the Hellinger distance as particular φ-divergence. Under an hypothesis of stationarity, the parametric marginal density is provided by solving the Kolmogorov forward equation. A particular emphasis is put on the non-parametric estimation of the sample marginal density which has to take into account sample dependence and kurtosis. A new window size determination is provided. The classical estimator is presented alternatively as a distance minimizer and as a pseudo-likelihood maximizer. The latter presentation opens the way to Bayesian inference. The method is applied to continuous time models of the interest rate. In particular, various models are tested using alternatively tests and their results are discussed.     

Optimal Time-Critical Scheduling via Resource Augmentation

Abstract. We consider two fundamental problems in dynamic scheduling: scheduling to meet deadlines in a preemptive multiprocessor setting, and scheduling to provide good response time in a number of scheduling environments. When viewed from the perspective of traditional worst-case analysis, no good on-line algorithms exist for these problems, and for some variants no good off-line algorithms exist unless P = NP . We study these problems using a relaxed notion of competitive analysis, introduced by Kalyanasundaram and Pruhs, in which the on-line algorithm is allowed more resources than the optimal off-line algorithm to which it is compared. Using this approach, we establish that several well-known on-line algorithms, that have poor performance from an absolute worst-case perspective, are optimal for the problems in question when allowed moderately more resources. For optimization of average flow time, these are the first results of any sort, for any NP -hard version of the problem, that indicate that it might be possible to design good approximation algorithms.     

Adaptive learning of dynamic Bayesian networks with changing structures by detecting geometric structures of time series

A dynamic Bayesian network (DBN) is one of popular approaches for relational knowledge discovery such as modeling relations or dependencies, which change over time, between variables of a dynamic system. In this paper, we propose an adaptive learning method (autoDBN) to learn DBNs with changing structures from multivariate time series. In autoDBN, segmentation of time series is achieved first through detecting geometric structures transformed from time series, and then model regions are found from the segmentation by designed finding strategies; in each found model region, a DBN model is established by existing structure learning methods; finally, model revisiting is developed to refine model regions and improve DBN models. These techniques provide a special mechanism to find accurate model regions and discover a sequence of DBNs with changing structures, which are adaptive to changing relations between multivariate time series. Experimental results on simulated and real time series show that autoDBN is very effective in finding accurate/reasonable model regions and gives lower error rates, outperforming the switching linear dynamic system method and moving window method.

一种检测TAL-freeness的代数方法

时间动作锁(Ti me-Action-Lock,TAL)指的是实时系统处于一种时间无法继续同时又没有任何动作能够发生的状态.Behzad和Kozo在时间自动机的几何学基础上提出了一种针对TAL-freeness的检测方法.但该方法要求必须将需要检测的模型转化为一种逻辑语言Rational Presburger Sentences后才能进行检测,因此使得验证过程比较繁琐.文中提出了一种检测TAL-freeness的代数方法,能够直接对系统模型进行直接验证,并且能够定位死锁原因.针对该方法,文中还给出了相应算法并提供了正确性证明与性能分析.     

Expected runtimes of evolutionary algorithms for the Eulerian cycle problem

Evolutionary algorithms are randomized search heuristics, which are applied to problems whose structure is not well understood, as well as to problems in combinatorial optimization. They have successfully been applied to different kinds of arc routing problems. To start the analysis of evolutionary algorithms with respect to the expected optimization time on these problems, we consider the Eulerian cycle problem. We show that a variant of the well-known (1+1)$(1+1)$ EA working on the important encoding of permutations is able to find an Eulerian tour of an Eulerian graph in expected polynomial time. Altering the operator used for mutation in the considered algorithm, the expected optimization time changes from polynomial to exponential.     

Single-machine scheduling with deteriorating jobs under a series–parallel graph constraint

This paper considers single-machine scheduling problems with deteriorating jobs, i.e., jobs whose processing times are an increasing function of their starting times. In addition, the jobs are related by a series–parallel graph. It is shown that for the general linear problem to minimize the makespan, polynomial algorithms exist. It is also shown that for the proportional linear problem of minimization of the total weighted completion time, polynomial algorithms exist, too.     

Improved Image Based Visual Servoing with Parallel Robot

The position regulation problem of an eye-in-hand type of parallel robot based pointing systems (PRBPS) is considered in this paper. A fuzzy logic system is first designed to compensate for the uncertainties of the parallel robot and the uncertainty of the image Jacobian, then a hybrid controller (HC) including the image-based nonlinear controller and the adaptive supervisory fuzzy logic controller (ASFLC) is derived by using the Lyapunov direct method to realize the position regulation (PR). The stability of the closed-loop system in the Lyapunov sense is proven theoretically. The fuzzy scaling matrix is combined with the HC to improve the performance of the control system. The simulation results demonstrate that the PRBPS realizes PR with very good robustness to the parameter uncertainties, and the control input torques and settling time are reduce greatly in the case of large initial feature errors.     

A neural networks learning algorithm for minor component analysis and its convergence analysis

The eigenvector associated with the smallest eigenvalue of the autocorrelation matrix of input signals is called minor component. Minor component analysis (MCA) is a statistical approach for extracting minor component from input signals and has been applied in many fields of signal processing and data analysis. In this letter, we propose a neural networks learning algorithm for estimating adaptively minor component from input signals. Dynamics of the proposed algorithm are analyzed via a deterministic discrete time (DDT) method. Some sufficient conditions are obtained to guarantee convergence of the proposed algorithm.     

Application of artificial neural network for determination of standard time in machining

The purpose of this article is to present the application of neural network for time per unit determination in small lot production in machining. A set of features considered as input vector and time consumption in manufacturing process was presented and treated as output of the neural net. A neural network was used as a machining model. Sensitivity analysis was made and proper topology of neural network was determined.