Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series.     

基于权值编码的组合拍卖竞胜标确定启发式算法研究

针对较大规模组合拍卖竞胜标确定问题(WDP),提出了基于权值编码的竞胜标确定启发式算法.改进了算法编码机制并嵌入基于WDP本质特点的启发式搜索规则,极大地提高了算法进化能力和求解效率.模拟实验结果表明该算法能够在较短时间内求出WDP最优解或满意近似解,为较大规模网上组合拍卖竞胜标确定问题提供了切实可行的求解算法.     

Condorcet Winners for Public Goods

In this work, we consider a public facility allocation problem decided through a voting process under the majority rule. A location of the public facility is a majority rule winner if there is no other location in the network where more than half of the voters would have been closer to than the majority rule winner. We develop fast algorithms for interesting cases with nice combinatorial structures. We show that the computing problem and the decision problem in the general case, where the number of public facilities is more than one and is considered part of the input size, are all NP-hard. Finally, we discuss majority rule decision making for related models.     

基于前景理论的混合不确定情景下在线多属性反向拍卖的赢者确定方法

在线反向拍卖在当今的经济社会发展中扮演越来越重要的角色,其主要应用于采购招标领域。而在实际的采购拍卖中有关商品属性和供应商信息等方面常会存在一定程度的不确定性,且这些不确定性的刻画又存在着多种模糊表述形式,这些都将增加采购方的风险预期和竞标供应商赢者确定的难度。为此,本文基于前景理论及模糊集理论,研究了同时存在精确数、区间数、三角模糊数、梯形模糊数和语义模糊术语五种属性描述方式的在线多属性反向拍卖的赢者确定问题,提出了一种更具一般性的混合不确定情景下的在线多属性反向拍卖赢者(中标者)确定方法。最后,通过数值算例和比较分析验证了本文所提方法的合理性与有效性,并通过稳健性分析进一步说明方法的稳定性和适用性。     

基于多项式混沌的全局敏感度分析

回顾基于多项式混沌和方差分解的全局敏感度分析方法,针对高维数随机空间和高阶多项式混沌展开面临的“维数灾难”问题,采用回归法、稀疏网格积分及基于l₁优化的稀疏重构技术（即压缩感知技术）来减少非嵌入式多项式混沌方法所需的样本配置点数目.针对几个典型响应面模型（包括Ishigami函数、Sobol函数、Corner peak函数和Morris函数）进行Sobol全局敏感度指标计算,展示多项式混沌方法在基于方差分解的全局敏感度分析中的有效性.     

高维空间中数据的相似性度量

高维空间中数据之间的相似性度量是目前数据挖掘、信息处理与检索等领域所面临的一个重要问题.文章在总结分析了高维数据的特点以及现有的一些度量方法的基础上,提出了一种新的度量方式,该方法在对高维数据进行相似性度量之前,首先对原始数据空间进行网格划分.文章的最后对其有效性作了定量分析,实验证明,该方式是行之有效的.     

美式看涨篮子期权解析近似定价模型

本文研究规范美式篮子看涨期权的定价问题.通常用来为美式看涨期权定价的格点法与蒙特卡罗模拟法,用于美式篮子看涨期权定价时,会产生"维数灾难".本文首先利用Vorst~([2])、Gentle~([3])以及Merton~([4,5])模型的结果,完成标的资产组合从算术平均向几何平均的转化;其次在Barone～Adesi和Whaley提出的单变量美式期权解析近似定价模型(以下简称BW模型)的基础上~([4]),提出了美式分红篮子看涨期权定价的一种解析近似方法.最后,进行了数值试验,取得了较好的结果.     

基于网上拍卖的共同价值托投标分析

基于信息不对称条件下的共同价值模型,刻画了网上拍卖过程中可能存在的托投标行为,并运用博弈理论结合竞价关系求解了竞标者的赢标概率和最优竞价策略．研究发现,在共同价值模型下,参与竞标的人数与嬴者诅咒的发生存在联系;在最高出价者赢标的概率模型基础上,分别建立了是否存在托投标行为时的竞标者收益模型,并求解了竞标者的均衡竞价策略．     

On Heuristics for Solving Winner Determination Problem in Combinatorial Auctions

The winner determination problem (WDP) in combinatorial auctions is the problem of, given a finite set of combinatorial bids B, finding a feasible subset B of B with a maximum revenue. WDP is known to be equivalent to the maximum weight set packing problem, and hard to approximate by polynomial time algorithms. This paper proposes three heuristic bid ordering schemes for solving WDP; the first two schemes take into account the number of goods shared by conflicting bids, and the third one is based on a recursive application of such local heuristic functions. We conducted several experiments to evaluate the goodness of the proposed schemes. The result of experiments implies that the first two schemes are particularly effective to improve the performance of the resulting heuristic search procedures. More concretely, they are scalable compared with the conventional linear programming (LP) relaxation based schemes, and could quickly provide an optimum solution under optimization schemes such as the branch-and-bound method. In addition, they exhibit a good anytime performance competitive to the LP-based schemes, although it is sensitive to configurable parameters controlling the strength of contributions of bid conflicts to the resultant bid ordering schemes.