Abstract:

For one-dimensional continuous time series, the stochastic volatility model and its inference methods have long been a subject of active research. Their extensions to multi-dimensional cases, however, have met a lot challenges ranging from modeling to computation. We here introduce a generalized mixture model and variational Bayes inference procedures for handling multidimensional volatility processes. The introduced model is then used as a latent structure for constructing heteroscedastic Gaussian processes, which is an attempt to address a key drawback of the standard Gaussian process that its structure is completely by one kernel function. We further demonstrate how to use variational approximations to carry out an explicit marginalization of the hidden functions, resulting in efficient parameter estimation and process forecasting. We demonstrate its advantages by both simulations and applications to real-data examples of regression, classification and state-space models.

Speaker:

刘军是哈佛大学统计系终身教授，曾任斯坦福大学统计系助理教授、副教授、终身教授，1985年本科毕业于北京大学数学系，1991年博士毕业于芝加哥大学。刘军教授于2002年获得北美五大统计协会联合颁发的COPSS Presidents' Award，是国际统计学界最具声望的荣誉。刘军教授还曾获得美国国家科学基金会的CAREER Award,国际数理统计学会Medallion Lecturer，伯努力学会Bernoulli Lecturer，美国数理统计学会和美国统计学会会士，晨兴应用数学金奖（三年一度），泛华统计协会杰出成就奖，ISI高被引用的数学家，泛华统计协会许宝騄奖（三年一度）等荣誉。刘军教授在序贯蒙特卡洛和粒子滤波方法做出奠基性的贡献，对马尔可夫链蒙特卡洛（MCMC）方法的设计构建了重要理论框架和新技术，并广泛应用这些理论和方法于工程学、生物信息学、大数据分析、个性化医疗等许多领域。在生物信息学方面，刘军教授将贝叶斯模型和MCMC方法成功应用于该领域，由刘军教授提出的“Gibbs保守串抽样和指针”是到目前为止生物学者寻找DNA和蛋白序列中精巧模式的两种最流行算法，在了解基因调控和蛋白同源性方面有非常成功的应用。近年来，刘军教授在统计学习理论和方法方面取得取得一系列突破性进展，对大数据处理方面有重大影响。