改进的MMLT全局照明渲染算法

针对多通路Metropolis光能传递算法（MMLT）不能很好地保证路径样本在路径空间中的连贯性,对子路径的重用率也较低的问题,提出了一种改进算法.通过先采样路径样本再从中选择的方式提高子路径重用率;然后对路径样本进行空间排序,以提高路径空间中的连贯性;最后设计了一套权值策略来决定不同采样方式所占比重.实验结果显示,该算法能够在相同条件下产生噪声更小的结果.     

Automatic glottal inverse filtering with the Markov chain Monte Carlo method

This paper presents a new glottal inverse filtering (GIF) method that utilizes a Markov chain Monte Carlo (MCMC) algorithm. First, initial estimates of the vocal tract and glottal flow are evaluated by an existing GIF method, iterative adaptive inverse filtering (IAIF). Simultaneously, the initially estimated glottal flow is synthesized using the Rosenberg–Klatt (RK) model and filtered with the estimated vocal tract filter to create a synthetic speech frame. In the MCMC estimation process, the first few poles of the initial vocal tract model and the RK excitation parameter are refined in order to minimize the error between the synthetic and original speech signals in the time and frequency domain. MCMC approximates the posterior distribution of the parameters, and the final estimate of the vocal tract is found by averaging the parameter values of the Markov chain. Experiments with synthetic vowels produced by a physical modeling approach show that the MCMC-based GIF method gives more accurate results compared to two known reference methods.     

Particle swarm optimization–Markov Chain Monte Carlo for accurate visual tracking with adaptive template update

A novel tracking method is proposed, which infers a target state and appearance template simultaneously. With this simultaneous inference, the method accurately estimates the target state and robustly updates the target template. The joint inference is performed by using the proposed particle swarm optimization–Markov chain Monte Carlo (PSO–MCMC) sampling method. PSO–MCMC is a combination of the particle swarm optimization (PSO) and Markov chain Monte Carlo sampling (MCMC), in which the PSO evolutionary algorithm and MCMC aim to find the target state and appearance template, respectively. The PSO can handle multi-modality in the target state and is therefore superior to a standard particle filter. Thus, PSO–MCMC achieves better performance in terms of accuracy when compared to the recently proposed particle MCMC. Experimental results demonstrate that the proposed tracker adaptively updates the target template and outperforms state-of-the-art tracking methods on a benchmark dataset.     

Time series of count data: modeling, estimation and diagnostics

Various models for time series of counts which can account for discreteness, overdispersion and serial correlation are compared. Besides observation- and parameter-driven models based upon corresponding conditional Poisson distributions, a dynamic ordered probit model as a flexible specification to capture the salient features of time series of counts is also considered. For all models, appropriate efficient estimation procedures are presented. For the parameter-driven specification this requires Monte-Carlo procedures like simulated maximum likelihood or Markov chain Monte Carlo. The methods, including corresponding diagnostic tests, are illustrated using data on daily admissions for asthma to a single hospital. Estimation results turn out to be remarkably similar across the different models.     

An Introduction to MCMC for Machine Learning

This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.     

Tracking highly correlated targets through statistical multiplexing

We consider a special problem of multi-target tracking, where a group of targets are highly correlated, usually demonstrating a common motion pattern with individual variations. We focus on the task of searching and provide a statistical framework of embedding the correlation among targets and the most recent observations into sampling, where the correlation is learned dynamically from the previous tracking results. Proposal distribution is updated during the sampling process fused with the motion prior and observation information. In this way, the observation of a single target is multiplexed statistically through mutual correlation among the multiple targets, and the correlation serves as both a prior information to improve the efficiency and a constraint to prevent trackers from drifting. Extensive experiments on tracking both naturally correlated and environment-constrained targets demonstrate superior and promising robust results with low complexity.     

A Sequential Monte Carlo Method for Bayesian Analysis of Massive Datasets

Markov chain Monte Carlo (MCMC) techniques revolutionized statistical practice in the 1990s by providing an essential toolkit for making the rigor and flexibility of Bayesian analysis computationally practical. At the same time the increasing prevalence of massive datasets and the expansion of the field of data mining has created the need for statistically sound methods that scale to these large problems. Except for the most trivial examples, current MCMC methods require a complete scan of the dataset for each iteration eliminating their candidacy as feasible data mining techniques.In this article we present a method for making Bayesian analysis of massive datasets computationally feasible. The algorithm simulates from a posterior distribution that conditions on a smaller, more manageable portion of the dataset. The remainder of the dataset may be incorporated by reweighting the initial draws using importance sampling. Computation of the importance weights requires a single scan of the remaining observations. While importance sampling increases efficiency in data access, it comes at the expense of estimation efficiency. A simple modification, based on the rejuvenation step used in particle filters for dynamic systems models, sidesteps the loss of efficiency with only a slight increase in the number of data accesses.To show proof-of-concept, we demonstrate the method on two examples. The first is a mixture of transition models that has been used to model web traffic and robotics. For this example we show that estimation efficiency is not affected while offering a 99% reduction in data accesses. The second example applies the method to Bayesian logistic regression and yields a 98% reduction in data accesses.     

An adaptive Monte Carlo integration algorithm with general division approach

We propose an adaptive Monte Carlo algorithm for estimating multidimensional integrals over a hyper-rectangular region. The algorithm uses iteratively the idea of separating the domain of integration into 2^s$2^s$subregions. The proposed algorithm can be applied directly to estimate the integral using an efficient way of storage. We test the algorithm for estimating the value of a 30-dimensional integral using a two-division approach. The numerical results show that the proposed algorithm gives better results than using one-division approach.     

Robust specification of the roughness penalty prior distribution in spatially adaptive Bayesian P-splines models

The potential important role of the prior distribution of the roughness penalty parameter in the resulting smoothness of Bayesian P-splines models is considered. The recommended specification for that distribution yields models that can lack flexibility in specific circumstances. In such instances, these are shown to correspond to a frequentist P-splines model with a predefined and severe roughness penalty parameter, an obviously undesirable feature. It is shown that the specification of a hyperprior distribution for one parameter of that prior distribution provides the desired flexibility. Alternatively, a mixture prior can also be used. An extension of these two models by enabling adaptive penalties is provided. The posterior of all the proposed models can be quickly explored using the convenient Gibbs sampler.     

SISAM and MIXIN: Two algorithms for the computation of posterior moments and densities using Monte Carlo integration

Two algorithms, and corresponding Fortran computer programs, for the computation of posterior moments and densities using the principle of importance sampling are described in detail. The first algorithm makes use of a multivariate Student t importance function as approximation of the posterior. It can be applied when the integrand is moderately skew. The second algorithm makes use of a decomposition: a multivariate normal importance function is used to generate directions (lines) and one-dimensional classical quadrature is used to evaluate the integrals defined on the generated lines. The second algorithm can be used in cases where the integrand is possibly very skew in any direction.     

一般性粒子滤波算法收敛特性

粒子滤波算法在处理最优滤波问题时受到了广泛的重视,对此类算法的收敛性研究是该领域研究的热点问题.首先介绍了一种变换的一般性粒子滤波算法,与一般性粒子滤波算法不同,在每次执行重要性采样步骤后,新算法需要判别是否需要重新执行重采样步骤和重要性采样步骤.随后对新算法的几乎必然收敛性进行了分析,并将对新算法的收敛性讨论推广到一般性粒子滤波算法中.研究了当感兴趣函数在扩展状态后验联合分布下四阶距存在并且递归次数有限时,由一般性粒子滤波算法得出的估计几乎收敛于最优估计的充分条件.最后,通过一组仿真实验来说明一般性粒子滤波算法的几乎必然收敛性.     

基于隐含变量的聚类集成模型

聚类集成能成为机器学习活跃的研究热点,是因为聚类集成能够保护私有信息、分布式处理数据和对知识进行重用,此外,噪声和孤立点对结果的影响较小.主要工作包括:第一,分析了把每一个基聚类器看成是原数据的一个属性这种处理方式的优越性,发现按此方法建立起来的聚类集成算法就具有良好的扩展性和灵活性;第二,在此基础之上,建立了latent variable cluster ensemble(LVCE)概率模型进行聚类集成,并且给出了LVCE 模型的Markovchain Monte Carlo(MCMC)算法.实验结果表明,LVCE 模型的MCMC 算法能够进行聚类集成并且达到良好的效果,同时可以体现数据聚类的紧密程度.     

Interacting sequential Monte Carlo samplers for trans-dimensional simulation

The methodology of interacting sequential Monte Carlo (SMC) samplers is introduced. SMC samplers are methods for sampling from a sequence of densities on a common measurable space using a combination of Markov chain Monte Carlo (MCMC) and sequential importance sampling/resampling (SIR) methodology. One of the main problems with SMC samplers when simulating from trans-dimensional, multimodal static targets is that transition kernels do not mix which leads to low particle diversity. In such situations poor Monte Carlo estimates may be derived. To deal with this problem an interacting SMC approach for static inference is introduced. The method proceeds by running SMC samplers in parallel on, initially, different regions of the state space and then moving the corresponding samples onto the entire state space. Once the samplers reach a common space the samplers are combined and allowed to interact. The method is intended to increase the diversity of the population of samples. It is established that interacting SMC admit a Feynman-Kac representation; this provides a framework for the convergence results that are developed. In addition, the methodology is demonstrated on a trans-dimensional inference problem in Bayesian mixture modelling and also, using adaptive methods, a mixture modelling problem in population genetics.     

AMCMC: An R interface for adaptive MCMC

We describe AMCMC, a software package for running adaptive MCMC algorithms on user-supplied density functions. AMCMC provides the user with an R interface, which in turn calls C programs for faster computations. The user can supply the density and functionals either as R objects, or as auxiliary C files. We describe experiments which illustrate that for fast performance in high dimensions, it is best that the latter option be used.     

Some exact tests for manifest properties of latent trait models

Item response theory is one of the modern test theories with applications in educational and psychological testing. Recent developments made it possible to characterize some desired properties in terms of a collection of manifest ones, so that hypothesis tests on these traits can, in principle, be performed. But the existing test methodology is based on asymptotic approximation, which is impractical in most applications since the required sample sizes are often unrealistically huge. To overcome this problem, a class of tests is proposed for making exact statistical inference about four manifest properties: covariances given the sum are non-positive (CSN), manifest monotonicity (MM), conditional association (CA), and vanishing conditional dependence (VCD). One major advantage is that these exact tests do not require large sample sizes. As a result, tests for CSN and MM can be routinely performed in empirical studies. For testing CA and VCD, the exact methods are still impractical in most applications, due to the unusually large number of parameters to be tested. However, exact methods are still derived for them as an exploration toward practicality. Some numerical examples with applications of the exact tests for CSN and MM are provided.     

Improved MCMC sampling methods for estimating weighted sums in Winnow with application to DNF learning

A Markov chain Monte Carlo method has previously been introduced to estimate weighted sums in multiplicative weight update algorithms when the number of inputs is exponential. However, the original algorithm still required extensive simulation of the Markov chain in order to get accurate estimates of the weighted sums. We propose an optimized version of the original algorithm that produces exactly the same classifications while often using fewer Markov chain simulations. We also apply three other sampling techniques and empirically compare them with the original Metropolis sampler to determine how effective each is in drawing good samples in the least amount of time, in terms of accuracy of weighted sum estimates and in terms of Winnow’s prediction accuracy. We found that two other samplers (Gibbs and Metropolized Gibbs) were slightly better than Metropolis in their estimates of the weighted sums. For prediction errors, there is little difference between any pair of MCMC techniques we tested. Also, on the data sets we tested, we discovered that all approximations of Winnow have no disadvantage when compared to brute force Winnow (where weighted sums are exactly computed), so generalization accuracy is not compromised by our approximation. This is true even when very small sample sizes and mixing times are used. An early version of this paper appeared as Tao and Scott (2003).     

Implementation of Monte Carlo integration for the analysis of product-form queueing networks

MonteQueue is a new public-domain software package which rapidly solves large and small multiclass product-form queueing networks with multiple- and single-server stations over a wide range of traffic conditions. MonteQueue obtains estimates of performance measures by applying importance sampling to sum and integral representations of the network's normalization constants. This paper discusses the implementation issues and surveys of the theoretical properties of the four importance sampling techniques included in MonteQueue. It also presents new numerical data which compare the performance of the four techniques.