Multiple Markov Research Articles

Confronting uncertainty in model-based geostatistics using Markov Chain Monte Carlo simulation

This paper demonstrates for the first time the use of Markov Chain Monte Carlo (MCMC) simulation for parameter inference in model-based soil geostatistics. We implemented the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm to jointly summarize the posterior distribution of variogram parameters and the coefficients of a linear spatial model, and derive estimates of predictive uncertainty. The DREAM method runs multiple different Markov chains in parallel and jumps in each chain are generated from a discrete proposal distribution containing a fixed multiple of the difference of the states of randomly chosen pairs of other chains. This approach automatically scales the orientation and scale of the proposal distribution, and is especially designed to maintain detailed balance and ergodicity, thereby generating an exact approximation of the posterior probability density function (pdf) of the parameters of the linear model and variogram. This approach is tested using three different data sets from Australia involving variogram estimation of soil thickness, kriging of soil pH, and spatial prediction of soil organic carbon content. The results showed some advantages of MCMC over the conventional method of moments and residual maximum likelihood (REML) estimation. The posterior pdf derived with MCMC conveys important information about parameter uncertainty, multi-dimensional parameter correlation, and thus how many significant parameters are warranted by the calibration data. Parameter uncertainty constitutes only a small part of total prediction uncertainty for the case studies considered here. The prediction accuracies using MCMC and REML are similar. The variogram estimated using conventional approaches (method of moments, and without simulation) lies within the 95% prediction uncertainty interval of the posterior distribution derived with DREAM. Altogether our results show that conventional kriging and regression-kriging still remain a viable option for production mapping.

Abnormal crowd behavior detection using high-frequency and spatio-temporal features

Abnormal crowd behavior detection is an important research issue in computer vision. The traditional methods first extract the local spatio-temporal cuboid from video. Then the cuboid is described by optical flow or gradient features, etc. Unfortunately, because of the complex environmental conditions, such as severe occlusion, over-crowding, etc., the existing algorithms cannot be efficiently applied. In this paper, we derive the high-frequency and spatio-temporal (HFST) features to detect the abnormal crowd behaviors in videos. They are obtained by applying the wavelet transform to the plane in the cuboid which is parallel to the time direction. The high-frequency information characterize the dynamic properties of the cuboid. The HFST features are applied to the both global and local abnormal crowd behavior detection. For the global abnormal crowd behavior detection, Latent Dirichlet allocation is used to model the normal scenes. For the local abnormal crowd behavior detection, Multiple Hidden Markov Models, with an competitive mechanism, is employed to model the normal scenes. The comprehensive experiment results show that the speed of detection has been greatly improved using our approach. Moreover, a good accuracy has been achieved considering the false positive and false negative detection rates.

Knotting probabilities after a local strand passage in unknotted self-avoiding polygons

We investigate, both theoretically and numerically, the knotting probabilities after a local strand passage is performed in an unknotted self-avoiding polygon (SAP) on the simple cubic lattice. In the polygons studied, it is assumed that two polygon segments have already been brought close together for the purpose of performing a strand passage. This restricts the polygons considered to those that contain a specific pattern called Θ at a fixed location; an unknotted polygon containing Θ is called a Θ-SAP. It is proved that the number of n-edge Θ-SAPs grows exponentially (with n) at the same rate as the total number of n-edge unknotted SAPs (those with no prespecified strand passage structure). Furthermore, it is proved that the same holds for subsets of n-edge Θ-SAPs that yield a specific after-strand-passage knot-type. Thus, the probability of a given after-strand-passage knot-type does not grow (or decay) exponentially with n. Instead, it is conjectured that these after-strand-passage knot probabilities approach, as n goes to infinity, knot-type dependent amplitude ratios lying strictly between 0 and 1. This conjecture is supported by numerical evidence from Monte Carlo data generated using a composite (aka multiple) Markov chain Monte Carlo BFACF algorithm developed to study Θ-SAPs. A new maximum likelihood method is used to estimate the critical exponents relevant to this conjecture. We also obtain strong numerical evidence that the after-strand-passage knotting probability depends on the local structure around the strand-passage site. If the local structure and the crossing sign at the strand-passage site are considered, then we observe that the more ‘compact’ the local structure, the less likely the after-strand-passage polygon is to be knotted. This trend for compactness versus knotting probability is consistent with results obtained for other strand-passage models; however, we are the first to note the influence of the crossing-sign information. We use two measures of ‘compactness’: one involves the size of a smallest polygon that contains the structure and the other is in terms of an ‘opening’ angle. The opening angle definition is consistent with one that is measurable from single molecule DNA experiments. The theoretical and numerical approaches presented here are more broadly applicable to other SAP models.

Population MCMC methods for history matching and uncertainty quantification

This paper presents the application of a population Markov Chain Monte Carlo (MCMC) technique to generate history-matched models. The technique has been developed and successfully adopted in challenging domains such as computational biology but has not yet seen application in reservoir modelling. In population MCMC, multiple Markov chains are run on a set of response surfaces that form a bridge from the prior to posterior. These response surfaces are formed from the product of the prior with the likelihood raised to a varying power less than one. The chains exchange positions, with the probability of a swap being governed by a standard Metropolis accept/reject step, which allows for large steps to be taken with high probability. We show results of Population MCMC on the IC Fault Model—a simple three-parameter model that is known to have a highly irregular misfit surface and hence be difficult to match. Our results show that population MCMC is able to generate samples from the complex, multi-modal posterior probability distribution of the IC Fault model very effectively. By comparison, previous results from stochastic sampling algorithms often focus on only part of the region of high posterior probability depending on algorithm settings and starting points.

Gingipains fromPorphyromonas gingivalis— complex domain structures confer diverse functions

Gingipains, a group of arginine or lysine specific cysteine proteinases (also known as RgpA, RgpB and Kgp), have been recognized as major virulence factors in Porphyromonas gingivalis. This bacterium is one of a handful of pathogens that cause chronic periodontitis. Gingipains are involved in adherence to and colonization of epithelial cells, haemagglutination and haemolysis of erythrocytes, disruption and manipulation of the inflammatory response, and the degradation of host proteins and tissues. RgpA and Kgp are multi-domain proteins composed of catalytic domains and haemagglutinin/adhesin (HA) regions. The structure of the HA regions have previously been defined by a gingipain domain structure hypothesis which is a set of putative domain boundaries derived from the sequences of fragments of these proteins extracted from the cell surface. However, multiple sequence alignments and hidden Markov models predict an alternative domain architecture for the HA regions of gingipains. In this alternate model, two or three repeats of the so-called "cleaved adhesin" domains (and one other undefined domain in some strains) are the modules which constitute the substructure of the HA regions. Recombinant forms of these putative cleaved adhesin domains are indeed stable folded protein modules and recently determined crystal structures support the hypothesis of a modular organisation of the HA region. Based on the observed K2 and K3 structures as well as multiple sequence alignments, it is proposed that all the cleaved adhesin domains in gingipains will share the same β-sandwich jelly roll fold. The new domain model of the structure for gingipains and the haemagglutinin (HagA) proteins of P. gingivalis will guide future functional studies of these virulence factors.

Weighted Maximum Posterior Marginals for Random Fields Using an Ensemble of Conditional Densities From Multiple Markov Chain Monte Carlo Simulations

The ability of classification systems to adjust their performance (sensitivity/specificity) is essential for tasks in which certain errors are more significant than others. For example, mislabeling cancerous lesions as benign is typically more detrimental than mislabeling benign lesions as cancerous. Unfortunately, methods for modifying the performance of Markov random field (MRF) based classifiers are noticeably absent from the literature, and thus most such systems restrict their performance to a single, static operating point (a paired sensitivity/specificity). To address this deficiency we present weighted maximum posterior marginals (WMPM) estimation, an extension of maximum posterior marginals (MPM) estimation. Whereas the MPM cost function penalizes each error equally, the WMPM cost function allows misclassifications associated with certain classes to be weighted more heavily than others. This creates a preference for specific classes, and consequently a means for adjusting classifier performance. Realizing WMPM estimation (like MPM estimation) requires estimates of the posterior marginal distributions. The most prevalent means for estimating these--proposed by Marroquin--utilizes a Markov chain Monte Carlo (MCMC) method. Though Marroquin's method (M-MCMC) yields estimates that are sufficiently accurate for MPM estimation, they are inadequate for WMPM. To more accurately estimate the posterior marginals we present an equally simple, but more effective extension of the MCMC method (E-MCMC). Assuming an identical number of iterations, E-MCMC as compared to M-MCMC yields estimates with higher fidelity, thereby 1) allowing a far greater number and diversity of operating points and 2) improving overall classifier performance. To illustrate the utility of WMPM and compare the efficacies of M-MCMC and E-MCMC, we integrate them into our MRF-based classification system for detecting cancerous glands in (whole-mount or quarter) histological sections of the prostate.

Load balancing on temporally heterogeneous cluster of workstations for parallel simulated annealing

Simulated annealing (SA) is a general-purpose optimization technique widely used in various combinatorial optimization problems. However, the main drawback of this technique is a long computation time required to obtain a good quality of solution. Clusters have emerged as a feasible and popular platform for parallel computing in many applications. Computing nodes on many of the clusters available today are temporally heterogeneous. In this study, multiple Markov chain (MMC) parallel simulated annealing (PSA) algorithms have been implemented on a temporally heterogeneous cluster of workstations to solve the graph partitioning problem and their performance has been analyzed in detail. Temporal heterogeneity of a cluster of workstations is harnessed by employing static and dynamic load balancing techniques to further improve efficiency and scalability of the MMC PSA algorithms.

A multiple Markov switching model for actuarial use in South Africa

This paper introduces a new class of Markov switching models where switches in variables are not perfectly correlated. Maximum-likelihood estimates of the parameters are derived and shown to require only the smoothed inferences obtained from a univariate analysis of the variables. The framework is used to estimate a multiple Markov switching (MMS) model of South African financial and economic variables, which can be used for various actuarial applications, especially those involving long-term projections. Users may wish to set certain parameters in relation to future expectations rather than simply using estimates based on past data, but that process is not covered in this paper. KEYWORDS Multivariate, multiple Markov switching, long-term, financial projections, actuarial, stochastic model, time-series models

Architectures of the unique domains associated with the DEAD-box helicase motif

Helicases are motor proteins of biological system, which catalyze the opening of energetically stable duplex nucleic acids in an ATP-dependent manner and thereby are involved in almost all aspects of nucleic acid metabolism including cell cycle progression. They contain several conserved domains including the DEAD-box and also several unique domains associated with these. The Pfam database (http://pfam.janelia.org/) is a large collection of protein families, each represented by multiple sequence alignments and hidden Markov models (HMMs). A diverse range of proteins are found in nature, and the functional specificity to each protein, to a greater extent, is imparted by its domain architecture. To this extent, a DEAD-box ATP-dependent RNA helicase (LOC_Os01g36890; Genomic sequence length: 6284 nucleotides; CDS length: 1299 nucleotides; Protein length: 432 amino acids) was studied. The protein sequence was imported for domain search on Pfam. This particular Pfam entry after covering a large proportion of the sequences in the underlying database has generated a more comprehensive coverage across a wide range of phyla of the known domains that are associated with the typical DEAD-box helicase motif. A total of 362 domain architectures were recollected from the Pfam database for the Family: DEAD (PF00270). We have therefore systematically analyzed the domains closely associated with DEAD-motif, which occur in a variety of proteins and can provide insights into their function.

Likelihood Ratio Based Score Fusion for Audio-Visual Speaker Identification in Challenging Environment

It is well known to enhance the performance of noise robust speaker identification using visual speech information with audio utterances. This paper presents an approach to evaluate the performance of a noise robust audio-visual speaker identification system using likelihood ratio based score fusion in challenging environment. Though the traditional HMM based audio-visual speaker identification system is very sensitive to the speech parameter variation, the proposed likelihood ratio based score fusion method is found to be stance and performs well for improving the robustness and naturalness of human-computerinteraction. In this paper, we investigate the proposed audiovisual speaker identification system in typical office environments conditions. To do this, we investigated two approaches that utilize speech utterance with visual features to improve speaker identification performance in acoustically and visually challenging environment: one seeks to eliminate the noise from the acoustic and visual features by using speech and facial image pre-processing techniques. The other task combines speech and facial features that have been used by the multiple Discrete Hidden Markov Model classifiers with likelihood ratio based score fusion. It is shown that the proposed system can improve a significant amount of performance for audio-visual speaker identification in challenging official environment conditions.

MULTIPLE MARKOV GENERALIZED GAUSSIAN PROCESSES AND THEIR DUALITIES

A stochastic process describes evolutional random phenomena towards future. Corresponding with this direction, there will be a process describing, as it were, backward evolution from future to present. The dual process is a realization of this fact. We restrict our attention to Gaussian processes for which multiple Markov property is well investigated. This property expresses way of dependence of involved randomness as time goes by. We can therefore expect that such a process with multiple Markov property would present an exact form of the dual process. We shall show that having defined generalized Gaussian process with multiple Markov property, we can construct the dual process satisfying the properties that we claim. The analysis for this can be done in the space of Hida distributions.

Learn From Thy Neighbor: Parallel-Chain and Regional Adaptive MCMC

Starting with the seminal paper of Haario, Saksman, and Tamminen (Haario, Saksman, and Tamminen 2001), a substantial amount of work has been done to validate adaptive Markov chain Monte Carlo algorithms. In this paper we focus on two practical aspects of adaptive Metropolis samplers. First, we draw attention to the deficient performance of standard adaptation when the target distribution is multimodal. We propose a parallel chain adaptation strategy that incorporates multiple Markov chains which are run in parallel. Second, we note that the current adaptive MCMC paradigm implicitly assumes that the adaptation is uniformly efficient on all regions of the state space. However, in many practical instances, different “optimal” kernels are needed in different regions of the state space. We propose here a regional adaptation algorithm in which we account for possible errors made in defining the adaptation regions. This corresponds to the more realistic case in which one does not know exactly the optimal regions for adaptation. The methods focus on the random walk Metropolis sampling algorithm but their scope is much wider. We provide theoretical justification for the two adaptive approaches using the existent theory build for adaptive Markov chain Monte Carlo. We illustrate the performance of the methods using simulations and analyze a mixture model for real data using an algorithm that combines the two approaches.

Sports Video Mining via Multichannel Segmental Hidden Markov Models

We study sports video mining as a machine learning and statistical inference problem. We focus on mid-level semantic structures that can serve as building blocks for high-level semantic analysis. Particularly, we are interested in how to infer multiple coexistent structures jointly. We present a new multichannel segmental hidden Markov model (MCSHMM) that is a unique probabilistic graphical model with two advantages. One is the integration of both hierarchical and parallel dynamic structures that offers more flexibility and capacity of capturing the interaction between multiple Markov chains. The other is the incorporation of the segmental HMM (SHMM) to deal with variable-length observations. In addition, we develop a maximum a posteriori (MAP) estimator to optimize the model structure and parameters simultaneously. The proposed MCSHMM is used for American football video analysis. The experiment result shows that the MCSHMM outperforms existing HMMs and has potential to be extended for other video mining tasks.

A likelihood ratio test for stationarity of rating transitions

We study the time-stationarity of rating transitions, modelled by a time-continuous discrete-state Markov process and derive a likelihood ratio test. For multiple Markov processes from a multiplicative intensity model, maximum likelihood parameter estimates can be written as martingale transform of the processes, counting transitions between the rating states, so that the profile partial likelihood ratio is asymptotically χ 2 -distributed. An application to an internal rating data set reveals highly significant instationarity.

A parallel simulated annealing algorithm based on functional feature tree modeling for 3D engineering layout design

Computation complexity and modeling complexity are primary clog in 3D engineering layout design. In this paper, a parallel simulated annealing based on multiple Markov chains is employed to deal with the computation complexity. The algorithm increases computing efficiency by allocating computation burden to networked computers. To cope with the modeling complexity, machine components and space limitation are modeled by a hierarchical, feature-based modeling method—the functional feature tree modeling method. And multiple complex design constraints can be described by the representation. In order to support whole layout design solving process, a Computer Aided Layout Design System is introduced briefly. This system not only implements the algorithm and the components representation, but also integrates some other subsystems as evaluation system, constrains editor etc. The methods are demonstrated through a real engineering application, a vehicle engine compartment layout design.

Acoustic Factor Analysis for Streamed Hidden Markov Modeling

This paper presents a novel streamed hidden Markov model (HMM) framework for speech recognition. The factor analysis (FA) principle is adopted to explore the common factors from acoustic features. The streaming regularities in building HMMs are governed by the correlation between cepstral features, which is inherent in common factors. Those features corresponding to the same factor are generated by the identical HMM state. Accordingly, the multiple Markov chains are adopted to characterize the variation trends in different dimensions of cepstral vectors. An FA streamed HMM (FASHMM) method is developed to relax the assumption of standard HMM topology, namely, that all features of a speech frame perform the same state emission. The proposed FASHMM is more flexible than the streamed factorial HMM (SFHMM) where the streaming was empirically determined. To reduce the number of factor loading matrices in FA, we evaluated the similarity between individual matrices to find the optimal solution to parameter clustering of FA models. A new decoding algorithm was presented to perform FASHMM speech recognition. FASHMM carries out the streamed Markov chains for a sequence of multivariate Gaussian mixture observations through the state transitions of the partitioned vectors. In the experiments, the proposed method reduced the recognition error rates significantly when compared with the standard HMM and SFHMM methods.

Parallelization of Markov Chain Generation and its Application to the Multicanonical Method

We develop a simple algorithm to parallelize generation processes of Markov chains. In this algorithm, multiple Markov chains are generated in parallel and jointed together to make a longer Markov chain. The joints between the constituent Markov chains are processed using the detailed balance. We apply the parallelization algorithm to multicanonical calculations of the two-dimensional Ising model and demonstrate accurate estimation of multicanonical weights.

Hierarchical Multiple Markov Chain Model for Unsupervised Texture Segmentation

In this paper, we present a novel multiscale texture model and a related algorithm for the unsupervised segmentation of color images. Elementary textures are characterized by their spatial interactions with neighboring regions along selected directions. Such interactions are modeled, in turn, by means of a set of Markov chains, one for each direction, whose parameters are collected in a feature vector that synthetically describes the texture. Based on the feature vectors, the texture are then recursively merged, giving rise to larger and more complex textures, which appear at different scales of observation: accordingly, the model is named Hierarchical Multiple Markov Chain (H-MMC). The Texture Fragmentation and Reconstruction (TFR) algorithm, addresses the unsupervised segmentation problem based on the H-MMC model. The "fragmentation" step allows one to find the elementary textures of the model, while the "reconstruction" step defines the hierarchical image segmentation based on a probabilistic measure (texture score) which takes into account both region scale and inter-region interactions. The performance of the proposed method was assessed through the Prague segmentation benchmark, based on mosaics of real natural textures, and also tested on real-world natural and remote sensing images.

PBEAM: A parallel implementation of BEAM for genome-wide inference of epistatic interactions

The software tool PBEAM provides a parallel implementation of the BEAM, which is the first algorithm for large scale epistatic interaction mapping, including genome-wide studies with hundreds of thousands of markers. BEAM describes markers and their interactions with a Bayesian partitioning model and computes the posterior probability of each marker sets via Markov Chain Monte Carlo (MCMC). PBEAM takes the advantage of simulating multiple Markov chains simultaneously. This design can efficiently reduce ~n-fold execution time in the circumstance of n CPUs. The implementation of PBEAM is based on MPI libraries. PBEAM is available for download at http://bioinfo.au.tsinghua.edu.cn/pbeam/

Randomized Algorithms with Splitting: Why the Classic Randomized Algorithms Do Not Work and How to Make them Work

We show that the original classic randomized algorithms for approximate counting in NP-hard problems, like for counting the number of satisfiability assignments in a SAT problem, counting the number of feasible colorings in a graph and calculating the permanent, typically fail. They either do not converge at all or are heavily biased (converge to a local extremum). Exceptions are convex counting problems, like estimating the volume of a convex polytope. We also show how their performance could be dramatically improved by combining them with the classic splitting method, which is based on simulating simultaneously multiple Markov chains. We present several algorithms of the combined version, which we simple call the splitting algorithms. We show that the most advance splitting version coincides with the cloning algorithm suggested earlier by the author. As compared to the randomized algorithms, the proposed splitting algorithms require very little warm-up time while running the MCMC from iteration to iteration, since the underlying Markov chains are already in steady-state from the beginning. What required is only fine tuning, i.e. keeping the Markov chains in steady-state while moving from iteration to iteration. We present extensive simulation studies with both the splitting and randomized algorithms for different NP-hard counting problems.