A path-based framework for analyzing large markov models

Reliability and dependability modeling can be employed during many stages of analysis of a computing system to gain insights into its critical behaviors. To provide useful results, realistic models of systems are often necessarily large and complex. Numerical analysis of these models presents a formidable challenge because the sizes of their state-space descriptions grow exponentially in proportion to the sizes of the models. On the other hand, simulation of the models requires analysis of many trajectories in order to compute statistically correct solutions. This dissertation presents a novel framework for performing both numerical analysis and simulation. The new numerical approach computes bounds on the solutions of transient measures in large continuous-time Markov chains (CTMCs). It extends existing path-based and uniformization-based methods by identifying sets of paths that are equivalent with respect to a reward measure and related to one another via a simple structural relationship. This relationship makes it possible for the approach to explore multiple paths at the same time,· thus significantly increasing the number of paths that can be explored in a given amount of time. Furthermore, the use of a structured representation for the state space and the direct computation of the desired reward measure (without ever storing the solution vector) allow it to analyze very large models using a very small amount of storage. Often, path-based techniques must compute many paths to obtain tight bounds. In addition to presenting the basic path-based approach, we also present algorithms for computing more paths and tighter bounds quickly. One resulting approach is based on the concept of path composition whereby precomputed subpaths are composed to compute the whole paths efficiently. Another approach is based on selecting important paths (among a set of many paths) for evaluation. Many path-based techniques suffer from having to evaluate many (unimportant) paths. Evaluating the important ones helps to compute tight bounds efficiently and quickly.

Neighborhood disadvantage and physical activity : baseline results from the HABITAT multilevel longitudinal study

PURPOSE: To examine the association between neighborhood disadvantage and physical activity (PA). ---------- METHODS: We use data from the HABITAT multilevel longitudinal study of PA among mid-aged (40-65 years) men and women (n=11, 037, 68.5% response rate) living in 200 neighborhoods in Brisbane, Australia. PA was measured using three questions from the Active Australia Survey (general walking, moderate, and vigorous activity), one indicator of total activity, and two questions about walking and cycling for transport. The PA measures were operationalized using multiple categories based on time and estimated energy expenditure that were interpretable with reference to the latest PA recommendations. The association between neighborhood disadvantage and PA was examined using multilevel multinomial logistic regression and Markov Chain Monte Carlo simulation. The contribution of neighborhood disadvantage to between-neighborhood variation in PA was assessed using the 80% interval odds ratio. ---------- RESULTS: After adjustment for sex, age, living arrangement, education, occupation, and household income, reported participation in all measures and levels of PA varied significantly across Brisbane’s neighborhoods, and neighborhood disadvantage accounted for some of this variation. Residents of advantaged neighborhoods reported significantly higher levels of total activity, general walking, moderate, and vigorous activity; however, they were less likely to walk for transport. There was no statistically significant association between neighborhood disadvantage and cycling for transport. In terms of total PA, residents of advantaged neighborhoods were more likely to exceed PA recommendations. ---------- CONCLUSIONS: Neighborhoods may exert a contextual effect on residents’ likelihood of participating in PA. The greater propensity of residents in advantaged neighborhoods to do high levels of total PA may contribute to lower rates of cardiovascular disease and obesity in these areas

Reading the play : adaptation by prediction of agent motion

An adaptive agent improves its performance by learning from experience. This paper describes an approach to adaptation based on modelling dynamic elements of the environment in order to make predictions of likely future state. This approach is akin to an elite sports player being able to “read the play”, allowing for decisions to be made based on predictions of likely future outcomes. Modelling of the agent‟s likely future state is performed using Markov Chains and a technique called “Motion and Occupancy Grids”. The experiments in this paper compare the performance of the planning system with and without the use of this predictive model. The results of the study demonstrate a surprising decrease in performance when using the predictions of agent occupancy. The results are derived from statistical analysis of the agent‟s performance in a high fidelity simulation of a world leading real robot soccer team.

Infinite-horizon policy-gradient estimation

Gradient-based approaches to direct policy search in reinforcement learning have received much recent attention as a means to solve problems of partial observability and to avoid some of the problems associated with policy degradation in value-function methods. In this paper we introduce GPOMDP, a simulation-based algorithm for generating a biased estimate of the gradient of the average reward in Partially Observable Markov Decision Processes (POMDPs) controlled by parameterized stochastic policies. A similar algorithm was proposed by Kimura, Yamamura, and Kobayashi (1995). The algorithm's chief advantages are that it requires storage of only twice the number of policy parameters, uses one free parameter β ∈ [0,1) (which has a natural interpretation in terms of bias-variance trade-off), and requires no knowledge of the underlying state. We prove convergence of GPOMDP, and show how the correct choice of the parameter β is related to the mixing time of the controlled POMDP. We briefly describe extensions of GPOMDP to controlled Markov chains, continuous state, observation and control spaces, multiple-agents, higher-order derivatives, and a version for training stochastic policies with internal states. In a companion paper (Baxter, Bartlett, & Weaver, 2001) we show how the gradient estimates generated by GPOMDP can be used in both a traditional stochastic gradient algorithm and a conjugate-gradient procedure to find local optima of the average reward. ©2001 AI Access Foundation and Morgan Kaufmann Publishers. All rights reserved.

On adaptive HMM state estimation

In this paper new online adaptive hidden Markov model (HMM) state estimation schemes are developed, based on extended least squares (ELS) concepts and recursive prediction error (RPE) methods. The best of the new schemes exploit the idempotent nature of Markov chains and work with a least squares prediction error index, using a posterior estimates, more suited to Markov models then traditionally used in identification of linear systems.

Computational Techniques for Haplotype Inference and for Local Alignment Significance

This thesis which consists of an introduction and four peer-reviewed original publications studies the problems of haplotype inference (haplotyping) and local alignment significance. The problems studied here belong to the broad area of bioinformatics and computational biology. The presented solutions are computationally fast and accurate, which makes them practical in high-throughput sequence data analysis. Haplotype inference is a computational problem where the goal is to estimate haplotypes from a sample of genotypes as accurately as possible. This problem is important as the direct measurement of haplotypes is difficult, whereas the genotypes are easier to quantify. Haplotypes are the key-players when studying for example the genetic causes of diseases. In this thesis, three methods are presented for the haplotype inference problem referred to as HaploParser, HIT, and BACH. HaploParser is based on a combinatorial mosaic model and hierarchical parsing that together mimic recombinations and point-mutations in a biologically plausible way. In this mosaic model, the current population is assumed to be evolved from a small founder population. Thus, the haplotypes of the current population are recombinations of the (implicit) founder haplotypes with some point--mutations. HIT (Haplotype Inference Technique) uses a hidden Markov model for haplotypes and efficient algorithms are presented to learn this model from genotype data. The model structure of HIT is analogous to the mosaic model of HaploParser with founder haplotypes. Therefore, it can be seen as a probabilistic model of recombinations and point-mutations. BACH (Bayesian Context-based Haplotyping) utilizes a context tree weighting algorithm to efficiently sum over all variable-length Markov chains to evaluate the posterior probability of a haplotype configuration. Algorithms are presented that find haplotype configurations with high posterior probability. BACH is the most accurate method presented in this thesis and has comparable performance to the best available software for haplotype inference. Local alignment significance is a computational problem where one is interested in whether the local similarities in two sequences are due to the fact that the sequences are related or just by chance. Similarity of sequences is measured by their best local alignment score and from that, a p-value is computed. This p-value is the probability of picking two sequences from the null model that have as good or better best local alignment score. Local alignment significance is used routinely for example in homology searches. In this thesis, a general framework is sketched that allows one to compute a tight upper bound for the p-value of a local pairwise alignment score. Unlike the previous methods, the presented framework is not affeced by so-called edge-effects and can handle gaps (deletions and insertions) without troublesome sampling and curve fitting.

Primordial Isocurvature Perturbation in Light of CMB and LSS Data

The increased accuracy in the cosmological observations, especially in the measurements of the comic microwave background, allow us to study the primordial perturbations in grater detail. In this thesis, we allow the possibility for a correlated isocurvature perturbations alongside the usual adiabatic perturbations. Thus far the simplest six parameter \Lambda CDM model has been able to accommodate all the observational data rather well. However, we find that the 3-year WMAP data and the 2006 Boomerang data favour a nonzero nonadiabatic contribution to the CMB angular power sprctrum. This is primordial isocurvature perturbation that is positively correlated with the primordial curvature perturbation. Compared with the adiabatic \Lambda CMD model we have four additional parameters describing the increased complexity if the primordial perturbations. Our best-fit model has a 4% nonadiabatic contribution to the CMB temperature variance and the fit is improved by \Delta\chi^2 = 9.7. We can attribute this preference for isocurvature to a feature in the peak structure of the angular power spectrum, namely, the widths of the second and third acoustic peak. Along the way, we have improved our analysis methods by identifying some issues with the parametrisation of the primordial perturbation spectra and suggesting ways to handle these. Due to the improvements, the convergence of our Markov chains is improved. The change of parametrisation has an effect on the MCMC analysis because of the change in priors. We have checked our results against this and find only marginal differences between our parametrisation.

Stochastic modelling of flexible manufacturing systems

Mathematical modelling plays a vital role in the design, planning and operation of flexible manufacturing systems (FMSs). In this paper, attention is focused on stochastic modelling of FMSs using Markov chains, queueing networks, and stochastic Petri nets. We bring out the role of these modelling tools in FMS performance evaluation through several illustrative examples and provide a critical comparative evaluation. We also include a discussion on the modelling of deadlocks which constitute an important source of performance degradation in fully automated FMSs.

Optimal control of arrivals to queues with delayed queue length information

We consider discrete-time versions of two classical problems in the optimal control of admission to a queueing system: i) optimal routing of arrivals to two parallel queues and ii) optimal acceptance/rejection of arrivals to a single queue. We extend the formulation of these problems to permit a k step delay in the observation of the queue lengths by the controller. For geometric inter-arrival times and geometric service times the problems are formulated as controlled Markov chains with expected total discounted cost as the minimization objective. For problem i) we show that when k = 1, the optimal policy is to allocate an arrival to the queue with the smaller expected queue length (JSEQ: Join the Shortest Expected Queue). We also show that for this problem, for k greater than or equal to 2, JSEQ is not optimal. For problem ii) we show that when k = 1, the optimal policy is a threshold policy. There are, however, two thresholds m(0) greater than or equal to m(1) > 0, such that mo is used when the previous action was to reject, and mi is used when the previous action was to accept.

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Information dissemination in socially aware networks under the linear threshold model

We provide new analytical results concerning the spread of information or influence under the linear threshold social network model introduced by Kempe et al. in, in the information dissemination context. The seeder starts by providing the message to a set of initial nodes and is interested in maximizing the number of nodes that will receive the message ultimately. A node's decision to forward the message depends on the set of nodes from which it has received the message. Under the linear threshold model, the decision to forward the information depends on the comparison of the total influence of the nodes from which a node has received the packet with its own threshold of influence. We derive analytical expressions for the expected number of nodes that receive the message ultimately, as a function of the initial set of nodes, for a generic network. We show that the problem can be recast in the framework of Markov chains. We then use the analytical expression to gain insights into information dissemination in some simple network topologies such as the star, ring, mesh and on acyclic graphs. We also derive the optimal initial set in the above networks, and also hint at general heuristics for picking a good initial set.

Modelling and analysis of new coolstreaming for P2P IPTV

Peer to peer networks are being used extensively nowadays for file sharing, video on demand and live streaming. For IPTV, delay deadlines are more stringent compared to file sharing. Coolstreaming was the first P2P IPTV system. In this paper, we model New Coolstreaming (newer version of Coolstreaming) via a queueing network. We use two time scale decomposition of Markov chains to compute the stationary distribution of number of peers and the expected number of substreams in the overlay which are not being received at the required rate due to parent overloading. We also characterize the end-to-end delay encountered by a video packet received by a user and originated at the server. Three factors contribute towards the delay. The first factor is the mean shortest path length between any two overlay peers in terms of overlay hops of the partnership graph which is shown to be O (log n) where n is the number of peers in the overlay. The second factor is the mean number of routers between any two overlay neighbours which is seen to be at most O (log N-I) where N-I is the number of routers in the internet. Third factor is the mean delay at a router in the internet. We provide an approximation of this mean delay E W]. Thus, the mean end to end delay in New Coolstreaming is shown to be upper bounded by O (log E N]) (log N-I) E (W)] where E N] is the mean number of peers at a channel.

Zero-sum risk-sensitive stochastic games on a countable state space

Infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled Markov chains with countably many states are analyzed. Upper and lower values for these games are established. The existence of value and saddle-point equilibria in the class of Markov strategies is proved for the discounted-cost game. The existence of value and saddle-point equilibria in the class of stationary strategies is proved under the uniform ergodicity condition for the ergodic-cost game. The value of the ergodic-cost game happens to be the product of the inverse of the risk-sensitivity factor and the logarithm of the common Perron-Frobenius eigenvalue of the associated controlled nonlinear kernels. (C) 2013 Elsevier B.V. All rights reserved.

Formal methods for control synthesis in partially observed environments : application to autonomous robotic manipulation

Modern robots are increasingly expected to function in uncertain and dynamically challenging environments, often in proximity with humans. In addition, wide scale adoption of robots requires on-the-fly adaptability of software for diverse application. These requirements strongly suggest the need to adopt formal representations of high level goals and safety specifications, especially as temporal logic formulas. This approach allows for the use of formal verification techniques for controller synthesis that can give guarantees for safety and performance. Robots operating in unstructured environments also face limited sensing capability. Correctly inferring a robot's progress toward high level goal can be challenging.

This thesis develops new algorithms for synthesizing discrete controllers in partially known environments under specifications represented as linear temporal logic (LTL) formulas. It is inspired by recent developments in finite abstraction techniques for hybrid systems and motion planning problems. The robot and its environment is assumed to have a finite abstraction as a Partially Observable Markov Decision Process (POMDP), which is a powerful model class capable of representing a wide variety of problems. However, synthesizing controllers that satisfy LTL goals over POMDPs is a challenging problem which has received only limited attention.

This thesis proposes tractable, approximate algorithms for the control synthesis problem using Finite State Controllers (FSCs). The use of FSCs to control finite POMDPs allows for the closed system to be analyzed as finite global Markov chain. The thesis explicitly shows how transient and steady state behavior of the global Markov chains can be related to two different criteria with respect to satisfaction of LTL formulas. First, the maximization of the probability of LTL satisfaction is related to an optimization problem over a parametrization of the FSC. Analytic computation of gradients are derived which allows the use of first order optimization techniques.

The second criterion encourages rapid and frequent visits to a restricted set of states over infinite executions. It is formulated as a constrained optimization problem with a discounted long term reward objective by the novel utilization of a fundamental equation for Markov chains - the Poisson equation. A new constrained policy iteration technique is proposed to solve the resulting dynamic program, which also provides a way to escape local maxima.

The algorithms proposed in the thesis are applied to the task planning and execution challenges faced during the DARPA Autonomous Robotic Manipulation - Software challenge.

Interpretação de imagens multitemporais de sensoriamento remoto.

Estudos multitemporais de dados de sensoriamento remoto dedicam-se ao mapeamento temático de uso da terra em diferentes instâncias de tempo com o objetivo de identificar as mudanças ocorridas em uma região em determinado período. Em sua maioria, os trabalhos de classificação automática supervisionada de imagens de sensoriamento remoto não utilizam um modelo de transformação temporal no processo de classificação. Pesquisas realizadas na última década abriram um importante precedente ao comprovarem que a utilização de um modelo de conhecimento sobre a dinâmica da região (modelo de transformação temporal), baseado em Cadeias de Markov Fuzzy (CMF), possibilita resultados superiores aos produzidos pelos classificadores supervisionados monotemporais. Desta forma, o presente trabalho enfoca um dos aspectos desta abordagem pouco investigados: a combinação de CMF de intervalos de tempo curtos para classificar imagens de períodos longos. A área de estudo utilizada nos experimentos é um remanescente florestal situado no município de Londrina-PR e que abrange todo o limite do Parque Estadual Mata dos Godoy. Como dados de entrada, são utilizadas cinco imagens do satélite Landsat 5 TM com intervalo temporal de cinco anos. De uma forma geral, verificou-se, a partir dos resultados experimentais, que o uso das Cadeias de Markov Fuzzy contribuiu significativamente para a melhoria do desempenho do processo de classificação automática em imagens orbitais multitemporais, quando comparado com uma classificação monotemporal. Ainda, pôde-se observar que as classificações com base em matrizes estimadas para períodos curtos sempre apresentaram resultados superiores aos das classificações com base em matrizes estimadas para períodos longos. Também, que a superioridade da estimação direta frente à extrapolação se reduz com o aumento da distância temporal. Os resultados do presente trabalho poderão servir de motivação para a criação de sistemas automáticos de classificação de imagens multitemporais. O potencial de sua aplicação se justifica pela aceleração do processo de monitoramento do uso e cobertura da terra, considerando a melhoria obtida frente a classificações supervisionadas tradicionais.