Sequential Importance Sampling Algorithm Research Articles

Sequential importance sampling for estimating expectations over the space of perfect matchings

This paper makes three contributions to estimating the number of perfect matching in bipartite graphs. First, we prove that the popular sequential importance sampling algorithm works in polynomial time for dense bipartite graphs. More carefully, our algorithm gives a (1±ϵ)-approximation for the number of perfect matchings of a λ-dense bipartite graph, using O(n1−2λλϵ−2) samples. With size n on each side and for 1 2>λ>0, a λ-dense bipartite graph has all degrees greater than (λ+1 2)n. Second, practical applications of the algorithm requires many calls to matching algorithms. A novel preprocessing step is provided which makes significant improvements. Third, three applications are provided. The first is for counting Latin squares, the second is a practical way of computing the greedy algorithm for a card guessing game with feedback and the third is for stochastic block models. In all three examples, sequential importance sampling allows treating practical problems of reasonably large sizes.

Randomized sequential importance sampling for estimating the number of perfect matchings in bipartite graphs

We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We expect our methods to be useful for other applied problems.

A nonparametric-learning visual servoing framework for robot manipulator in unstructured environments

Current visual servoing methods used in robot manipulation require system modeling and parameters, only working in structured environments. This paper presents a nonparametric visual servoing for a robot manipulator operated in unstructured environments. A Gaussian-mapping likelihood process is used in Bayesian stochastic state estimation (SSE) for Robotic coordination control, in which the Monte Carlo sequential importance sampling (MCSIS) algorithm and a learning-remedied method are created for robotic visual-motor mapping estimation. The self-learning strategy described takes advantage of remedy the particles deterioration to maintain the robust performance at a low rate of particle sampling, rather than likes MCSIS rely on enlarge the sampling variance to cover the whole state distribution. Additionally, the servoing controller is deduced for robotic coordination directly by visual observation. The stability of the proposed framework is illustrated by Lyapunov theory and applied to a manipulator with eye-in-hand configuration no system parameters. Finally, the simulation and experimental results demonstrate consistently that the proposed algorithm involving learning-remedied outperforms traditional visual servoing approaches.

Efficient generation of random derangements with the expected distribution of cycle lengths

We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random fixed-point-free involutions only, a. k. a. random perfect matchings on the complete graph. Our data indicate that the algorithms generate random samples with the expected distribution of cycle lengths, which we derive, and for relatively small samples, which can actually be very large in absolute numbers, we argue that they generate samples indistinguishable from the uniform distribution. Both algorithms are simple to understand and implement and possess a performance comparable to or better than those of currently known methods. Simulations suggest that the mixing time of the algorithm based on random restricted transpositions (in the total variance distance with respect to the distribution of cycle lengths) is $$O(n^{a}\log {n}^{2})$$ with $$a \simeq \frac{1}{2}$$ and n the length of the derangement. We prove that the sequential importance sampling algorithm generates random derangements in O(n) time with probability O(1/n) of failing.

SEQUENTIAL IMPORTANCE SAMPLING FOR MULTIRESOLUTION KINGMAN-TAJIMA COALESCENT COUNTING.

Statistical inference of evolutionary parameters from molecular sequence data relies on coalescent models to account for the shared genealogical ancestry of the samples. However, inferential algorithms do not scale to available data sets. A strategy to improve computational efficiency is to rely on simpler coalescent and mutation models, resulting in smaller hidden state spaces. An estimate of the cardinality of the state-space of genealogical trees at different resolutions is essential to decide the best modeling strategy for a given dataset. To our knowledge, there is neither an exact nor approximate method to determine these cardinalities. We propose a sequential importance sampling algorithm to estimate the cardinality of the sample space of genealogical trees under different coalescent resolutions. Our sampling scheme proceeds sequentially across the set of combinatorial constraints imposed by the data, which in this work are completely linked sequences of DNA at a non recombining segment. We analyze the cardinality of different genealogical tree spaces on simulations to study the settings that favor coarser resolutions. We apply our method to estimate the cardinality of genealogical tree spaces from mtDNA data from the 1000 genomes and a sample from a Melanesian population at the β-globin locus.

A Sequential Importance Sampling Algorithm for Counting Linear Extensions

In recent decades, a number of profound theorems concerning approximation of hard counting problems have appeared. These include estimation of the permanent, estimating the volume of a convex polyhedron, and counting (approximately) the number of linear extensions of a partially ordered set. All of these results have been achieved using probabilistic sampling methods, specifically Monte Carlo Markov Chain (MCMC) techniques. In each case, a rapidly mixing Markov chain is defined that is guaranteed to produce, with high probability, an accurate result after only a polynomial number of operations. Although of polynomial complexity, none of these results lead to a practical computational technique, nor do they claim to. The polynomials are of high degree and a non-trivial amount of computing is required to get even a single sample. Our aim in this article is to present practical Monte Carlo methods for one of these problems, counting linear extensions. Like related work on estimating the coefficients of the reliability polynomial, our technique is based on improving the so-called Knuth counting algorithm by incorporating an importance function into the node selection technique giving a sequential importance sampling (SIS) method. We define and report performance on two importance functions.

Multilevel Sequential Importance Sampling for Rare Event Estimation

The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial differential equation (PDE). Since numerical evaluations of PDEs are computationally expensive, estimating such probabilities of failure by Monte Carlo sampling is intractable. More efficient sampling methods from reliability analysis, such as Subset Simulation, are popular, but can still be impracticable if the PDE evaluations are very costly. In this article, we develop a novel, highly efficient estimator for probabilities of rare events. Our method is based on a Sequential Importance sampler using discretizations of PDE-based limit state functions with different accuracies. A twofold adaptive algorithm ensures that we obtain an estimate based on the desired discretization accuracy. In contrast to the Multilevel Subset Simulation estimator of [Ullmann, Papaioannou 2015; SIAM/ASA J. Uncertain. Quantif. 3(1):922-953], our estimator overcomes the nestedness problem. Of particular importance in Sequential Importance sampling algorithms is the correct choice of the MCMC kernel. Instead of the popular adaptive conditional sampling method, we propose a new algorithm that uses independent proposals from an adaptively constructed von Mises-Fischer-Nakagami distribution. The proposed algorithm is applied to test problems in 1D and 2D space, respectively, and is compared to the Multilevel Subset Simulation estimator and to single-level versions of Sequential Importance Sampling and Subset Simulation.

Permanental generating functions and sequential importance sampling

We introduce techniques for deriving closed form generating functions for enumerating permutations with restricted positions keeping track of various statistics. The method involves evaluating permanents with variables as entries. These are applied to determine the sample size required for a novel sequential importance sampling algorithm for generating random perfect matchings in classes of bipartite graphs.

A particle filter-based data assimilation framework for discrete event simulations

With the advent of new sensor technologies and communication solutions, the availability of data for discrete event systems has greatly increased. This motivates research on data assimilation for discrete event simulations that has not yet fully matured. This paper presents a particle filter-based data assimilation framework for discrete event simulations. The framework is formally defined based on the Discrete Event System Specification formalism. To effectively apply particle filtering in discrete event simulations, we introduce an interpolation operation that considers the elapsed time (i.e., the time elapsed since the last state transition) when retrieving the model state (which was ignored in related work) in order to obtain updated state values. The data assimilation problem finally boils down to estimating the posterior distribution of a state trajectory with variable dimension. This seems to be problematic; however, it is proven that in practice we can safely apply the sequential importance sampling algorithm to update the random measure (i.e., a set of particles and their importance weights) that approximates this posterior distribution of the state trajectory with variable dimension. To illustrate the working of the proposed data assimilation framework, a case is studied in a gold mine system to estimate truck arrival times at the bottom of the vertical shaft. The results show that the framework is able to provide accurate estimation results in discrete event simulations; it is also shown that the framework is robust to errors both in the simulation model and in the data.

Gaussian Copula Regression in R

This article describes the R package gcmr for fitting Gaussian copula marginal regression models. The Gaussian copula provides a mathematically convenient framework to handle various forms of dependence in regression models arising, for example, in time series, longitudinal studies or spatial data. The package gcmr implements maximum likelihood inference for Gaussian copula marginal regression. The likelihood function is approximated with a sequential importance sampling algorithm in the discrete case. The package is designed to allow a flexible specification of the regression model and the dependence structure. Illustrations include negative binomial modeling of longitudinal count data, beta regression for time series of rates and logistic regression for spatially correlated binomial data.

Resampling: An improvement of importance sampling in varying population size models

Sequential importance sampling algorithms have been defined to estimate likelihoods in models of ancestral population processes. However, these algorithms are based on features of the models with constant population size, and become inefficient when the population size varies in time, making likelihood-based inferences difficult in many demographic situations. In this work, we modify a previous sequential importance sampling algorithm to improve the efficiency of the likelihood estimation. Our procedure is still based on features of the model with constant size, but uses a resampling technique with a new resampling probability distribution depending on the pairwise composite likelihood. We tested our algorithm, called sequential importance sampling with resampling (SISR) on simulated data sets under different demographic cases. In most cases, we divided the computational cost by two for the same accuracy of inference, in some cases even by one hundred. This study provides the first assessment of the impact of such resampling techniques on parameter inference using sequential importance sampling, and extends the range of situations where likelihood inferences can be easily performed.

Pseudo-Two-Dimensional (P2D) Reformulation Modeling of Li-Ion Batteries Using Kalman Filter (KF), Particle Filter (PF), and Hybrid Particle Filter (HPF) Algorithms

Accurate prediction of cell potential is necessary to extend the replacement interval of Lithium ion (Li-ion) batteries. This requires developing models that are capable of estimating battery state of charge (SOC), state of health (SOH), and remaining useful life (RUL). Previous studies have been completed to realize SOC, SOH, and RUL using equivalent circuit models (ECMs) with the KF technique. These ECMs have been used because they are computationally faster than physical based models. However, in their mathematical equations, ECMs do not fully account for the electrochemical material that makes up the battery or isothermal characteristics that continuously change during charging and discharging of the battery cells. Physical based battery modeling permits continuous monitoring of Li-ion cells during simple and complex isothermal changes for charging and discharging profiles. This paper examines multiple P2D models of Li-ion batteries using KF, PF, and HPF for a series, parallel, and series/parallel combination battery switching microcontroller based battery management system (BMS). Physical Models Physical based models are computationally complex, but they have the advantage of performing comprehensive analysis on the effects of both the solid state and the liquid state of the Li-ion battery, by modelling, porous electrode theory coupled with transport phenomena, and electrochemical reactions represented by coupled nonlinear partial differential equations in one or two dimensions. Efforts in [1], as related to battery degradation, focused on a physical based P2D reformulated model characterized by solid-electrolyte interface layer growth, constant current–constant voltage, and capacity fade to determine the manner in which extreme temperature and high charging rates affect the battery “cycle-life” and “calendar life.” This paper will simulate a reformulated P2D SOC and SOH convergence based model using the governing equations of a Single Particle Model (SPM) with lithium active particles as in [2] and [3]. Kalman Filter Methodology The KF is a linear quadratic estimation algorithm which uses observation measurements during a given time period to achieve a greater estimation of the battery system. EB (1) is the KF state model used in [4] and [5] to implement a SPM to estimate SOC of Li-ion cells. KF is an effective recursive prediction algorithm that works in two-steps: the prediction step (using the previous time step (k-1), measurement data, and Gaussian distributed white noise with covariance to forecast the current state) and the weighted average of the approximate next measurement. EB (1) Particle Filter Methodology The PF is a non-linear recursive Monte Carlo algorithm which estimates the posterior density of the state variable given a set of observation variables. The recursive Bayesian filter is implemented by the sequential importance sampling (SIS) algorithm, by associating weights to random samples representing the required posterior density. The SIS features are then adapted by the sequential importance resampling (SIR) algorithm in order to complete the resampling phase. The posterior PDF approximation can be defined by EB 2 and in [6]. EB (2) Hybrid Particle Filter (HPF) Methodology The HPF is a combination of the KF and PF algorithms for a given set of observation variables. In the HPF model, instead of a proposal and optimal random sample, the KF is implemented to get the initial values for Xk (proposal). EB (3) Results Battery discharged data is presented using the KF, PF, and HPF algorithms in Fig (1). Compared to the KF and PF models, the HPF model has a quicker initial convergence and better approximates the measured data across the discharge profile. Figure 1 Filter Comparison: Kalman, Particle, and Hybrid Particle Future work will include multiple reformulated physical based P2D PF battery technology models to simulate SOC, SOH, and RUL of a BMS. References Subramanian, Venkat R., et al. "Mathematical Model Reformulation for Lithium-Ion Battery Simulations: Galvanostatic Boundary Conditions." ECS 156.4 (2009): A260-71. Print.Northrop, Paul W. C., et al. "Efficient Simulation and Reformulation of Lithium-Ion Battery Models for Enabling Electric Transportation." ECS 161.8 (2014): E3149-57. Print.Prada, E., et al. “Simplified Electrochemical and Thermal Model of LiFePO4-Graphite Li-Ion Batteries for Fast Charge Applications.” ECS 159.9 (2012): A1508-19. PrintSanthanagopalan, Shriram, et al. "Review of Models for Predicting the Cycling Performance of Lithium Ion Batteries." JPS 156.2 (2006): 620-8. Print.Rahimian, S.K., S. Rayman, and R.E. White. “State of Charge and Loss of Active Material Estimation of a Lithium Ion Cell under Low Earth Orbit Condition Using Kalman Filtering Approaches.” ECS (2014): A860-A872.Arulampalam, M. S., et al. "A Tutorial on Particle Filters for Online nonlinear/non-Gaussian Bayesian Tracking." Signal Processing, IEEE Transactions on 50.2 (2002): 174-88. Print. Figure 1

Kalman Filtering with Unknown Sensor Measurement Losses

Abstract: This work studies the state estimation problem of a networked linear system where a sensor and an estimator are connected via a lossy network. If the measurement loss is known to the estimator, the minimum variance estimate is easily computed by the intermittent Kalman filter (IKF). However, this does not hold for the case of unknown measurement losses, and we have to address the non-Gaussianity/non-linearity of the networked system. By exploiting the measurement loss process and the IKF, we design three recursive suboptimal filters for state estimation, i.e., BKF-I, BKF-II and RBPF. The BKF-I is based on the MAP estimator of the loss process and the BKF-II is derived by an estimate of the conditional loss probability. The RBPF is an effective sequential importance sampling algorithm by marginalizing out the loss process. A target tracking example is included to illustrate their effectiveness and shows the tradeoff between computation complexity and estimation accuracy of the proposed filters.

Estimate the States of Pseudo-Two-Dimensional (P2D) Reformulation Model Li-Ion Battery Management System Using Non-Linear Particle Filter (PF) Compared to Linear Kalman Filter (KF)

Today’s battery cell environment, with the steady advances in technology and limited global resources, makes it imperative to know the approximate battery potential. In order to reduce cost and extend replacement interval of lithium ion (Li-ion) battery by knowing the best estimation of the battery cell State of Charge (SOC), State of Health (SOH), and Remaining Useful Life (RUL). Previous studies have been completed to realize SOC, SOH, and RUL using Equivalent Circuit Model (ECM) with the Kalman Filter technic. ECMs results have been used in previous studies, because they are computationally faster than physical based modelling, however, ECMs do not fully account for the electrochemical material that makes up the battery in their mathematical equations or isothermal characteristics that continuously change during charging and discharging of the battery cells. Physical based battery modelling permits continuous monitoring of Li-ion cells during simple and complex isothermal changes for charging and discharging profiles. This paper examines multiple P2D Li-ion technologies using PF versus KF for a series, parallel, and series/parallel combination battery switching microcontroller based battery management system (BMS). Physical Models Physical based models are computationally complex but they have the advantage of performing comprehensive analysis on the effects of both the solid state and the liquid state of the Li-ion battery, by modelling, porous electrode theory coupled with transport phenomena, and electrochemical reactions represented by coupled nonlinear partial differential equations in one or two dimensions. Efforts by Subramanian et al. [1] focused on a physical based P2D reformulated model characterized by solid-electrolyte interface layer growth, constant current–constant voltage, and capacity fade as it related to battery degradation to determine the manner in which extreme temperature and high charging rates affect the battery “cycle-life” and “calendar life.” This paper will simulate a reformulated P2D SOC and SOH convergence based model using the governing equations of a Single Particle Model (SPM) with lithium active particles as in Northrop [2] and Prada [3]. Equations 1-3 establish the boundary condition and Butler-Volmer kinetics formula for the Li-ion battery. Eq (1), Eq (2), Eq (3) Kalman Filter Methodology The KF is a linear quadratic estimation algorithm which uses observation measurements during a given time period to achieve a greater estimation of the battery system. Equation 4 is the Kalman Filter state model; Santhanagopalan [4] and Rahimian [5] used to implement a SPM with Kalman filtering methods to estimate SOC of Li-ion cells. KF is an effective recursive prediction algorithm that works in two-steps: the prediction step (using the previous time step (k-1), measurement data, and Gaussian distributed white noise with covariance to forecast the current state) and the weighted average of the approximate next measurement. Eq (4) Particle Filter Methodology The PF is a non-linear recursive Monte Carlo algorithm which estimates the posterior density of the state variable given a set of observation variables. The recursive Bayesian filter is implemented by the sequential importance sampling (SIS) algorithm, by associating weights to random samples representing the required posterior density. The SIS features are then adapted by the sequential importance resampling (SIR) algorithm in order to complete the resampling phase. The posterior PDF approximation can be defined by equation 5 and in [5]. Eq (5) Results Figure 1 Simulated Measured (noisy), SIS, and SIR filtered battery discharge data. Figure 1 Battery Voltage Profile Future work will include multiple reformulated physical based P2D PF battery technology models to simulate SOC, SOH, and RUL of a BMS. References Subramanian, Venkat R., et al. "Mathematical Model Reformulation for Lithium-Ion Battery Simulations: Galvanostatic Boundary Conditions." ECS 156.4 (2009): A260-71. Print.Northrop, Paul W. C., et al. "Efficient Simulation and Reformulation of Lithium-Ion Battery Models for Enabling Electric Transportation." ECS 161.8 (2014): E3149-57. Print.Prada, E., et al. “Simplified Electrochemical and Thermal Model of LiFePO4-Graphite Li-Ion Batteries for Fast Charge Applications.” ECS 159.9 (2012): A1508-19. PrintSanthanagopalan, Shriram, et al. "Review of Models for Predicting the Cycling Performance of Lithium Ion Batteries." JPS 156.2 (2006): 620-8. Print.Rahimian, S.K., S. Rayman, and R.E. White. “State of Charge and Loss of Active Material Estimation of a Lithium Ion Cell under Low Earth Orbit Condition Using Kalman Filtering Approaches.” ECS (2014): A860-A872.Arulampalam, M. S., et al. "A Tutorial on Particle Filters for Online nonlinear/non-Gaussian Bayesian Tracking." Signal Processing, IEEE Transactions on 50.2 (2002): 174-88. Print. Figure 1

Using Pseudo-Two-Dimensional (P2D) Reformulation Model with a Particle Filter to Estimate State of Charge, State of Health, and Remaining Useful Life in Li-Ion Battery Management System (BMS)

Discovering the precise state of charge (SOC), state of health (SOH), and remaining useful life (RUL) while monitoring depth of discharge (DOD) for Lithium ion (Li-ion) batteries can be computational enormous. Electrical engineers using equivalent circuit models (ECM) or enhanced equivalent circuit models (EECM) have achieved an acceptable level of accuracy modelling the current, voltage, and temperature behaviors to get SOC, SOH, RUL, and DOD. ECMs and EECMs are computationally fast but do not fully account for the electrochemical material that makes up the battery in their mathematical equations or isothermal characteristics that continuously change during charging and discharging. Chemical engineers have achieved greater levels of accuracy using physical-based models over ECMs and EECMs. Unfortunately, the number of factors and variables needed to compute the system of differential algebraic equations for the nonlinear physical-based models to achieve this level of precise data is computationally too expensive for real-time systems. In today’s environment, the use of filters has provided a bridge between empirical and physical based models. This paper examines an ECM and a porous electrode pseudo two-dimensional (P2D) model using particle filter (PF) technology for a series, parallel, and series/parallel combination battery switching microcontroller based battery management system (BMS). Mathematical and Physical Models BMSs are developed to manage the charging and discharging profile, and basic knowledge of all the states that the battery topology goes through is paramount in order to design a safe and more sustainable battery system. ECMs are used in BMSs because they can model battery characteristics for a desired state using resistors and capacitors to emulate the internal battery cell resistance and capacitance behaviors. Because ECMs are linearly based mathematical equations, simulation of these models can be performed quickly. Additionally, Kalman filtering techniques (KFT) have been used extensively with ECMs to assist in the estimation of the SOC and SOH for BMSs. However, the effectiveness of ECMs and KFTs are not optimal for the non-linear behavior of batteries. Physical based models have the advantage of performing comprehensive analysis on the effects of both the solid phase and the liquid phase, but they can be computationally complex. Modelling, porous electrode theory coupled with transport phenomena, and electrochemical reactions represented by coupled nonlinear partial differential equations in one or two dimensions give physical based models an advantage over ECMs. Santhanagopalan [1] and Rahimian [2] have used the single particle model (SPM) implementing Kalman filtering methods to estimate SOC of Li-ion cells. Efforts by Subramanian et al. [3] focused on a physical based P2D reformulated model characterized by solid-electrolyte interface layer growth, constant current–constant voltage, and capacity fade as it related to battery degradation to determine the manner in which extreme temperature and high charging rates affect the battery “calendar life.” This paper will simulate a reformulated P2D SOC and SOH convergence based model using the governing equations of a SPM with lithium active particles as in Northrop [4]: Eq (1), Eq (2), Eq (3) Particle Filter Methodology The PF is an algorithm based on a recursive Monte Carlo technique of estimating the posterior density of the state variable given a set of observation variables. The sequential importance sampling (SIS) algorithm implements the recursive Bayesian filter by associating weights to random samples representing the required posterior density. The sequential importance resampling (SIR) filter adapts the SIS features and adds a resampling phase. The posterior PDF approximation can be defined as in [5]: Eq (4), Eq (5) Results Figure 1(a) shows the simulated discharge (at 1C rate) of a 1.2 Volt Li-ion battery at 100% SOC using an empirical ECM in MatLab Simulink. Figure 1(b) includes simulated measured (noisy), SIS, and SIR filtered battery discharge data. Figure 1 Battery Voltage Profile Future work will include a reformulated physical based P2D PF battery model to simulate SOC, SOH, and RUL of a BMS. References Santhanagopalan, Shriram, et al. "Review of Models for Predicting the Cycling Performance of Lithium Ion Batteries." JPS 156.2 (2006): 620-8. Print. Rahimian, S.K., S. Rayman, and R.E. White. “State of Charge and Loss of Active Material Estimation of a Lithium Ion Cell under Low Earth Orbit Condition Using Kalman Filtering Approaches.” ECS (2014): A860-A872. Subramanian, Venkat R., et al. "Mathematical Model Reformulation for Lithium-Ion Battery Simulations: Galvanostatic Boundary Conditions." ECS 156.4 (2009): A260-71. Print.Northrop, Paul W. C., et al. "Efficient Simulation and Reformulation of Lithium-Ion Battery Models for Enabling Electric Transportation." ECS 161.8 (2014): E3149-57. Print.Arulampalam, M. S., et al. "A Tutorial on Particle Filters for Online nonlinear/non-Gaussian Bayesian Tracking." Signal Processing, IEEE Transactions on 50.2 (2002): 174-88. Print. Figure 1

Sequential Monte Carlo for counting vertex covers in general graphs

In this paper we describe a sequential importance sampling (SIS) procedure for counting the number of vertex covers in general graphs. The optimal SIS proposal distribution is the uniform over a suitably restricted set, but is not implementable. We will consider two proposal distributions as approximations to the optimal. Both proposals are based on randomization techniques. The first randomization is the classic probability model of random graphs, and in fact, the resulting SIS algorithm shows polynomial complexity for random graphs. The second randomization introduces a probabilistic relaxation technique that uses Dynamic Programming. The numerical experiments show that the resulting SIS algorithm enjoys excellent practical performance in comparison with existing methods. In particular the method is compared with cachet--an exact model counter, and the state of the art SampleSearch, which is based on Belief Networks and importance sampling.

A New Approach to Importance Sampling in Taylor’s Stochastic Volatility Model

This article presents the general analysis of finite high-dimensional integrals using the Importance Sampling (IS) in aim to the parameter estimation of Taylor’s stochastic volatility (SV) model. After we proceed to make an alternative derivation for Sequential Importance Sampling (SIS) in previous literatures, we propose a new approach to select the optimal parameters of sampler, which is called as Universal Importance Sampling (UIS). UIS minimizes the Monte Carlo variance and numerically performs at least the same accurately as the SIS algorithm, but the computational efficiency get greatly improved. We apply both methods and investigate the SV model on the data, then make comparisons of the results.

Fast Sequential Importance Sampling to Estimate the Graph Reliability Polynomial

The reliability polynomial of a graph counts its connected subgraphs of various sizes. Algorithms based on sequential importance sampling (SIS) have been proposed to estimate a graph’s reliability polynomial. We develop an improved SIS algorithm for estimating the reliability polynomial. The new algorithm runs in expected time O(mlogn α(m,n)) at worst and ≈m in practice, compared to Θ(m 2) for the previous algorithm. We analyze the error bounds of this algorithm, including comparison to alternative estimation algorithms. In addition to the theoretical analysis, we discuss methods for estimating the variance and describe experimental results on a variety of random graphs.

Spatiotemporal Alignment of Visual Signals on a Special Manifold

We investigate the problem of spatiotemporal alignment of videos, signals, or feature sequences extracted from them. Specifically, we consider the scenario where the spatiotemporal misalignments can be characterized by parametric transformations. Using a nonlinear analytical structure referred to as an alignment manifold, we formulate the alignment problem as an optimization problem on this nonlinear space. We focus our attention on semantically meaningful videos or signals, e.g., those describing or capturing human motion or activities, and propose a new formalism for temporal alignment accounting for executing rate variations among instances of the same video event. The strategy taken in this effort bridges the family of geometric optimization and the family of stochastic algorithms: We regard the search for optimal alignment parameters as a recursive state estimation problem for a particular dynamic system evolving on the alignment manifold. Subsequently, a Sequential Importance Sampling procedure on the alignment manifold is designed for effective alignment. We further extend the basic Sequential Importance Sampling algorithm into a new version called Stochastic Gradient Sequential Importance Sampling, in which we incorporate a steepest descent structure on the alignment manifold and provide a more efficient particle propagation mechanism. We demonstrate the performance of alignment using manifolds on several types of input data that arise in vision problems.

Negative Examples for Sequential Importance Sampling of Binary Contingency Tables

The sequential importance sampling (SIS) algorithm has gained considerable popularity for its empirical success. One of its noted applications is to the binary contingency tables problem, an important problem in statistics, where the goal is to estimate the number of 0/1 matrices with prescribed row and column sums. We give a family of examples in which the SIS procedure, if run for any subexponential number of trials, will underestimate the number of tables by an exponential factor. This result holds for any of the usual design choices in the SIS algorithm, namely the ordering of the columns and rows. These are apparently the first theoretical results on the efficiency of the SIS algorithm for binary contingency tables. Finally, we present experimental evidence that the SIS algorithm is efficient for row and column sums that are regular. Our work is a first step in determining the class of inputs for which SIS is effective.