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A tutorial on particle filtering and smoothing: fifteen years later
 OXFORD HANDBOOK OF NONLINEAR FILTERING
, 2011
"... Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. r ..."
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Cited by 206 (15 self)
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Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. recursively as observations become available, and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, uptodate survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.
Event queries on correlated probabilistic streams (full version
, 2008
"... A major problem in detecting events in streams of data is that the data can be imprecise (e.g. RFID data). However, current stateoftheart event detection systems such as Cayuga [14], SASE [46] or SnoopIB[1], assume the data is precise. Noise in the data can be captured using techniques such as hi ..."
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Cited by 60 (16 self)
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A major problem in detecting events in streams of data is that the data can be imprecise (e.g. RFID data). However, current stateoftheart event detection systems such as Cayuga [14], SASE [46] or SnoopIB[1], assume the data is precise. Noise in the data can be captured using techniques such as hidden Markov models. Inference on these models creates streams of probabilistic events which cannot be directly queried by existing systems. To address this challenge we propose Lahar1, an event processing system for probabilistic event streams. By exploiting the probabilistic nature of the data, Lahar yields a much higher recall and precision than deterministic techniques operating over only the most probable tuples. By using a novel static analysis and novel algorithms, Lahar processes data orders of magnitude more efficiently than a naïve approach based on sampling. In this paper, we present Lahar’s static analysis and core algorithms. We demonstrate the quality and performance of our approach through experiments with our prototype implementation and comparisons with alternate methods.
Unscented RauchTungStriebel Smoother
"... This article considers the application of the unscented transform to optimal smoothing of nonlinear state space models. In this article, a new RauchTungStriebel type form of the fixedinterval unscented Kalman smoother is derived. The new smoother differs from the previously proposed twofilter f ..."
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Cited by 37 (3 self)
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This article considers the application of the unscented transform to optimal smoothing of nonlinear state space models. In this article, a new RauchTungStriebel type form of the fixedinterval unscented Kalman smoother is derived. The new smoother differs from the previously proposed twofilter formulation based unscented Kalman smoother in the sense that it is not based on running two independent filters forward and backward in time. Instead, a separate backward smoothing pass is used, which recursively computes corrections to the forward filtering result. The smoother equations are derived as approximations to the formal Bayesian optimal smoothing equations. The performance of the new smoother is demonstrated with a simulation.
Automatic online tuning for fast Gaussian summation
"... Many machine learning algorithms require the summation of Gaussian kernel functions, an expensive operation if implemented straightforwardly. Several methods have been proposed to reduce the computational complexity of evaluating such sums, including tree and analysis based methods. These achieve va ..."
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Cited by 35 (13 self)
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Many machine learning algorithms require the summation of Gaussian kernel functions, an expensive operation if implemented straightforwardly. Several methods have been proposed to reduce the computational complexity of evaluating such sums, including tree and analysis based methods. These achieve varying speedups depending on the bandwidth, dimension, and prescribed error, making the choice between methods difficult for machine learning tasks. We provide an algorithm that combines tree methods with the Improved Fast Gauss Transform (IFGT). As originally proposed the IFGT suffers from two problems: (1) the Taylor series expansion does not perform well for very low bandwidths, and (2) parameter selection is not trivial and can drastically affect performance and ease of use. We address the first problem by employing a tree data structure, resulting in four evaluation methods whose performance varies based on the distribution of sources and targets and input parameters such as desired accuracy and bandwidth. To solve the second problem, we present an online tuning approach that results in a black box method that automatically chooses the evaluation method and its parameters to yield the best performance for the input data, desired accuracy, and bandwidth. In addition, the new IFGT parameter selection approach allows for tighter error bounds. Our approach chooses the fastest method at negligible additional cost, and has superior performance in comparisons with previous approaches. 1
Sequential Monte Carlo smoothing for general state space Hidden Markov Models
 Ann. Appl. Probab
, 2011
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Online Empirical Evaluation of Tracking Algorithms
, 2009
"... Evaluation of tracking algorithms in the absence of ground truth is a challenging problem. There exist a variety of approaches for this problem, ranging from formal model validation techniques to heuristics that look for mismatches between track properties and the observed data. However, few of thes ..."
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Cited by 12 (0 self)
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Evaluation of tracking algorithms in the absence of ground truth is a challenging problem. There exist a variety of approaches for this problem, ranging from formal model validation techniques to heuristics that look for mismatches between track properties and the observed data. However, few of these methods scale up to the task of visual tracking where the models are usually nonlinear and complex, and typically lie in a high dimensional space. Further, scenarios that cause track failures and/or poor tracking performance are also quite diverse for the visual tracking problem. In this paper, we propose an online performance evaluation strategy for tracking systems based on particle filters using a timereversed Markov chain. The keu intuition of our proposed methodology relies on the timereversible nature of physical motion exhibited by most objects, which in turn should be possessed by a good tracker. In the presence of tracking failures due to occlusion, low SNR or modeling errors, this reversible nature of the tracker is violated. We use this property for detection of track failures. To evaluate the performance of the tracker at time instant t, we use the posterior of the tracking algorithm to initialize a timereversed Markov chain. We compute the posterior density of track parameters at the starting time t = 0 by filtering back in time to the initial time instant. The distance between the
An expectation maximization algorithm for continuous markov decision processes with arbitrary rewards
 IN TWELFTH INT. CONF. ON ARTIFICIAL INTELLIGENCE AND STATISTICS (AISTATS
, 2009
"... We derive a new expectation maximization algorithm for policy optimization in linear Gaussian Markov decision processes, where the reward function is parameterized in terms of a flexible mixture of Gaussians. This approach exploits both analytical tractability and numerical optimization. Consequentl ..."
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Cited by 12 (2 self)
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We derive a new expectation maximization algorithm for policy optimization in linear Gaussian Markov decision processes, where the reward function is parameterized in terms of a flexible mixture of Gaussians. This approach exploits both analytical tractability and numerical optimization. Consequently, on the one hand, it is more flexible and general than closedform solutions, such as the widely used linear quadratic Gaussian (LQG) controllers. On the other hand, it is more accurate and faster than optimization methods that rely on approximation and simulation. Partial analytical solutions (though costly) eliminate the need for simulation and, hence, avoid approximation error. The experiments will show that for the same cost of computation, policy optimization methods that rely on analytical tractability have higher value than the ones that rely on simulation.
EP for Efficient Stochastic Control with Obstacles
"... We address the problem of continuous stochastic optimal control in the presence of hard obstacles. Due to the nonsmooth character of the obstacles, the traditional approach using dynamic programming in combination with function approximation tends to fail. We consider a recently introduced special ..."
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Cited by 8 (1 self)
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We address the problem of continuous stochastic optimal control in the presence of hard obstacles. Due to the nonsmooth character of the obstacles, the traditional approach using dynamic programming in combination with function approximation tends to fail. We consider a recently introduced special class of control problems for which the optimal control computation is reformulated in terms of a path integral. The path integral is typically intractable, but amenable to techniques developed for approximate inference.We argue that the variational approach fails in this case due to the nonsmooth cost function. Sampling techniques are simple to implement and converge to the exact results given enough samples. However, the infinite cost associated with hard obstacles renders the sampling procedures inefficient in practice. We suggest Expectation Propagation (EP) as a suitable approximation method, and compare the quality and efficiency of the resulting control with an MC sampler on a car steering task and a ball throwing task. We conclude that EP can solve these challenging problems much better than a sampling approach.
Particle Filtering and Smoothing: Fifteen years Later, Handbook of Nonlinear Filtering
"... Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit finitedimensional solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online mann ..."
Abstract

Cited by 7 (0 self)
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Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit finitedimensional solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner (that is, recursively, as observations become available), and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, uptodate survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.