We propose an algorithm for simultaneously detecting and locating changepoints in a time series, and a framework for predicting the distribution of the next point in the series. The kernel of the algorithm is a system of equations that computes, for each index i, the probability that the last (most recent) change point occurred at i. We evaluate this algorithm by applying it to the change point detection problem and comparing it to the generalized likelihood ratio (GLR) algorithm. We find that our algorithm is as good as GLR, or better, over a wide range of scenarios, and that the advantage increases as the signal-to-noise ratio decreases.
In a seminal paper on the tracking problem, Chernoff and Zacks present a Bayesian estimator for the current mean of a process with abrupt changes @cite_1 . Like us, they start with an estimator that assumes there is at most one change, and then use it to generate an approximate estimator in the general case. Their algorithm makes the additional assumption that the change size is distributed normally; our algorithm does not require this assumption. Also, our algorithm generates a predictive distribution for the next value in the series, rather than an estimate of the current mean.
@cite_1
2095283167 2112329933 2523331129 2096404799
Abstract : A tracking problem is considered. Observations are taken on the successive positions of an object traveling on a path, and it is desired to estimate its current position. The objective is to arrive at a simple formula which implicitly accounts for possible changes in direction and discounts observations taken before the latest change. To develop a reasonable procedure, a simpler problem is studied. Successive observations are taken on n independently and normally distributed random variables X sub 1, X sub 2, ..., X sub n with means mu sub 1, mu sub 2, ..., mu sub n and variance 1. Each mean mu sub i is equal to the preceding mean mu sub (i-1) except when an occasional change takes place. The object is to estimate the current mean mu sub n. This problem is studied from a Bayesian point of view. An 'ad hoc' estimator is described, which applies a combination of the A.M.O.C. Bayes estimator and a sequence of tests designed to locate the last time point of change. The various estimators are then compared by a Monte Carlo study of samples of size 9. This Bayesian approach seems to be more appropriate for the related problem of testing whether a change in mean has occurred. This test procedure is simpler than that used by Page. The power functions of the two procedures are compared. (Author) 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 time-reversed Markov chain. The key intuition of our proposed methodology relies on the time-reversible 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 time-reversed 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 posterior density of the time-reversed chain (at t = 0) and the prior density used to initialize the tracking algorithm forms the decision statistic for evaluation. It is observed that when the data are generated by the underlying models, the decision statistic takes a low value. We provide a thorough experimental analysis of the evaluation methodology. Specifically, we demonstrate the effectiveness of our approach for tackling common challenges such as occlusion, pose, and illumination changes and provide the Receiver Operating Characteristic (ROC) curves. Finally, we also show the applicability of the core ideas of the paper to other tracking algorithms such as the Kanade-Lucas-Tomasi (KLT) feature tracker and the mean-shift tracker. Generally speaking, research in the field of estimation involves designing strong estimators, i.e., those which converge with probability 1, as the number of samples increases indefinitely. But when the underlying distribution is nonstationary, one should rather seek for weak estimators, i.e., those which can unlearn when the distribution has changed. One such estimator, the so-called stochastic learning weak estimator (SLWE) was based on the principles of continuous stochastic learning automata (LA). A problem that has been unsolved has been that of designing such weak estimators in the context of systems with finite memory, which is what we investigate here. In this paper, we propose a new family of stochastic discretized weak estimators which can track time-varying binomial 1 distributions. As opposed to the SLWE, our proposed estimator is discretized, 2 i.e., the estimate can assume only a finite number of values. By virtue of discretization, our estimator realizes extremely fast adjustments of the running estimates by executing jumps, and it is thus able to robustly, and very quickly, track changes in the parameters of the distribution after a switch has occurred. The design principle of our strategy is based on a solution for the stochastic search on the line problem. In order to achieve efficient estimation, we have to first infer (or rather simulate) an Artificial Oracle which informs the LA whether to go right or left, which is then utilized to infer whether we are to increase the current estimate or to decrease it. This paper briefly reports pioneering and conclusive experimental results that demonstrate the ability of the proposed estimator to cope with nonstationary environments. 1 The extension to multinomial and to other distributions is straightforward. We introduce an algorithm for tracking deformable objects from a sequence of point clouds. The proposed tracking algorithm is based on a probabilistic generative model that incorporates observations of the point cloud and the physical properties of the tracked object and its environment. We propose a modified expectation maximization algorithm to perform maximum a posteriori estimation to update the state estimate at each time step. Our modification makes it practical to perform the inference through calls to a physics simulation engine. This is significant because (i) it allows for the use of highly optimized physics simulation engines for the core computations of our tracking algorithm, and (ii) it makes it possible to naturally, and efficiently, account for physical constraints imposed by collisions, grasping actions, and material properties in the observation updates. Even in the presence of the relatively large occlusions that occur during manipulation tasks, our algorithm is able to robustly track a variety of types of deformable objects, including ones that are one-dimensional, such as ropes; two-dimensional, such as cloth; and three-dimensional, such as sponges. Our implementation can track these objects in real time.