This paper describes a probabilistic decomposition of human dynamics at multiple abstractions, and shows how to propagate hypotheses across space, time, and abstraction levels. Recognition in this framework is the succession of very general low level grouping mechanisms to increased specific and learned model based grouping techniques at higher levels. Hard decision thresholds are delayed and resolved by higher level statistical models and temporal context. Low-level primitives are areas of coherent motion found by EM clustering, mid-level categories are simple movements represented by dynamical systems, and highlevel complex gestures are represented by Hidden Markov Models as successive phases of simple movements. We show how such a representation can be learned from training data, and apply it to the example of human gait recognition. 1 Introduction This paper addresses the problem of learning and recognizing human and other biological movements in video sequences of an unconstrai...

We define ordered subset processing for standard algorithms (such as Expectation Maximization, EM) for image restoration from projections. Ordered subsets methods group projection data into an ordered sequence of subsets (or blocks). An iteration of ordered subsets EM is defined as a single pass through all the subsets, in each subset using the current estimate to initialise application of EM with that data subset. This approach is similar in concept to block-Kaczmarz methods introduced by Eggermont et al [1] for iterative reconstruction. Simultaneous iterative reconstruction (SIRT) and multiplicative algebraic reconstruction (MART) techniques are well known special cases. Ordered subsets EM (OS-EM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm. OS-EM is applicable in both single photon (SPECT) and positron emission tomography (PET). In simulation studies in SPECT the OS-EM algorithm provides an order-ofmagnitude acceleration ...

The expectation-maximization (EM) method can facilitate maximizing likelihood functions that arise in statistical estimation problems. In the classical EM paradigm, one iteratively maximizes the conditional loglikelihood of a single unobservable complete data space, rather than maximizing the intractable likelihood function for the measured or incomplete data. EM algorithms update all parameters simultaneously, which has two drawbacks: 1) slow convergence, and 2) difficult maximization steps due to coupling when smoothness penalties are used. This paper describes the space-alternating generalized EM (SAGE) method, which updates the parameters sequentially by alternating between several small hidden-data spaces defined by the algorithm designer. We prove that the sequence of estimates monotonically increases the penalizedlikelihood objective, we derive asymptotic convergence rates, and we provide sufficient conditions for monotone convergence in norm. Two signal processing applicatio...

This paper reviews and compares three maximum likelihood algorithms for transmission tomography. One of these algorithms is the EM algorithm, one is based on a convexity argument devised by De Pierro in the context of emission tomography, and one is an ad hoc gradient algorithm. The algorithms enjoy desirable local and global convergence properties and combine gracefully with Bayesian smoothing priors. Preliminary numerical testing of the algorithms on simulated data suggest that the convex algorithm and the ad hoc gradient algorithm are computationally superior to the EM algorithm. This superiority stems from the larger number of exponentiations required by the EM algorithm. The convex and gradient algorithms are well adapted to parallel computing. Key words: maximum likelihood, smoothing prior, EM algorithm, convergence I. Introduction T HE value of the EM algorithm in emission tomography is now well established [22], [17], [24]. Not as widely appreciated is the potential of the EM...

The EM algorithm is a popular method for parameter estimation in a variety of problems involving missing data. However, the EM algorithm often requires signi cant computational resources and has been dismissed as impractical for large databases. We presenttwo approaches that signi cantly reduce the computational cost of applying the EM algorithm to databases with a large number of cases, including databases with large dimensionality. Both approaches are based on partial E-steps for which we can use the results of Neal and Hinton (1998) to obtain the standard convergence guarantees of EM. The rst approach is a version of the incremental EM, described in Neal and Hinton (1998), which cycles through data cases in blocks. The number of cases in each block dramatically e ects the e ciency of the algorithm. We provide a method for selecting a near optimal block size. The second approach, which we call lazy EM, will, at scheduled iterations, evaluate the signi cance of each data case and then proceed for several iterations actively using only the signi cant cases. We demonstrate that both methods can signi cantly reduce computational costs through their application to high-dimensional real-world and synthetic mixture modeling problems for large databases. Keywords: Expectation Maximization Algorithm, incremental EM, lazy EM, online EM, data blocking, mixture models, clustering.

Probabilistic expert systems based on Bayesian networks (BNs) require initial specification of both a qualitative graphical structure and quantitative assessment of conditional probability tables. This paper considers statistical batch learning of the probability tables on the basis of incomplete data and expert knowledge. The EM algorithm with a generalized conjugate gradient acceleration method has been dedicated to quantification of BNs by maximum posterior likelihood estimation for a super-class of the recursive graphical models. This new class of models allows a great variety of local functional restrictions to be imposed on the statistical model, which hereby extents the control and applicability of the constructed method for quantifying BNs. Introduction The construction of probabilistic expert systems (Pearl 1988, Andreassen et al. 1989) based on Bayesian networks (BNs) is often a challenging process. It is typically divided into two parts: First the constructi...

We compare three different stochastic versions of the EM algorithm: The SEM algorithm, the SAEM algorithm and the MCEM algorithm. We suggest that the most relevant contribution of the MCEM methodology is what we call the simulated annealing MCEM algorithm, which turns out to be very close to SAEM. We focus particularly on the mixture of distributions problem. In this context, we review the available theoretical results on the convergence of these algorithms and on the behavior of SEM as the sample size tends to infinity. The second part is devoted to intensive Monte Carlo numerical simulations and a real data study. We show that, for some particular mixture situations, the SEM algorithm is almost always preferable to the EM and simulated annealing versions SAEM and MCEM. For some very intricate mixtures, however, none of these algorithms can be confidently used. Then, SEM can be used as an efficient data exploratory tool for locating significant maxima of the likelihood function. In the real data case, we show that the SEM stationary distribution provides a contrasted view of the loglikelihood by emphasizing sensible maxima.

this paper are motivated and aimed at analyzing some common types of survival data from different medical studies. We will center our attention to the following topics.

was supported by ONR grants N00014-96-1-0192 and N00014-96-1-0330. The authors are Clustering on principal curves combines parametric modeling of noise with nonparametric modeling of feature shape. This is useful for detecting curvilinear features in spatial point patterns, with or without background noise. Applications of this include the detection of curvilinear mine elds from reconnaissance images, some of the points in which represent false detections, and the detection of seismic faults from earthquake catalogs. Our algorithm for principal curve clustering is in two steps: the rst is hierarchical and agglomerative (HPCC), and the second consists of iterative relocation based on the Classi cation EM algorithm (CEM-PCC). HPCC is used to combine potential feature clusters, while CEM-PCC re nes the results and deals with background noise. It is importanttohave a good starting point for the algorithm: this can be found manually or automatically using, for example, nearest neighbor clutter removal or model-based clustering. We choose the number of features and the amount of smoothing simultaneously using approximate Bayes

We apply the idea of averaging ensembles of estimators to probability density estimation.