Expectation–maximization algorithm

About: Expectation–maximization algorithm is a research topic. Over the lifetime, 11823 publications have been published within this topic receiving 528693 citations. The topic is also known as: EM algorithm & Expectation Maximization.

A Maximum Likelihood Approach to Emission Image Reconstruction from Projections

Abstract: The stochastic nature of the measurements used for image reconstruction from projections has largely been ignored in the past. If taken into account, the stochastic nature has been used to calculate the performance of algorithms which were developed independent of probabilistic considerations. This paper utilizes the knowledge of the probability density function of the measurements from the outset, and derives a reconstruction scheme which is optimal in the maximum likelihood sense. This algorithm is shown to yield an image which is unbiased -- that is, on the average it equals the object being reconstructed -- and which has the minimum variance of any estimator using the same measurements. As such, when operated in a stochastic environment, it will perform better than any current reconstruction technique, where the performance measures are the bias and viariance.

Unsupervised learning of human motion

Abstract: An unsupervised learning algorithm that can obtain a probabilistic model of an object composed of a collection of parts (a moving human body in our examples) automatically from unlabeled training data is presented. The training data include both useful "foreground" features as well as features that arise from irrelevant background clutter - the correspondence between parts and detected features is unknown. The joint probability density function of the parts is represented by a mixture of decomposable triangulated graphs which allow for fast detection. To learn the model structure as well as model parameters, an EM-like algorithm is developed where the labeling of the data (part assignments) is treated as hidden variables. The unsupervised learning technique is not limited to decomposable triangulated graphs. The efficiency and effectiveness of our algorithm is demonstrated by applying it to generate models of human motion automatically from unlabeled image sequences, and testing the learned models on a variety of sequences.

Fitting regression models to case-control data by maximum likelihood

Abstract: SUMMARY We consider fitting categorical regression models to data obtained by either stratified or nonstratified case-control, or response selective, sampling from a finite population with known population totals in each response category. With certain models, such as the logistic with appropriate constant terms, a method variously known as conditional maximum likelihood (Breslow & Cain, 1988) or pseudo-conditional likelihood (Wild, 1991), which involves the prospective fitting of a pseudo-model, results in maximum likelihood estimates of case-control data. We extend these results by showing the maximum likelihood estimates for any model can be found by iterating this process with a simple updating of offset parameters. Attention is also paid to estimation of the asymptotic covariance matrix. One benefit of the results of this paper is the ability to obtain maximum likelihood estimates of the parameters of logistic models for stratified case-control studies, compare Breslow & Cain (1988), Scott & Wild (1991), using an ordinary logistic regression program, even when the stratum constants are modelled.