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.

Maximum Likelihood in a Generalized Linear Finite Mixture Model by Using the EM Algorithm

Abstract: A generalized linear finite mixture model and an EM algorithm to fit the model to data are described. By this approach the finite mixture model is embedded within the general framework of generalized linear models (GLMs). Implementation of the proposed EM algorithm can be readily done in statistical packages with facilities for GLMs. A practical example is presented where a generalized linear finite mixture model of ten Weibull distributions is adopted. The example is concerned with the flow cytometric measurement of the DNA content of spermatids in a mutant mouse, which shows non-disjunction of specific chromosomes during meiosis.

The MM Alternative to EM

Abstract: The EM algorithm is a special case of a more general algorithm called the MM algorithm. Specific MM algorithms often have nothing to do with missing data. The first M step of an MM algorithm creates a surrogate function that is optimized in the second M step. In minimization, MM stands for majorize--minimize; in maximization, it stands for minorize--maximize. This two-step process always drives the objective function in the right direction. Construction of MM algorithms relies on recognizing and manipulating inequalities rather than calculating conditional expectations. This survey walks the reader through the construction of several specific MM algorithms. The potential of the MM algorithm in solving high-dimensional optimization and estimation problems is its most attractive feature. Our applications to random graph models, discriminant analysis and image restoration showcase this ability.

Fast Joint Detection-Estimation of Evoked Brain Activity in Event-Related fMRI Using a Variational Approach

Abstract: In standard within-subject analyses of event-related functional magnetic resonance imaging (fMRI) data, two steps are usually performed separately: detection of brain activity and estimation of the hemodynamic response. Because these two steps are inherently linked, we adopt the so-called region-based joint detection-estimation (JDE) framework that addresses this joint issue using a multivariate inference for detection and estimation. JDE is built by making use of a regional bilinear generative model of the BOLD response and constraining the parameter estimation by physiological priors using temporal and spatial information in a Markovian model. In contrast to previous works that use Markov Chain Monte Carlo (MCMC) techniques to sample the resulting intractable posterior distribution, we recast the JDE into a missing data framework and derive a variational expectation-maximization (VEM) algorithm for its inference. A variational approximation is used to approximate the Markovian model in the unsupervised spatially adaptive JDE inference, which allows automatic fine-tuning of spatial regularization parameters. It provides a new algorithm that exhibits interesting properties in terms of estimation error and computational cost compared to the previously used MCMC-based approach. Experiments on artificial and real data show that VEM-JDE is robust to model misspecification and provides computational gain while maintaining good performance in terms of activation detection and hemodynamic shape recovery.

Real-time Body Tracking Using a Gaussian Process Latent Variable Model

Abstract: In this paper, we present a tracking framework for capturing articulated human motions in real-time, without the need for attaching markers onto the subject's body. This is achieved by first obtaining a low dimensional representation of the training motion data, using a nonlinear dimensionality reduction technique called back-constrained GPLVM. A prior dynamics model is then learnt from this low dimensional representation by partitioning the motion sequences into elementary movements using an unsupervised EM clustering algorithm. The temporal dependencies between these elementary movements are efficiently captured by a Variable Length Markov Model. The learnt dynamics model is used to bias the propagation of candidate pose feature vectors in the low dimensional space. By combining this with an efficient volumetric reconstruction algorithm, our framework can quickly evaluate each candidate pose against image evidence captured from multiple views. We present results that show our system can accurately track complex structured activities such as ballet dancing in real-time.