The HMM (Hidden Markov Model) is a probabilistic model of the joint probability of a collection of random variables with both observations and states. The GMM (Gaussian Mixture Model) is a finite mixture probability distribution model. Although the two models have a close relationship, they are always discussed independently and separately. The EM (Expectation-Maximum) algorithm is a general me...

We propose an Expectation-Maximization (EM) algorithm which works on binary decision diagrams (BDDs). The proposed algorithm, BDD-EM algorithm, opens a way to apply BDDs to statistical learning. The BDD-EM algorithm makes it possible to learn probabilities in statistical models described by Boolean formulas, and the time complexity is proportional to the size of BDDs representing them. We apply...

We perform sequence estimation for CPM signals transmitted in a time varying multipath channel. The EM (Expectation-Maximization) algorithm, an iterative proce dure for producing maximum likelihood estimates, is applied to handle the unknown channel. In order to enable implementation of the EM algorithm in this system, a simplification of this algorithm is derived. Channel estimates derived fro...

Introduction My aim is to introduce the Expectation Maximization EM algorithm to you especially some of its theory I will skip proofs but I will derive many formulae that have practical use The EM algorithm is iterative and you should be familiar with its convergence properties I will discuss them in detail I will present applications of the EM algorithm to signal and image processing in a comp...

In this paper, we study a flow shop batch processing machines scheduling problem. The fuzzy due dates are considered to make the problem more close to the reality. The objective function is taken as the weighted sum of fuzzy earliness and fuzzy tardiness. In order to tackle the given problem, we propose a hybrid electromagnetism-like (EM) algorithm, in which the EM is hybridized with a diversif...

We introduce mixed LICORS, an algorithm for learning nonlinear, high-dimensional dynamics from spatio-temporal data, suitable for both prediction and simulation. Mixed LICORS extends the recent LICORS algorithm (Goerg and Shalizi, 2012) from hard clustering of predictive distributions to a non-parametric, EM-like soft clustering. This retains the asymptotic predictive optimality of LICORS, but,...

In a previous class, we discussed an algorithm for learning a probabilistic matrix model which describes a fixed-length motif in a set of sequences S : : : S over an alphabet A. This algorithm is one of a class of methods collectively known as expectation maximization, or EM. We will describe the general EM algorithm, then derive the motif-finding algorithm by applying EM to learn a specific pr...

The EM algorithm is a popular method for computing maximum likelihood estimates or posterior modes in models that can be formulated in terms of missing data or latent structure. Although easy implementation and stable convergence help to explain the popularity of the algorithm, its convergence is sometimes notoriously slow. In recent years, however, various adaptations have significantly improv...

We present a noise-injected version of the Expectation-Maximization (EM) algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that additive noise speeds up the average convergence of the EM algorithm to a local maximum of the likelihood surface if a positivity condition holds. Corollary...