Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial configurations and fails to find the global optimum. On the other hand, in the field of physics, quantum annealing (QA) was proposed as a novel optimization appro...

The paper gives a brief review of the expectation-maximization algorithm (Dempster, Laird, and Rubin 1977) in the comprehensible framework of discrete mathematics. In Section 2, two prominent estimation methods, the relative-frequency estimation and the maximum-likelihood estimation are presented. Section 3 is dedicated to the expectation-maximization algorithm and a simpler variant, the genera...

The EM algorithm is a popular and useful algorithm for "nding the maximum likelihood estimator in incomplete data problems. Each iteration of the algorithm consists of two simple steps: an E-step, in which a conditional expectation is calculated, and an M-step, where the expectation is maximized. In some problems, however, the EM algorithm cannot be applied since the conditional expectation req...

The iterative maximum-likelihood expectation-maximization (ML-EM) algorithm is an excellent algorithm for image reconstruction and usually provides better images than the filtered backprojection (FBP) algorithm. However, a windowed FBP algorithm can outperform the ML-EM in certain occasions, when the least-squared difference from the true image, that is, the least-squared error (LSE), is used a...

The performance of many traffic control strategies depends on how much the traffic flow models have been accurately calibrated. One of the most applicable traffic flow model in traffic control and management is LWR or METANET model. Practically, key parameters in LWR model, including free flow speed and critical density, are parameterized using flow and speed measurements gathered by inductive ...

Factor graphs allow large probability distributions to be stored efficiently and facilitate fast computation of marginal probabilities, but the difficulty of training them has limited their use. Given a large set of data points, the training process should yield factors for which the observed data has a high likelihood. We present a factor graph learning algorithm which on each iteration merges...

1 ‘Parameter expanded’ and standard expectation maximisation algorithms are de2 scribed for reduced rank estimation of covariance matrices by restricted maximum 3 likelihood, fitting the leading principal components only. Convergence behaviour of 4 these algorithms is examined for several examples and contrasted to that of the aver5 age information algorithm, and implications for practical anal...

Background Policy makers need models to be able to detect groups at high risk of HIV infection. Incomplete records and dirty data are frequently seen in national data sets. Presence of missing data challenges the practice of model development. Several studies suggested that performance of imputation methods is acceptable when missing rate is moderate. One of the issues which was of less concern...