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 log-likelihood of a single unobservable complete data space, rather than maximizing the intractable likelihood function for the measured or incomplete data. EM algorithms update all paramete...

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 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 log-likelihood of a single unobservable complete data space, rather than maximizing the intractable likelihood function for the measured or incomplete data. EM algorithms update all paramete...

In computer vision, image segmentation problem is to partition a digital image into multiple parts. The goal is to change the representation of the image and make it more meaningful and easier to analyze [11]. In this assignment, we will show how an image segmentation algorithm works in a real application. In the Electronic Field Guide (EFG) project, researchers want to segment the leaf region ...

The purpose of this tutorial is to give you an example of how to take a simple discrete probabilistic model and derive the expectation maximization updates for it and then turn them into code. We give some examples and identify the key ideas that make the algorithms work. These are meant to be as intuitive as possible, but for those curious about the underlying mathematics, we also provide some...

This tutorial discusses the Expectation Maximization (EM) algorithm of Dempster, Laird and Rubin [1]. The approach taken follows that of an unpublished note by Stuart Russel, but fleshes out some of the gory details. In order to ensure that the presentation is reasonably self-contained, some of the results on which the derivation of the algorithm is based are presented prior to the main results...

We present the CEM (Conditional Expectation Maximization) algorithm as an extension of the EM (Expectation Maximization) algorithm to conditional density estimation under missing data. A bounding and maximization process is given to speciically optimize conditional likelihood instead of the usual joint likelihood. We apply the method to conditioned mixture models and use bounding techniques to ...

We present the CEM (Conditional Expectation Maximization) algorithm as an extension of the EM (Expectation Maximization) algorithm to conditional density estimation under missing data. A bounding and maximization process is given to speci cally optimize conditional likelihood instead of the usual joint likelihood. We apply the method to conditioned mixture models and use bounding techniques to ...