Predictive risk estimation for the expectation maximization algorithm with Poisson data

The Expectation Maximization Algorithm

This note represents my attempt at explaining the EM algorithm (Hartley, 1958; Dempster et al., 1977; McLachlan and Krishnan, 1997). This is just a slight variation on TomMinka’s tutorial (Minka, 1998), perhaps a little easier (or perhaps not). It includes a graphical example to provide some intuition. 1 Intuitive Explanation of EM EM is an iterative optimizationmethod to estimate some unknown ...

Data Synthesis with Expectation-Maximization

A problem of increasing importance in computer graphics is to generate data with the style of some previous training data, but satisfying new constraints. If we use a probabilistic latent variable model, then learning the model will normally be performed using Expectation-Maximization (EM), or one of its generalizations. We show that data synthesis for such problems can also be performed using ...

Expectation Maximization Deconvolution Algorithm

In this paper, we use a general mathematical and experimental methodology to analyze image deconvolution. The main procedure is to use an example image convolving it with a know Gaussian point spread function and then develop algorithms to recover the image. Observe the deconvolution process by adding Gaussian and Poisson noise at different signal to noise ratios. In addition, we will describe ...

Expectation-Maximization (EM) algorithm

The Noisy Expectation-Maximization Algorithm

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...