In image matching applications such as tracking and stereo matching, it is common to use the sum-of-squareddi erences (SSD) measure to determine the best match for an image template. However, this measure is sensitive to outliers and is not robust to template variations. We describe a robust measure and eÆcient search strategy for template matching with a binary or greyscale template using a ma...

One popular class of unsupervised algorithms are competitive algorithms. In the traditional view of competition, only one competitor, the winner, adapts for any given case. I propose to view competitive adaptation as attempting to fit a blend of simple probability generators (such as gaussians) to a set of data-points. The maximum likelihood fit of a model of this type suggests a "softer" form ...

This module introduces the maximum likelihood estimator. We show how the MLE implements the likelihood principle. Methods for computing th MLE are covered. Properties of the MLE are discussed including asymptotic e ciency and invariance under reparameterization. The maximum likelihood estimator (MLE) is an alternative to the minimum variance unbiased estimator (MVUE). For many estimation proble...

1 Summary of Lecture 12 In the last lecture we derived a risk (MSE) bound for regression problems; i.e., select an f ∈ F so that E[(f(X)− Y )]− E[(f∗(X)− Y )] is small, where f∗(x) = E[Y |X = x]. The result is summarized below. Theorem 1 (Complexity Regularization with Squared Error Loss) Let X = R, Y = [−b/2, b/2], {Xi, Yi}i=1 iid, PXY unknown, F = {collection of candidate functions}, f : R → ...

In this paper we present a visual learning approach that uses non-parametric probability estimators. We use entropy analysis over the training set in order to select the features that best represent the pattern class of faces, and set up discrete probability models. These models are tested in the context of maximum likelihooddetection of faces. Excellent results are reported in terms of the cor...

We introduce an estimator for the population mean based on maximizing likelihoods formed by parameterizing a kernel density estimate. Due to these origins, we have dubbed the estimator the maximum kernel likelihood estimate (mkle). A speedy computational method to compute the mkle based on binning is implemented in a simulation study which shows that the mkle at an optimal bandwidth is decidedl...

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 ...

In this paper, we review an extension of the learning rules in a Principal Component Analysis network which has been derived to be optimal for a specific probability density function. We note that this probability density function is one of a family of pdfs and investigate the learning rules formed in order to be optimal for several members of this family. We show that, whereas previous authors...

Maximnm likelihood estimates are reported to be best under all circumstances. Yet there are numerous simple examples where they plainly misbehave. One gives some eranmples for problems that had not been invented for the purpose of annoying ms,aximunm likelihood fans. Another example, imitated from B'hadu'r, has been specially created with just such a purpose in mind. Next, we present a list of ...