Probability models for information processing and machine perception

Probability models and their graphical descriptions provide a principled underlying formalism for constructing and describing models for data. Such models can be constructed for many important problems involving the processing and analysis of information in the form of: matrices of numbers, images, and time series of vectors. I look at four problems with important real world applications in general data processing, image, video and audio processing. I use probability models of joint distributions for which the graphical descriptions of the models contain repeating sub-structures and non-linearities. I derive optimization algorithms which take advantage of the structure of the problems and models. I give a brief introduction to graphical probability models and methods for optimizing such models. I discuss variational methods and their relationship to other inference and optimization approaches. This thesis makes a number of contributions. First, I present a model for jointly clustering the rows and columns of a matrix and permuting a matrix into block constant form. I develop a new algorithm for model optimization based on sequentially considering the data. This algorithm proves to be superior to many other alternatives based on synthetic data experiments and results on "DNA chip" experiments. Secondly, I present a new method for combining images taken with different camera settings into a higher dynamic range image using only pixel values. I derive priors for imaging functions using a generative model of the derivative structure of functions. This derivation is novel in that it ties together Generative Models, Smoothness Regularization and Gaussian Processes. I derive a new optimization technique to estimate both functions and high dynamic range irradiance estimates. Thirdly, I present a new appearance model for visual objects called a Probabilistic Montage. I present variations of the model and derive optimization algorithms. Finally, I present a new method for noise robust speech recognition and show how it is possible to approximate likelihoods in a non-linear model for this problem using parameterized Gaussian basis functions. This leads to an efficient algorithm in a principled model for cleaning noisy speech and produces highly competitive results.