Applying Discrete PCA in Data Analysis

Methods for analysis of principal components in discrete data have existed for some time under various names such as grade of membership modelling, probabilistic latent semantic analysis, and genotype inference with admixture. In this paper we explore a number of extensions to the common theory, and present some application of these methods to some common statistical tasks. We show that these methods can be interpreted as a discrete version of ICA. We develop a hierarchical version yielding components at different levels of detail, and additional techniques for Gibbs sampling. We compare the algorithms on a text prediction task using support vector machines, and to information retrieval.

Predicting Regional Classification of Levantine Ivory Sculptures: A Machine Learning Approach

Art historians and archaeologists have long grappled with the regional classification of ancient Near Eastern ivory carvings. Based on the visual similarity of sculptures, individuals within these fields have proposed object assemblages linked to hypothesized regional production centers. Using quantitative rather than visual methods, we here approach this classification task by exploiting computational methods from machine learning currently used with success in a variety of statistical problems in science and engineering. We first construct a prediction function using 66 categorical features as inputs and regional style as output. The model assigns regional style group (RSG), with 98 percent prediction accuracy. We then rank these features by their mutual information with RSG, quantifying single-feature predictive power. Using the highest- ranking features in combination with nomographic visualization, we have found previously unknown relationships that may aid in the regional classification of these ivories and their interpretation in art historical context.

Quantifying and Visualizing Attribute Interactions

Interactions are patterns between several attributes in data that cannot be inferred from any subset of these attributes. While mutual information is a well-established approach to evaluating the interactions between two attributes, we surveyed its generalizations as to quantify interactions between several attributes. We have chosen McGill's interaction information, which has been independently rediscovered a number of times under various names in various disciplines, because of its many intuitively appealing properties. We apply interaction information to visually present the most important interactions of the data. Visualization of interactions has provided insight into the structure of data on a number of domains, identifying redundant attributes and opportunities for constructing new features, discovering unexpected regularities in data, and have helped during construction of predictive models; we illustrate the methods on numerous examples. A machine learning method that disregards interactions may get caught in two traps: myopia is caused by learning algorithms assuming independence in spite of interactions, whereas fragmentation arises from assuming an interaction in spite of independence.