Cached Sufficient Statistics for Efficient Machine Learning with Large Datasets

This paper introduces new algorithms and data structures for quick counting for machine learning datasets. We focus on the counting task of constructing contingency tables, but our approach is also applicable to counting the number of records in a dataset that match conjunctive queries. Subject to certain assumptions, the costs of these operations can be shown to be independent of the number of records in the dataset and loglinear in the number of non-zero entries in the contingency table. We provide a very sparse data structure, the ADtree, to minimize memory use. We provide analytical worst-case bounds for this structure for several models of data distribution. We empirically demonstrate that tractably-sized data structures can be produced for large real-world datasets by (a) using a sparse tree structure that never allocates memory for counts of zero, (b) never allocating memory for counts that can be deduced from other counts, and (c) not bothering to expand the tree fully near its leaves. We show how the ADtree can be used to accelerate Bayes net structure finding algorithms, rule learning algorithms, and feature selection algorithms, and we provide a number of empirical results comparing ADtree methods against traditional direct counting approaches. We also discuss the possible uses of ADtrees in other machine learning methods, and discuss the merits of ADtrees in comparison with alternative representations such as kd-trees, R-trees and Frequent Sets.Comment: See http://www.jair.org/ for any accompanying file

Detecting change points in the large-scale structure of evolving networks

Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving networks is change-point detection, in which we both identify the times at which the large-scale pattern of interactions changes fundamentally and quantify how large and what kind of change occurred. Here, we formalize for the first time the network change-point detection problem within an online probabilistic learning framework and introduce a method that can reliably solve it. This method combines a generalized hierarchical random graph model with a Bayesian hypothesis test to quantitatively determine if, when, and precisely how a change point has occurred. We analyze the detectability of our method using synthetic data with known change points of different types and magnitudes, and show that this method is more accurate than several previously used alternatives. Applied to two high-resolution evolving social networks, this method identifies a sequence of change points that align with known external "shocks" to these networks