An Accelerated Chow and Liu Algorithm: Fitting Tree Distributions to High Dimensional Sparse Data

Chow and Liu introduced an algorithm for fitting a multivariate distribution with a tree (i.e. a density model that assumes that there are only pairwise dependencies between variables) and that the graph of these dependencies is a spanning tree. The original algorithm is quadratic in the dimesion of the domain, and linear in the number of data points that define the target distribution $P$. This paper shows that for sparse, discrete data, fitting a tree distribution can be done in time and memory that is jointly subquadratic in the number of variables and the size of the data set. The new algorithm, called the acCL algorithm, takes advantage of the sparsity of the data to accelerate the computation of pairwise marginals and the sorting of the resulting mutual informations, achieving speed ups of up to 2-3 orders of magnitude in the experiments.

Learning Classes Correlated to a Hierarchy

Trees are a common way of organizing large amounts of information by placing items with similar characteristics near one another in the tree. We introduce a classification problem where a given tree structure gives us information on the best way to label nearby elements. We suggest there are many practical problems that fall under this domain. We propose a way to map the classification problem onto a standard Bayesian inference problem. We also give a fast, specialized inference algorithm that incrementally updates relevant probabilities. We apply this algorithm to web-classification problems and show that our algorithm empirically works well.

Delegation, Arbitration and High-Level Service Discovery as Key Elements of a Software Infrastructure for Pervasive Computing

The dream of pervasive computing is slowly becoming a reality. A number of projects around the world are constantly contributing ideas and solutions that are bound to change the way we interact with our environments and with one another. An essential component of the future is a software infrastructure that is capable of supporting interactions on scales ranging from a single physical space to intercontinental collaborations. Such infrastructure must help applications adapt to very diverse environments and must protect people's privacy and respect their personal preferences. In this paper we indicate a number of limitations present in the software infrastructures proposed so far (including our previous work). We then describe the framework for building an infrastructure that satisfies the abovementioned criteria. This framework hinges on the concepts of delegation, arbitration and high-level service discovery. Components of our own implementation of such an infrastructure are presented.