Kenneth W. Church+ and Ping Li*

+Machine Learning and Applied Statistics Group MSR
*Statistics Department, Stanford University

Using Sketches to estimate associations

UW/Microsoft Symposium, 10/28/05

Suppose one wanted to use page hits to estimate associations or mutual information, as Turney, Etzioni and others have done. We should not have to look at the entire corpus (e.g., the Web) to know if two (or more) words are associated or not. A powerful sampling technique called Sketches was originally introduced to remove duplicate Web pages. We generalize Sketches to estimate contingency tables and associations, using a maximum likelihood estimator to find the most likely contingency table given the sample, the margins (document frequencies) and the size of the collection. The proposed method has smaller (about 1/2) errors and more flexibility than the original sketch method. Also, the proposed method can be extended naturally to estimate multi-way associations, formulated as a convex programming problem. As expected, computational work and statistical accuracy (variance or errors) depend on sampling rate, as will be shown both theoretically and empirically. Sampling methods become more and more important with larger and larger collections. At Web scale, sampling rates as low as 10-4 may suffice.

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