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st: bootstrapping from graphs

From   Paul Cohen <[email protected]>
To   [email protected]
Subject   st: bootstrapping from graphs
Date   Mon, 24 Jan 2005 22:57:00 -0800

Suppose I have a list of transactions between individuals --- Bill spoke to Jane, Fred called John, etc. I assume the list is not complete, it is a sample of transactions and perhaps a very sparse one. Moreover, I assume that the transactions are not independent; Bill might have called Jane because Alex called Bill. Suppose I make some inferences about the sample. For instance, I run the betweenness-centrality algorithm and infer that Bill and Jane belong to one organization whereas Fred and John belong to another. The overarching question is, how can I assess probabilities for these inferences? One thought is to bootstrap the transactions and estimate inference probabilities as the proportion of bootstrap samples in which the inference appears. As to the nonindependence of the transactions, I thought one might use a version of block bootstrap by saying, for instance, that transactions that co-occur within an interval must be resampled together.

I have searched for papers on resampling from graphs (as graphs represent relations between individuals) without success. Can someone point me in the right direction, please.

Here's a specific problem: If Bill does in fact know Fred and interact with him occasionally, but no transaction involving Bill and Fred appears in the sample, then no nonparametric bootstrap sample will include a transaction between Bill and Fred. On the other hand, if we make a parametric model of the transactions (i.e., they are modeled by a random graph) then any two individuals may be connected in a bootstrap sample. Both approaches seem wrong. Can anyone point me to literature on resampling from graphs in which all the links are not observed?



Dr. Paul Cohen
Director, Center for Research on Unexpected Events
Deputy Director, Intelligent Systems Division
Information Sciences Institute
University of Southern California
310 448 9342

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