TRIPODS Winter School & Workshop- Eric D. Kolaczyk
Abstract– Thousands of scientific articles have been published in the last 20 years with the word “network” in the title. And the vast majority of these report network summary statistics of one type or another. However, these numbers are rarely accompanied by any quantification of uncertainty. Yet any error inherent in the measurements underlying the construction of the network, or in the network construction procedure itself, necessarily must propagate to any summary statistics reported. Perhaps surprisingly, there is little in the way of formal statistical methodology for this problem. I summarize results from our recent work, for the case of estimating the density of low-order subgraphs. Under a simple model of network error, we show that consistent estimation of such densities is impossible when the rates of error are unknown and only a single network is observed. We then develop method-of-moment estimators of subgraph density and error rates for the case where a minimal number of network replicates are available (i.e., just 2 or 3). These estimators are shown to be asymptotically normal as the number of vertices increases to infinity. We also provide confidence intervals for quantifying the uncertainty in these estimates, implemented through a novel bootstrap algorithm. We illustrate the use of our estimators in the context of gene coexpression networks — the correction for measurement error is found to have potentially substantial impact on standard summary statistics. This is joint work with Qiwei Yao and Jinyuan Chang.