Significant Subgraph Mining for Neural Network Inference with Multiple Comparisons Correction

Abstract

We describe how the recently introduced method of significant subgraph mining can be employed as a useful tool in network comparison. It is applicable whenever the goal is to compare two sets of unweighted graphs and to determine differences in the processes that generate them. We provide an extension of the method to dependent graph generating processes as the occur for example in within-subject experimental designs. Furthermore, we present an extensive investigation of error-statistical properties of the method in simulation using Erd[o]s-Renyi models and in empirical data. In particular, we perform an empirical power analysis for transfer entropy networks inferred from resting state MEG data comparing autism spectrum patients with neurotypical controls. From this analysis one may estimate that the appropriate sample size for similar studies should be chosen in the order of n=60 per group or larger. Author summaryA key objective of neuroscientifc research is to determine how different parts of the brain are connected. The end result of such investigations is always a graph consisting of nodes corresponding to brain regions or nerve cells and edges between the nodes indicating if they are connected or not. The connections may be structural (an actual anatomical connection) but can also be functional - meaning that there is a statistical dependency between the activity in one part of the brain and the activity in another. A prime example of the latter type of connection would be the information flow between brain areas. Differences in the patterns of connectivity are likely to be responsible for and indicative of various neurological disorders such as autism spectrum disorders. It is therefore important that efficient methods to detect such differences are available. The key problem in developing methods for comparing patterns of connectivity is that there is generally a vast number of different patterns (it can easily exceed the number of stars in the milky way). In this paper we describe how the recently developed method of significant subgraph mining accounts for this problem and how it can be usefully employed in neuroscientifc research.