Significant subgraph mining for neural network inference with multiple comparisons correction.

We describe how the recently introduced method of significant subgraph mining can be employed as a useful tool in neural 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 they occur, for example, in within-subject experimental designs. Furthermore, we present an extensive investigation of the error-statistical properties of the method in simulation using Erdos-Rényi models and in empirical data in order to derive practical recommendations for the application of subgraph mining in neuroscience. 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. Finally, we provide a Python implementation as part of the openly available IDTxl toolbox.

Introducing a differentiable measure of pointwise shared information.

Partial information decomposition of the multivariate mutual information describes the distinct ways in which a set of source variables contains information about a target variable. The groundbreaking work of Williams and Beer has shown that this decomposition cannot be determined from classic information theory without making additional assumptions, and several candidate measures have been proposed, often drawing on principles from related fields such as decision theory. None of these measures is differentiable with respect to the underlying probability mass function. We here present a measure that satisfies this property, emerges solely from information-theoretic principles, and has the form of a local mutual information. We show how the measure can be understood from the perspective of exclusions of probability mass, a principle that is foundational to the original definition of mutual information by Fano. Since our measure is well defined for individual realizations of random variables it lends itself, for example, to local learning in artificial neural networks. We also show that it has a meaningful Möbius inversion on a redundancy lattice and obeys a target chain rule. We give an operational interpretation of the measure based on the decisions that an agent should take if given only the shared information.