Large-scale estimation of random graph models with local dependence

The Importance of Being Correlated: Implications of Dependence in Joint Spectral Inference across Multiple Networks

Spectral inference on multiple networks is a rapidly-developing subfield of graph statistics. Recent work has demonstrated that joint, or simultaneous, spectral embedding of multiple independent networks can deliver more accurate estimation than individual spectral decompositions of those same networks. Such inference procedures typically rely heavily on independence assumptions across the multiple network realizations, and even in this case, little attention has been paid to the induced network correlation that can be a consequence of such joint embeddings. In this paper, we present a generalized omnibus embedding methodology and we provide a detailed analysis of this embedding across both independent and correlated networks, the latter of which significantly extends the reach of such procedures, and we describe how this omnibus embedding can itself induce correlation. This leads us to distinguish between inherent correlation-that is, the correlation that arises naturally in multisample network data-and induced correlation, which is an artifice of the joint embedding methodology. We show that the generalized omnibus embedding procedure is flexible and robust, and we prove both consistency and a central limit theorem for the embedded points. We examine how induced and inherent correlation can impact inference for network time series data, and we provide network analogues of classical questions such as the effective sample size for more generally correlated data. Further, we show how an appropriately calibrated generalized omnibus embedding can detect changes in real biological networks that previous embedding procedures could not discern, confirming that the effect of inherent and induced correlation can be subtle and transformative. By allowing for and deconstructing both forms of correlation, our methodology widens the scope of spectral techniques for network inference, with import in theory and practice.

Testing biological network motif significance with exponential random graph models

Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions. However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over 10 years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s41109-021-00434-y.

Great minds think alike, or do they often differ? Research topic overlap and the formation of scientific teams

Over the last century scientific research has become an increasingly collaborative endeavor. Commentators have pointed to different factors which contribute to this trend, including the specialization of science and growing need for diversity of interest and expertise areas in a scientific team. Very few studies, however, have precisely evaluated how the diversity of interest topics between researchers is related to the emergence of collaboration. Existing theoretical arguments suggest a curvilinear relationship between topic similarity and collaboration: too little similarity can complicate communication and agreement, yet too much overlap can increase competition and limit the potential for synergy. We test this idea using data on six years of publications across all disciplines at a large U.S. research university (approximately 14,300 articles, 12,500 collaborations, and 3,400 authors). Employing topic modelling and network statistical models, we analyze the relationship between topic overlap and the likelihood of coauthorship between two researchers while controlling for potential confounders. We find an inverted-U relationship in which the probability of collaboration initially increases with topic similarity, then rapidly declines after peaking at a similarity "sweet spot". Collaboration is most likely at low-to-moderate levels of topic overlap, which are substantially lower than the average self-similarity of scientists or research groups. These findings - which we replicate for different units of analysis (individuals and groups), genders of collaborators, disciplines, and collaboration types (intra- and interdisciplinary) - support the notion that researchers seek collaborators to augment their scientific and technical human capital. We discuss implications for theories of scientific collaboration and research policy.