The development of models for multiple heterogeneous network data is of critical importance both in statistical network theory and across multiple application domains. Although single-graph inference is well-studied, multiple graph inference is largely unexplored, in part because of the challenges inherent in appropriately modeling graph differences and yet retaining sufficient model simplicity to render estimation feasible. This paper addresses exactly this gap, by introducing a new model, the common subspace independent-edge (COSIE) multiple random graph model, which describes a heterogeneous collection of networks with a shared latent structure on the vertices but potentially different connectivity patterns for each graph. The COSIE model encompasses many popular network representations, including the stochastic blockmodel. The model is both flexible enough to meaningfully account for important graph differences and tractable enough to allow for accurate inference in multiple networks. In particular, a joint spectral embedding of adjacency matrices - the multiple adjacency spectral embedding (MASE) - leads, in a COSIE model, to simultaneous consistent estimation of underlying parameters for each graph. Under mild additional assumptions, MASE estimates satisfy asymptotic normality and yield improvements for graph eigenvalue estimation and hypothesis testing. In both simulated and real data, the COSIE model and the MASE embedding can be deployed for a number of subsequent network inference tasks, including dimensionality reduction, classification, hypothesis testing and community detection. Specifically, when MASE is applied to a dataset of connectomes constructed through diffusion magnetic resonance imaging, the result is an accurate classification of brain scans by patient and a meaningful determination of heterogeneity across scans of different subjects.

pdf/inference-for-multiple-heterogeneous-networks-with-a-common-4ku06b6gp1.pdf

Inference for multiple heterogeneous networks with a common invariant subspace

The neuropil is a complicated 3D tangle of neural and glial processes. Recent advances in microconnectomics has made it possible to reconstruct neural circuits from serial-section electron microscopy at the micron scale. Electron microscopy allows even higher resolution reconstructions on the nanometer scale. Nanoconnectomic reconstructions approaching molecular resolution allow us to explore the topology of extracellular space and the precision with which synapses are modified by patterns of neural activity. The reconstruction of a neural circuit is an essential step in understanding how signals are processed in the circuit; without this ‘wiring diagram,’ it is difficult to interpret the signals recorded from elements in the circuit. Connectomics attempts to reconstruct complete circuits, which can be accomplished at many spatial scales, as illustrated in Fig. 1. At the microconnectomic level, recent studies have focused on the retina (Kim et al., Nature 509:331–336, 2014) and the visual cortex (Bock et al., Nature 471:177–182, 2011). At the macroconnectomic level, the long-range cortical connections can be trace with diffusion tensor imaging (Van Essen, Neuron 80:775–790, 2013). This chapter will focus on nanoconnectomics, whose goal is to produce an accurate reconstruction of the neuropil at the nanometer scale.

In-Vivo Connectivity in Monkeys -- Micro-, Meso- and Macro-Connectomics of the Brain

While statistical analysis of a single network has received a lot of attention in recent years, with a focus on social networks, analysis of a sample of networks presents its own challenges which require a different set of analytic tools. Here we study the problem of classification of networks with labeled nodes, motivated by applications in neuroimaging. Brain networks are constructed from imaging data to represent functional connectivity between regions of the brain, and previous work has shown the potential of such networks to distinguish between various brain disorders, giving rise to a network classification problem. Existing approaches tend to either treat all edge weights as a long vector, ignoring the network structure, or focus on graph topology as represented by summary measures while ignoring the edge weights. Our goal is to design a classification method that uses both the individual edge information and the network structure of the data in a computationally efficient way, and that can produce a parsimonious and interpretable representation of differences in brain connectivity patterns between classes. We propose a graph classification method that uses edge weights as predictors but incorporates the network nature of the data via penalties that promote sparsity in the number of nodes, in addition to the usual sparsity penalties that encourage selection of edges. We implement the method via efficient convex optimization and provide a detailed analysis of data from two fMRI studies of schizophrenia.

pdf/network-classification-with-applications-to-brain-28ylyi1xfc.pdf

Network classification with applications to brain connectomics

Using brain atlases to localize regions of interest is a requirement for making neuroscientifically valid statistical inferences. These atlases, represented in volumetric or surface coordinate spaces, can describe brain topology from a variety of perspectives. Although many human brain atlases have circulated the field over the past fifty years, limited effort has been devoted to their standardization. Standardization can facilitate consistency and transparency with respect to orientation, resolution, labeling scheme, file storage format, and coordinate space designation. Our group has worked to consolidate an extensive selection of popular human brain atlases into a single, curated, open-source library, where they are stored following a standardized protocol with accompanying metadata, which can serve as the basis for future atlases. The repository containing the atlases, the specification, as well as relevant transformation functions is available in the neuroparc OSF registered repository or https://github.com/neurodata/neuroparc .

/pdf/standardizing-human-brain-parcellations-2a9e8ze5cu.pdf

Standardizing human brain parcellations.

The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a solution to this problem via a graph matching matched filter: centering and padding the smaller adjacency matrix and applying graph matching methods to align it to the larger network. The centering and padding schemes can be incorporated into any algorithm that matches using adjacency matrices. Under a statistical model for correlated pairs of graphs, which yields a noisy copy of the small graph within the larger graph, the resulting optimization problem can be guaranteed to recover the true vertex correspondence between the networks. However, there are currently no efficient algorithms for solving this problem. To illustrate the possibilities and challenges of such problems, we use an algorithm that can exploit a partially known correspondence and show via varied simulations and applications to Drosophila and human connectomes that this approach can achieve good performance.

Matched Filters for Noisy Induced Subgraph Detection

Modern scientific discovery depends on collecting large heterogeneous datasets with many sources of variability, and applying domain-specific pipelines from which one can draw insight or clinical utility. For example, macroscale connectomics studies require complex pipelines to process raw functional or diffusion data and estimate connectomes. Individual studies tend to customize pipelines to their needs, raising concerns about their reproducibility, and adding to a longer list of factors that may differ across studies (including sampling, experimental design, and data acquisition protocols), resulting in failures to replicate. Mitigating these issues requires multi-study datasets and the development of pipelines that can be applied across them. We developed NeuroData9s MRI to Graphs (NDMG) pipeline using several functional and diffusion studies, including the Consortium for Reliability and Reproducibility, to estimate connectomes. Without any manual intervention or parameter tuning, NDMG ran on 25 different studies (~6,000 scans) from 15 sites, with each scan resulting in a biologically plausible connectome (as assessed by multiple quality assurance metrics at each processing stage). For each study, the connectomes from NDMG are more similar within than across individuals, indicating that NDMG is preserving biological variability. Moreover, the connectomes exhibit near perfect consistency for certain connectional properties across every scan, individual, study, site, and modality; these include stronger ipsilateral than contralateral connections and stronger homotopic than heterotopic connections. Yet, the magnitude of the differences varied across individuals and studies - much more so when pooling data across sites, even after controlling for study, site, and basic demographic variables (i.e., age, sex, and ethnicity). This indicates that other experimental variables (possibly those not measured or reported) are contributing to this variability, which if not accounted for can limit the value of aggregate datasets, as well as expectations regarding the accuracy of findings and likelihood of replication. We, therefore, provide a set of principles to guide the development of pipelines capable of pooling data across studies while maintaining biological variability and minimizing measurement error. This open science approach provides us with an opportunity to understand and eventually mitigate spurious results for both past and future studies.

https://www.biorxiv.org/content/biorxiv/early/2018/04/01/188706.full.pdf

A High-Throughput Pipeline Identifies Robust Connectomes But Troublesome Variability

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A High-Throughput Pipeline Identifies Robust Connectomes But Troublesome Variability