Toward a Multisubject Analysis of Neural Connectivity

Abstract

Directed acyclic graphs (DAGs) and associated probability models are widely used to model neural connectivity and communication channels. In many experiments, data are collected from multiple subjects whose connectivities may differ but are likely to share many features. In such circumstances it is natural to leverage similarity between subjects to improve statistical efficiency. The first exact algorithm for estimation of multiple related DAGs was recently proposed by Oates et al. (2014); in this letter we present examples and discuss implications of the methodology as applied to the analysis of fMRI data from a multi-subject experiment. Elicitation of tuning parameters requires care and we illustrate how this may proceed retrospectively based on technical replicate data. In addition to joint learning of subject-specific connectivity, we allow for heterogeneous collections of subjects and simultaneously estimate relationships between the subjects themselves. This letter aims to highlight the potential for exact estimation in the multi-subject setting.

A group analysis using the Multiregression Dynamic Models for fMRI networked time series

“…In this sense the use of information from other subjects in the learning individual networks, as the MEMN does, can therefore improve this estimation process. We note that Oates et al (2014a), Oates et al (2014b) presented a similar method to MEMN. These all the individual and subgroup networks are estimated simultaneously, and then the denser graphs are penalised.…”

“… The Multiregression Dynamic Model (MDM): It is a class of multivariate time series models which embeds putative causal hypotheses among its variables over time Queen and Smith (1993), Queen and Albers (2009), Costa et al (2015); The Multiregression Dynamic Model-Integer Programming Algorithm (MDM-IPA): It is an efficient search-and-score method that provides a search over the large class of networks based on an integer programming algorithm Bartlett and Cussen (2013), Costa et al (2015); The Multiregression Dynamic Model-Directed Graph Model (MDM-DGM): It is also a learning network algorithm but searchesfor graphical structure without the constraints of DAG (Costa et al, 2017); The Virtual-typical-subject (VTS) Approach: It ignores inter-subject variability, assuming that the information from different datasets come from the same subject Zheng and Rajapakse (2006), Rajapakse and Zhou (2007), Li et al (2008); The Common-structure (CS) Approach: It considers the same network structure but allows the parameters to differ between subjects Ramsey et al (2010), Li et al (2008); The Individual-structure (IS) Approach: It drives the learning network process individually in each dataset so that results are pooled into a single network Mechelli et al (2002), Li et al (2008), Oates (2013); The Group-structure (GS) Approach: It studies group homogeneity through cluster analysis, considering a particular measure of similarity between subjects Kherif et al (2004), Gates (2012); The Individual Estimation of Multiple Networks (IEMN) Approach: It is basically the GS approach, i.e. the individual networks are estimated independently whilst the subgroup networks made up of homogeneous subjects are estimated as a function of the same graphical structure for all individuals Kherif et al (2004), Gates (2012); The Marginal Estimation of Multiple Networks (MEMN) Approach: It searches both individual and subgroup networks considering a distance between homogeneoussubjects Oates (2013), Oates et al (2014a), Oates et al (2014b).…”

Exact estimation of multiple directed acyclic graphs

“…Data were acquired on each subject while they were in a state of quiet repose and preprocessed to obtain 10-dimensional time series representing the activity levels at 10 regions in each subject. The specific application is discussed in greater detail in the companion paper Oates et al (2014b).…”

“…Finally we close with a discussion of directions for further research. A companion paper that explores the fMRI application in more detail is available as Oates et al (2014b).…”

Joint estimation of multiple related biological networks

“…Related work that is based on DAGs includes Niculescu-Mizil and Caruana (2007), Werhli and Husmeier (2008), Dondelinger, Lèbre and Husmeier (2013). In a sequel to the present work, Oates, Costa and Nichols (2014) provide an exact algorithm for joint maximum a posteriori (MAP) estimate of multiple (static) DAGs. In contrast, here we focus on Bayesian model-averaging (as opposed to MAP estimation) and on time-course data (or, more generally, Bayesian networks with a fixed ordering of the variables).…”