Inferring criticality in neural networks

Abstract

It is often the case that while the specific interactions between individual constituents of complex systems are unknown, their correlations are measurable. Reconstructing the strength of the interactions from these correlations is known as an inverse problem. We focus on reconstructing interactions from functional magnetic resonance imaging (fMRI) studies of the human brain, where different regions of the brain are modelled as binary variables (on vs off). The overarching aim of this work was to analyse these datasets from the perspective of statistical physics and to under- stand whether the human brain exists at an order-disorder transition, i.e. a critical point. This was motivated by a growing body of evidence which suggests that many complex biological systems are tuned towards criticality. We construct equilibrium statistical physics models of the data via a machine learning scheme termed Inverse Ising inference. We initially show that typical estimators used for inverse Ising inference, such as pseudo-likelihood maximization (PLM), are biased by testing the inference on simulated data. Understanding the performance of the inference on small sample sizes is crucial to interpreting models fitted from real data, as the amount of data available in experimental studies is limited. Using the Sherrington-Kirkpatrick (SK) model as a benchmark, we show that PLM displays large biases in the critical regimes close to order-disorder transitions, which may alter the qualitative interpretation of the inferred model. The bias causes models inferred through PLM to appear closer to criticality than one would expect from the data. We introduce data-driven methods to correct this bias and explore their application in a small fMRI dataset. Our results indicate that additional care should be taken when attributing criticality to real-world datasets, as limited dataset sizes overstate the criticality of the inferred model. We also apply PLM to a large publicly available fMRI dataset from the human connectome project and find that the resting state network of the human brain corresponds to a near-critical paramagnetic state point. The inferred PLM model contains a highly structured coupling network with a heavy, power-law-like tail and we show that negative couplings play a vital role in mediating correlations within the network. We find that coupling networks are sparser than correlation networks, and suggest that inverse methods such as PLM should replace standard correlation-based approaches to network reconstruction in neuroimaging.

Date of Award	20 Jun 2023
Original language	English
Awarding Institution	University of Bristol
Supervisor	Francesco Turci (Supervisor) & Thomas Machon (Supervisor)