DEVELOPING MACHINE LEARNING TECHNIQUES FOR NETWORK CONNECTIVITY INFERENCE FROM TIME-SERIES DATA

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## Abstract

Inference of the connectivity structure of a network from the observed dynamics of the states of its nodes is a key issue in science, with wide-ranging applications such as determination of the synapses in nervous systems, mapping of interactions between genes and proteins in biochemical networks, distinguishing ecological relationships between different species in their habitats etc. In this thesis, we show that certain machine learning models, trained for the forecasting of experimental and synthetic time-series data from complex systems, can automatically learn the causal networks underlying such complex systems. Based on this observation, we develop new machine learning techniques for inference of causal interaction network connectivity structures underlying large, networked, noisy, complex dynamical systems, solely from the time-series of their nodal states.

In particular, our approach is to first train a type of machine learning architecture, known as the ‘reservoir computer’, to mimic the measured dynamics of an unknown network. We then use the trained reservoir computer system as an in silico computational model of the unknown network to estimate how small changes in nodal states propagate in time across that network. Since small perturbations of network nodal states are expected to spread along the links of the network, the estimated propagation of nodal state perturbations reveal the connections of the unknown network. Our technique is noninvasive, but is motivated by the widely used invasive network inference method, whereby the temporal propagation of active perturbations applied to the network nodes are observed and employed to infer the network links (e.g., tracing the effects of knocking down multiple genes, one at a time, can be used infer gene regulatory networks).

We discuss how we can further apply this methodology to infer causal network structures underlying different time-series datasets and compare the inferred network with the ground truth whenever available. We shall demonstrate three practical applications of this network inference procedure in (1) inference of network link strengths from time-series data of coupled, noisy Lorenz oscillators, (2) inference of time-delayed feedback couplings in opto-electronic oscillator circuit networks designed the laboratory, and, (3) inference of the synaptic network from publicly-available calcium fluorescence time-series data of C. elegans neurons. In all examples, we also explain how experimental factors like noise level, sampling time, and measurement duration systematically affect causal inference from experimental data.

The results show that synchronization and strong correlation among the dynamics of different nodal states are, in general, detrimental for causal network inference. Features that break synchrony among the nodal states, e.g., coupling strength, network topology, dynamical noise, and heterogeneity of the parameters of individual nodes, help the network inference. In fact, we show in this thesis that, for parameter regimes where the network nodal states are not synchronized, we can often achieve perfect causal network inference from simulated and experimental time-series data, using machine learning techniques, in a wide variety of physical systems. In cases where effects like observational noise, large sampling time, or small sampling duration hinder such perfect network inference, we show that it is possible to utilize specially-designed surrogate time-series data for assigning statistical confidence to individual inferred network links.

Given the general applicability of our machine learning methodology in time-series prediction and network inference, we anticipate that such techniques can be used for better model-building, forecasting, and control of complex systems in nature and in the lab.