complex networks
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A Game Theoretical Framework for Quantifying Causes in Neural Networks
Which nodes in a brain network causally influence one another, and how do such interactions utilize the underlying structural connectivity? One of the fundamental goals of neuroscience is to pinpoint such causal relations. Conventionally, these relationships are established by manipulating a node while tracking changes in another node. A causal role is then assigned to the first node if this intervention led to a significant change in the state of the tracked node. In this presentation, I use a series of intuitive thought experiments to demonstrate the methodological shortcomings of the current ‘causation via manipulation’ framework. Namely, a node might causally influence another node, but how much and through which mechanistic interactions? Therefore, establishing a causal relationship, however reliable, does not provide the proper causal understanding of the system, because there often exists a wide range of causal influences that require to be adequately decomposed. To do so, I introduce a game-theoretical framework called Multi-perturbation Shapley value Analysis (MSA). Then, I present our work in which we employed MSA on an Echo State Network (ESN), quantified how much its nodes were influencing each other, and compared these measures with the underlying synaptic strength. We found that: 1. Even though the network itself was sparse, every node could causally influence other nodes. In this case, a mere elucidation of causal relationships did not provide any useful information. 2. Additionally, the full knowledge of the structural connectome did not provide a complete causal picture of the system either, since nodes frequently influenced each other indirectly, that is, via other intermediate nodes. Our results show that just elucidating causal contributions in complex networks such as the brain is not sufficient to draw mechanistic conclusions. Moreover, quantifying causal interactions requires a systematic and extensive manipulation framework. The framework put forward here benefits from employing neural network models, and in turn, provides explainability for them.
Learning the structure and investigating the geometry of complex networks
Networks are widely used as mathematical models of complex systems across many scientific disciplines, and in particular within neuroscience. In this talk, we introduce two aspects of our collaborative research: (1) machine learning and networks, and (2) graph dimensionality. Machine learning and networks. Decades of work have produced a vast corpus of research characterising the topological, combinatorial, statistical and spectral properties of graphs. Each graph property can be thought of as a feature that captures important (and sometimes overlapping) characteristics of a network. We have developed hcga, a framework for highly comparative analysis of graph data sets that computes several thousands of graph features from any given network. Taking inspiration from hctsa, hcga offers a suite of statistical learning and data analysis tools for automated identification and selection of important and interpretable features underpinning the characterisation of graph data sets. We show that hcga outperforms other methodologies (including deep learning) on supervised classification tasks on benchmark data sets whilst retaining the interpretability of network features, which we exemplify on a dataset of neuronal morphologies images. Graph dimensionality. Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogeneities, or to intrinsically discrete systems such as networks. Deviating from approaches based on fractals, here, we present a new framework to define intrinsic notions of dimension on networks, the relative, local and global dimension. We showcase our method on various physical systems.
complex networks coverage
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