Some new tasks are trivial to learn, while others are essentially impossible; what determines how easy it is to learn the structure of a given task? Similar to how our priors about visual scenes demonstrably color our perception of the world, our priors about the structure of tasks shape our learning, decision-making, and generalization abilities. Drawing inspiration from the insights afforded to neuroscience by the characterization of visual priors, in this dissertation, we strive to quantify priors over abstract structures. In particular, we focus on graphs: the structure of interactions.
In Chapter 3, we describe the natural analogue of cumulants (e.g., mean, (co)variance, skew, kurtosis) for graphs, building a hierarchical description based on local correlations between an increasing number of connections. This provides a principled framework for quantifying the propensity of a network to display arbitrary substructures, and allows one to meaningfully compare networks of different sizes and edge densities.
In Chapter 4, we analyze graph structure globally, via the dynamics of diffusion, providing an algorithm that reduces a graph while preserving its large-scale structure. Our framework analytically unifies two areas of research, namely graph sparsification (removing edges) and graph coarsening (merging nodes), and is competitive with current state-of-the-art algorithms.
From a neuroscience perspective, we develop a novel method for quantifying human priors over graphs (Chapters 2 and 3). In Chapter 5, we apply this method to graphical representations of social and navigation tasks: two domains that have been relevant (over evolutionary timescales) to our everyday life. We find that the resulting priors exhibit non-trivial graphical structure. While some features appear to be general, such as the preferred amount of sparsity as a function of graph size, other features appear to be domain-specific, such as the preference for triadic closure in social interactions.
Through the development of principled methods for analyzing network structure and the use of an analytically tractable model of human learning on graphs, this work provides useful tools that could cross-pollinate with other active areas of research, such as artificial intelligence.
|Commitee:||Chazelle, Bernard, Griffths, Thomas, Botvinick, Matthew, Brody, Carlos|
|School Location:||United States -- New Jersey|
|Source:||DAI-B 81/8(E), Dissertation Abstracts International|
|Subjects:||Neurosciences, Applied Mathematics, Quantitative psychology|
|Keywords:||Cumulants, Graphs, MCMCP, Networks, Priors|
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