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I will give an overview of recent work on understanding learning processes on networks, specifically inference of a function: imagine trying to predict biochemical reactivity of a protein based on noisy measurements for "similar" molecules, where similarity is represented by links on a network whose nodes are the various proteins. In a Bayesian framework and using flexible priors (Gaussian processes) on the function to be learned, I will show that the cavity or replica methods can be used to predict the learning curve (mean squared error versus number of data points), exactly so in the limit of large random networks with some imposed degree distribution. I will then trace an arc from this research to my work on dynamics of protein interaction networks, glasses and dynamical phase transitions, and soft matter physics.

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Prof. Peter Sollich, King's College London
Hörsaal III der Physikalischen Institute
Contact: not specified