Professor Paul Fearnhead, Lancaster University - 14:00-1500

Efficient Approaches to Changepoint Problems with Dependence Across Segments

Changepoint detection is an increasingly important problem across a range of applications. It is most commonly encountered when analysing time-series data, where changepoints correspond to points in time where some feature of the data, for example its mean, changes abruptly. Often there are important computational constraints when analysing such data, with the number of data sequences and their lengths meaning that only very efficient methods for detecting changepoints are practically feasible.

A natural way of estimating the number and location of changepoints is to minimise a cost that trades-off a measure of fit to the data with the number of changepoints fitted. There are now some efficient algorithms that can exactly solve the resulting optimisation problem, but they are only applicable in situations where there is no dependence of the mean of the data across segments. Using such methods can lead to a loss of statistical efficiency in situations where e.g. it is known that the change in mean must be positive.

This talk will present a new class of efficient algorithms that can exactly minimise our cost whilst imposing certain constraints on the relationship of the mean before and after a change. These algorithms have links to recursions that are seen for discrete-state hidden Markov Models, and within sequential Monte Carlo. We demonstrate the usefulness of these algorithms on problems such as detecting spikes in calcium imaging data. Our algorithm can analyse data of length 100,000 in less than a second, and has been used by the Allen Brain Institute to analyse the spike patterns of over 60,000 neurons.

(This is joint work with Toby Hocking, Sean Jewell, Guillem Rigaill and Daniela Witten.)

Dr. Sandipan Roy, Department of Mathematical Science, University of Bath (15:00-16:00)

Network Heterogeneity and Strength of Connections

Abstract: Detecting strength of connection in a network is a fundamental problem in understanding the relationship among individuals. Often it is more important to understand how strongly the two individuals are connected rather than the mere presence/absence of the edge. This paper introduces a new concept of strength of connection in a network through a nonparameteric object called “Grafield”. “Grafield” is a piece-wise constant bi-variate kernel function that compactly represents the affinity or strength of ties (or interactions) between every pair of vertices in the graph. We estimate the “Grafield” function through a spectral analysis of the Laplacian matrix followed by a hard thresholding (Gavish & Donoho, 2014) of the singular values. Our estimation methodology is valid for asymmetric directed network also. As a by product we get an efficient procedure for edge probability matrix estimation as well. We validate our proposed approach with several synthetic experiments and compare with existing algorithms for edge probability matrix estimation. We also apply our proposed approach to three real datasets- understanding the strength of connection in (a) a social messaging network, (b) a network of political parties in US senate and (c) a neural network of neurons and synapses in C. elegans, a type of worm.