Rebecca Killick

Optimal Detection of Changepoints With a Linear Computational Cost

We consider the problem of detecting multiple changepoints in large data sets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example in genetics as we analyse larger regions of the genome, or in finance as we observe time-series over longer periods. We consider the common approach of detecting changepoints through minimising a cost function over possible numbers and locations of changepoints. This includes several established procedures for detecting changing points, such as penalised likelihood and minimum description length. We introduce a new ∗R. Killick is Senior Research Associate, Department of Mathematics & Statistics, Lancaster University, Lancaster, UK (E-mail: r.killick@lancs.ac.uk). P. Fearnhead is Professor, Department of Mathematics & Statistics, Lancaster University, Lancaster, UK (E-mail: p.fearnhead@lancs.ac.uk). I.A. Eckley is Senior Lecturer, Department of Mathematics & Statistics, Lancaster University, Lancaster, UK (E-mail: i.eckley@lancs.ac.uk). The authors are grateful to Richard Davis and Alice Cleynen for providing the Auto-PARM and PDPA software respectively. Part of this research was conducted whilst R. Killick was a jointly funded Engineering and Physical Sciences Research Council (EPSRC) / Shell Research Ltd graduate student at Lancaster University. Both I.A. Eckley and R. Killick also gratefully acknowledge the financial support of the EPSRC grant number EP/I016368/1. 1 ar X iv :1 10 1. 14 38 v3 [ st at .M E ] 9 O ct 2 01 2 method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost which, under mild conditions, is linear in the number of observations. This compares favourably with existing methods for the same problem whose computational cost can be quadratic or even cubic. In simulation studies we show that our new method can be orders of magnitude faster than these alternative exact methods. We also compare with the Binary Segmentation algorithm for identifying changepoints, showing that the exactness of our approach can lead to substantial improvements in the accuracy of the inferred segmentation of the data.

A wavelet-based approach for detecting changes in second order structure within nonstationary time series

This article proposes a test to detect changes in general autocovariance structure in nonstationary time series. Our approach is founded on the locally stationary wavelet (LSW) process model for time series which has previously been used for classification and segmentation of time series. Using this framework we form a likelihood-based hypothesis test and demonstrate its performance against existing methods on various simulated examples as well as applying it to a problem arising from ocean engineering.

Virtual machine warmup blows hot and cold

Virtual Machines (VMs) with Just-In-Time (JIT) compilers are traditionally thought to execute programs in two phases: the initial warmup phase determines which parts of a program would most benefit from dynamic compilation, before JIT compiling those parts into machine code; subsequently the program is said to be at a steady state of peak performance. Measurement methodologies almost always discard data collected during the warmup phase such that reported measurements focus entirely on peak performance. We introduce a fully automated statistical approach, based on changepoint analysis, which allows us to determine if a program has reached a steady state and, if so, whether that represents peak performance or not. Using this, we show that even when run in the most controlled of circumstances, small, deterministic, widely studied microbenchmarks often fail to reach a steady state of peak performance on a variety of common VMs. Repeating our experiment on 3 different machines, we found that at most 43.5% of pairs consistently reach a steady state of peak performance.

The Uncertainty of Storm Season Changes: Quantifying the Uncertainty of Autocovariance Changepoints

In oceanography, there is interest in determining storm season changes for logistical reasons such as equipment maintenance scheduling. In particular, there is interest in capturing the uncertainty associated with these changes in terms of the number and location of them. Such changes are associated with autocovariance changes. This article proposes a framework to quantify the uncertainty of autocovariance changepoints in time series motivated by this oceanographic application. More specifically, the framework considers time series under the locally stationary wavelet (LSW) framework, deriving a joint density for scale processes in the raw wavelet periodogram. By embedding this density within a hidden Markov model (HMM) framework, we consider changepoint characteristics under this multiscale setting. Such a methodology allows us to model changepoints and their uncertainty for a wide range of models, including piecewise second-order stationary processes, for example, piecewise moving average processes.

Just Browsing?: Understanding User Journeys in Online TV

Understanding the dynamics of user interactions and the behaviour of users as they browse for content is vital for advancements in content discovery, service personalisation, and recommendation engines which ultimately improve quality of user experience. In this paper, we analyse how more than 1,100 users browse an online TV service over a period of six months. Through the use of model-based clustering, we identify distinctive groups of users with discernible browsing patterns that vary during the course of the day.

Effect of aging on post-saccadic oscillations

ABSTRACT Recent research have shown that the eye movement data measured by an eye tracker does not necessarily reflect the exact rotations of the eyeball. For example, post‐saccadic eye movements may be more reflecting the relative movements between the pupil and the iris rather than the eyeball oscillations. Since, accurate measurement of eye movements is important in many studies, it is crucial to identify different factors that influence the dynamics of the eye movements measured by an eye tracker. Previous studies have shown that deformation of the internal structure of the iris and size of the pupil directly affect the amplitude of the post‐saccadic oscillations that are measured by video‐based eye trackers that are pupil‐based. In this paper, we look at the effect of aging on post‐saccadic oscillations. We recorded eye movements from a group of 43 young and 22 older participants during an abstract and a more natural viewing task. The recording was conducted with a video‐based eye tracker using the pupil center and corneal reflection. We anticipated that changes in the muscle strength as an effect of aging might affect, directly or indirectly, the post‐saccadic oscillations. Results showed that the size of the post‐saccadic oscillations were significantly larger for our older group. The results suggests that aging has to be considered as an important factor when studying the post‐saccadic eye movements.

Strategy selection versus flexibility: Using eye-trackers to investigate strategy use during mental rotation.

Spatial researchers have been arguing over the optimum cognitive strategy for spatial problem-solving for several decades. The current article aims to shift this debate from strategy dichotomies to strategy flexibility—a cognitive process, which although alluded to in spatial research, presents practical methodological challenges to empirical testing. In the current study, participants’ eye movements were tracked during a mental rotation task (MRT) using the Tobii ×60 eye-tracker. Results of a latent profile analysis, combining different eye movement parameters, indicated two distinct eye-patterns—fixating and switching patterns. The switching eye-pattern was associated with high mental rotation performance. There were no sex differences in eye-patterns. To investigate strategy flexibility, we used a novel application of the changepoint detection algorithm on eye movement data. Strategy flexibility significantly predicted mental rotation performance. Male participants demonstrated higher strategy flexibility than did female participants. Our findings highlight the importance of strategy flexibility in spatial thinking and have implications for designing spatial training techniques. The novel approaches to analyzing eye movement data in the current paper can be extended to research beyond the spatial domain.