A computationally efficient nonparametric approach for changepoint detection

In this paper we build on an approach proposed by Zou et al. (2014) for nonpara- metric changepoint detection. This approach defines the best segmentation for a data set as the one which minimises a penalised cost function, with the cost function defined in term of minus a non-parametric log-likelihood for data within each segment. Min- imising this cost function is possible using dynamic programming, but their algorithm had a computational cost that is cubic in the length of the data set. To speed up computation, Zou et al. (2014) resorted to a screening procedure which means that the estimated segmentation is no longer guaranteed to be the global minimum of the cost function. We show that the screening procedure adversely affects the accuracy of the changepoint detection method, and show how a faster dynamic programming algorithm, Pruned Exact Linear Time, PELT (Killick et al., 2012), can be used to find the optimal segmentation with a computational cost that can be close to linear in the amount of data. PELT requires a penalty to avoid under/over-fitting the model which can have a detrimental effect on the quality of the detected changepoints. To overcome this issue we use a relatively new method, Changepoints Over a Range of PenaltieS (CROPS) (Haynes et al., 2015), which finds all of the optimal segmentations for multiple penalty values over a continuous range. We apply our method to detect changes in heart rate during physical activity

Real-Time Predictive Modeling and Robust Avoidance of Pedestrians with Uncertain, Changing Intentions

To plan safe trajectories in urban environments, autonomous vehicles must be able to quickly assess the future intentions of dynamic agents. Pedestrians are particularly challenging to model, as their motion patterns are often uncertain and/or unknown a priori. This paper presents a novel changepoint detection and clustering algorithm that, when coupled with offline unsupervised learning of a Gaussian process mixture model (DPGP), enables quick detection of changes in intent and online learning of motion patterns not seen in prior training data. The resulting long-term movement predictions demonstrate improved accuracy relative to offline learning alone, in terms of both intent and trajectory prediction. By embedding these predictions within a chance-constrained motion planner, trajectories which are probabilistically safe to pedestrian motions can be identified in real-time. Hardware experiments demonstrate that this approach can accurately predict pedestrian motion patterns from onboard sensor/perception data and facilitate robust navigation within a dynamic environment.Comment: Submitted to 2014 International Workshop on the Algorithmic Foundations of Robotic

Changepoint detection for data intensive settings

Detecting a point in a data sequence where the behaviour alters abruptly, otherwise known as a changepoint, has been an active area of interest for decades. More recently, with the advent of the data intensive era, the need for automated and computationally efficient changepoint methods has grown. We here introduce several new techniques for doing this which address many of the issues inherent in detecting changes in a streaming setting. In short, these new methods, which may be viewed as non-trivial extensions of existing classical procedures, are intended to be as useful in as wide a set of situations as possible, while retaining important theoretical guarantees and ease of implementation. The first novel contribution concerns two methods for parallelising existing dynamic programming based approaches to changepoint detection in the single variate setting. We demonstrate that these methods can result in near quadratic computational gains, while retaining important theoretical guarantees. Our next area of focus is the multivariate setting. We introduce two new methods for data intensive scenarios with a fixed, but possibly large, number of dimensions. The first of these is an offline method which detects one change at a time using a new test statistic. We demonstrate that this test statistic has competitive power in a variety of possible settings for a given changepoint, while allowing the method to be versatile across a range of possible modelling assumptions. The other method we introduce for multivariate data is also suitable in the streaming setting. In addition, it is able to relax many standard modelling assumptions. We discuss the empirical properties of the procedure, especially insofar as they relate to a desired false alarm error rate

Bayesian changepoint analysis for atomic force microscopy and soft material indentation

Material indentation studies, in which a probe is brought into controlled physical contact with an experimental sample, have long been a primary means by which scientists characterize the mechanical properties of materials. More recently, the advent of atomic force microscopy, which operates on the same fundamental principle, has in turn revolutionized the nanoscale analysis of soft biomaterials such as cells and tissues. This paper addresses the inferential problems associated with material indentation and atomic force microscopy, through a framework for the changepoint analysis of pre- and post-contact data that is applicable to experiments across a variety of physical scales. A hierarchical Bayesian model is proposed to account for experimentally observed changepoint smoothness constraints and measurement error variability, with efficient Monte Carlo methods developed and employed to realize inference via posterior sampling for parameters such as Young's modulus, a key quantifier of material stiffness. These results are the first to provide the materials science community with rigorous inference procedures and uncertainty quantification, via optimized and fully automated high-throughput algorithms, implemented as the publicly available software package BayesCP. To demonstrate the consistent accuracy and wide applicability of this approach, results are shown for a variety of data sets from both macro- and micro-materials experiments--including silicone, neurons, and red blood cells--conducted by the authors and others.Comment: 20 pages, 6 figures; submitted for publicatio

Novel Methods for Efficient Changepoint Detection

This thesis introduces several novel computationally efficient methods for offline and online changepoint detection. The first part of the thesis considers the challenge of detecting abrupt changes in scenarios where there is some autocorrelated noise or where the mean fluctuates locally between the changes. In such situations, existing implementations can lead to substantial overestimation of the number of changes. In response to this challenge, we introduce DeCAFS, an efficient dynamic programming algorithm to deal with such scenarios. DeCAFS models local fluctuations as a random walk process and autocorrelated noise as an AR(1) process. Through theory and empirical studies we demonstrate that this approach has greater power at detecting abrupt changes than existing approaches. The second part of the thesis considers a practical, computational challenge that can arise with online changepoint detection within the real-time domain. We introduce a new procedure, called FOCuS, a fast online changepoint detection algorithm based on the simple Page-CUSUM sequential likelihood ratio test. FOCuS enables the online changepoint detection problem to be solved sequentially in time, through an efficient dynamic programming recursion. In particular, we establish that FOCuS outperforms current state-of-the-art algorithms both in terms of efficiency and statistical power, and can be readily extended to more general scenarios. The final part of the thesis extends ideas from the nonparametric changepoint detection literature to the online setting. Specifically, a novel algorithm, NUNC, is introduced to perform an online detection for changes in the distribution of real-time data. We explore the properties of two variants of this algorithm using both simulated and real data examples