Blind Change Point Detection And Regime Segmentation Using Gaussian Process Regression

Time-series analysis is used heavily in modeling and forecasting weather, economics, medical data as well as in various other fields. Change point detection (CPD) means finding abrupt changes in the time-series when the statistical property of a certain part of it starts to differ. CPD has attracted a lot of attention in the artificial intelligence, machine learning and data mining communities. In this thesis, a novel CPD algorithm is introduced for segmenting multivariate time-series data. The proposed algorithm is a general pipeline to process any high dimensional multivariate time-series data using nonlinear non-parametric dynamic system. It consists of manifold learning technique for dimensionality reduction, Gaussian process regression to model the non-linear dynamics of the data and predict the next possible time-step, as well as outlier detection based on Mahalanobis distance to determine the change points. The performance of the new CPD algorithm is assessed on synthetic as well as real-world data for validation. The pipeline is used on federal reserve economic data (FRED) to detect recession. Finally, functional magnetic resonance imaging (fMRI) data of larval zebrafish is used to segment regions of homogeneous brain activity

Robust Online Time Series Prediction with Recurrent Neural Networks

Time series forecasting for streaming data plays an important role in many real applications, ranging from IoT systems, cyber-networks, to industrial systems and healthcare. However the real data is often complicated with anomalies and change points, which can lead the learned models deviating from the underlying patterns of the time series, especially in the context of online learning mode. In this paper we present an adaptive gradient learning method for recurrent neural networks (RNN) to forecast streaming time series in the presence of anomalies and change points. We explore the local features of time series to automatically weight the gradients of the loss of the newly available observations with distributional properties of the data in real time. We perform extensive experimental analysis on both synthetic and real datasets to evaluate the performance of the proposed method

Unsupervised methods to discover events from spatio-temporal data

University of Minnesota Ph.D. dissertation. May 2016. Major: Computer Science. Advisor: Vipin Kumar. 1 computer file (PDF); ix, 110 pages.Unsupervised event detection in spatio-temporal data aims to autonomously identify when and/or where events occurred with little or no human supervision. It is an active field of research with notable applications in social, Earth, and medical sciences. While event detection has enjoyed tremendous success in many domains, it is still a challenging problem due to the vastness of data points, presence of noise and missing values, the heterogeneous nature of spatio-temporal signals, and the large variety of event types. Unsupervised event detection is a broad and yet open research area. Instead of exploring every aspect in this area, this dissertation focuses on four novel algorithms that covers two types of important events in spatio-temporal data: change-points and moving regions. The first algorithm in this dissertation is the Persistence-Consistency (PC) framework. It is a general framework that can increase the robustness of change-point detection algorithms to noise and outliers. The major advantage of the PC framework is that it can work with most modeling-based change-point detection algorithms and improve their performance without modifying the selected change-point detection algorithm. We use two real-world applications, forest fire detection using a satellite dataset and activity segmentation from a mobile health dataset, to test the effectiveness of this framework. The second and third algorithms in this dissertation are proposed to detect a novel type of change point, which is named as contextual change points. While most existing change points more or less indicate that the time series is different from what it was before, a contextual change point typically suggests an event that causes the relationship of several time series changes. Each of these two algorithms introduces one type of contextual change point and also presents an algorithm to detect the corresponding type of change point. We demonstrate the unique capabilities of these approaches with two applications: event detection in stock market data and forest fire detection using remote sensing data. The final algorithm in this dissertation is a clustering method that discovers a particular type of moving regions (or dynamic spatio-temporal patterns) in noisy, incomplete, and heterogeneous data. This task faces two major challenges: First, the regions (or clusters) are dynamic and may change in size, shape, and statistical properties over time. Second, numerous spatio-temporal data are incomplete, noisy, heterogeneous, and highly variable (over space and time). Our proposed approach fully utilizes the spatial contiguity and temporal similarity in the spatio-temporal data and, hence, can address the above two challenges. We demonstrate the performance of the proposed method on a real-world application of monitoring in-land water bodies on a global scale