Coresets for Time Series Clustering

We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors for real-time measurement and rapid drop in storage costs. In particular, we consider the setting where the time series data on N entities is generated from a Gaussian mixture model with autocorrelations over k clusters in Rd. Our main contribution is an algorithm to construct coresets for the maximum likelihood objective for this mixture model. Our algorithm is efficient, and, under a mild assumption on the covariance matrices of the Gaussians, the size of the coreset is independent of the number of entities N and the number of observations for each entity, and depends only polynomially on k, d and 1/ε, where ε is the error parameter. We empirically assess the performance of our coresets with synthetic data

Data Summarizations for Scalable, Robust and Privacy-Aware Learning in High Dimensions

The advent of large-scale datasets has offered unprecedented amounts of information for building statistically powerful machines, but, at the same time, also introduced a remarkable computational challenge: how can we efficiently process massive data? This thesis presents a suite of data reduction methods that make learning algorithms scale on large datasets, via extracting a succinct model-specific representation that summarizes the full data collection—a coreset. Our frameworks support by design datasets of arbitrary dimensionality, and can be used for general purpose Bayesian inference under real-world constraints, including privacy preservation and robustness to outliers, encompassing diverse uncertainty-aware data analysis tasks, such as density estimation, classification and regression. We motivate the necessity for novel data reduction techniques in the first place by developing a reidentification attack on coarsened representations of private behavioural data. Analysing longitudinal records of human mobility, we detect privacy-revealing structural patterns, that remain preserved in reduced graph representations of individuals’ information with manageable size. These unique patterns enable mounting linkage attacks via structural similarity computations on longitudinal mobility traces, revealing an overlooked, yet existing, privacy threat. We then propose a scalable variational inference scheme for approximating posteriors on large datasets via learnable weighted pseudodata, termed pseudocoresets. We show that the use of pseudodata enables overcoming the constraints on minimum summary size for given approximation quality, that are imposed on all existing Bayesian coreset constructions due to data dimensionality. Moreover, it allows us to develop a scheme for pseudocoresets-based summarization that satisfies the standard framework of differential privacy by construction; in this way, we can release reduced size privacy-preserving representations for sensitive datasets that are amenable to arbitrary post-processing. Subsequently, we consider summarizations for large-scale Bayesian inference in scenarios when observed datapoints depart from the statistical assumptions of our model. Using robust divergences, we develop a method for constructing coresets resilient to model misspecification. Crucially, this method is able to automatically discard outliers from the generated data summaries. Thus we deliver robustified scalable representations for inference, that are suitable for applications involving contaminated and unreliable data sources. We demonstrate the performance of proposed summarization techniques on multiple parametric statistical models, and diverse simulated and real-world datasets, from music genre features to hospital readmission records, considering a wide range of data dimensionalities.Nokia Bell Labs, Lundgren Fund, Darwin College, University of Cambridge Department of Computer Science & Technology, University of Cambridg

Community Sense and Response Systems

The proliferation of smartphones and other internet-enabled, sensor-equipped consumer devices enables us to sense and act upon the physical environment in unprecedented ways. This thesis considers Community Sense-and-Response (CSR) systems, a new class of web application for acting on sensory data gathered from participants' personal smart devices. The thesis describes how rare events can be reliably detected using a decentralized anomaly detection architecture that performs client-side anomaly detection and server-side event detection. After analyzing this decentralized anomaly detection approach, the thesis describes how weak but spatially structured events can be detected, despite significant noise, when the events have a sparse representation in an alternative basis. Finally, the thesis describes how the statistical models needed for client-side anomaly detection may be learned efficiently, using limited space, via coresets. The Caltech Community Seismic Network (CSN) is a prototypical example of a CSR system that harnesses accelerometers in volunteers' smartphones and consumer electronics. Using CSN, this thesis presents the systems and algorithmic techniques to design, build and evaluate a scalable network for real-time awareness of spatial phenomena such as dangerous earthquakes.</p