AbstractsComputer Science

Streaming is an important paradigm for handling high-speed data sets that are too large to fit in main memory. Prior work in data streams has shown how to estimate simple statistical parameters, such as histograms, heavy hitters, frequent moments, etc., on data streams. This dissertation focuses on a number of more sophisticated statistical analyses that are performed in near real-time, using limited resources. First, we present how to model stream data parametrically; in particular, we fit hierarchical (binomial multifractal) and non-hierarchical (Pareto) power-law models on a data stream. It yields algorithms that are fast, space-efficient, and provide accuracy guarantees. We also design fast methods to perform online model validation at streaming speeds. The second contribution of this dissertation addresses the problem of modeling an individual's behaviors via ``signature'' for nodes in communication graphs. We develop a formal framework for the usage of signatures on communication graphs and identify fundamental properties that are natural to signature schemes. We justify these properties by showing how they impact a set of applications. We then explore several signature schemes in our framework and evaluate them on real data in terms of these properties. This provides insights into suitable signature schemes for desired applications. Finally, the dissertation studies the detection of changes in models on data with unknown distributions. We adapt the sound statistical method of sequential probability ratio test to the online streaming case, without independence assumption. The resulting algorithm works seamlessly without window limitations inherent in prior work, and is highly effective at detecting changes quickly. Furthermore, we formulate and extend our streaming solution to the local change detection problem that has not been addressed earlier. As concrete applications of our techniques, we complement our analytic and algorithmic results with experiments on network traffic data to demonstrate the practicality of our methods at line speeds, and the potential power of streaming techniques for statistical modeling in data mining.