Speaker: Prof Ioannis Kontoyiannis, Department of Engineering, University of Cambridge, UK
Title: "Finding Complex Structure in Discrete Time Series"
Abstract: The identification of useful temporal structure in discrete time series
is an important component of algorithms used for many tasks in statistical
inference and machine learning. Most early approaches developed were
ineffective in practice, because the amount of data required for reliable
modeling grew exponentially with memory length. On the other hand,
many of the more modern methodologies that make use of more flexible
and parsimonious models, result in algorithms that do not scale well
and are computationally ineffective for larger data sets.
We will discuss a class of novel methodological tools for effective Bayesian
inference for general discrete time series, which offer promising results
on both small and big data. Our starting point is the development of a rich
class of Bayesian hierarchical models for variable-memory Markov chains,
based on ideas stemming from the class of context tree weighting data
compression algorithms. The particular prior structure we adopt
makes it possible to design effective, linear-time algorithms
that can compute most of the important features of the resulting posterior
and predictive distributions without resorting to simulation.
We have applied the resulting tools to numerous application-specific tasks
(including on-line prediction, segmentation, classification, anomaly
detection, entropy estimation, and causality testing) on data sets from
a very broad range of applications. Results on both simulated and real
data will be presented, with an emphasis on data sets from neuroscience
and genetics studies.