Outlier-Robust Convex Segmentation

We derive a convex optimization problem for the task of segmenting sequential data, which explicitly treats presence of outliers. We describe two algorithms for solving this problem, one exact and one a top-down novel approach, and we derive a consistency results for the case of two segments and no outliers. Robustness to outliers is evaluated on two real-world tasks related to speech segmentation. Our algorithms outperform baseline segmentation algorithms.Comment: * Accepted to AAAI-15, this version includes the appendix/supplementary material referenced in the AAAI-15 submission, as well as color figures * This version include some minor typos correctio

Greedy Gaussian Segmentation of Multivariate Time Series

We consider the problem of breaking a multivariate (vector) time series into segments over which the data is well explained as independent samples from a Gaussian distribution. We formulate this as a covariance-regularized maximum likelihood problem, which can be reduced to a combinatorial optimization problem of searching over the possible breakpoints, or segment boundaries. This problem can be solved using dynamic programming, with complexity that grows with the square of the time series length. We propose a heuristic method that approximately solves the problem in linear time with respect to this length, and always yields a locally optimal choice, in the sense that no change of any one breakpoint improves the objective. Our method, which we call greedy Gaussian segmentation (GGS), easily scales to problems with vectors of dimension over 1000 and time series of arbitrary length. We discuss methods that can be used to validate such a model using data, and also to automatically choose appropriate values of the two hyperparameters in the method. Finally, we illustrate our GGS approach on financial time series and Wikipedia text data

Outlier-Robust Convex Segmentation

Abstract We address the task of segmenting sequential data using convex optimization problem, which is specifically designed to work in the context of outliers in the data. We propose two algorithms for solving this problem, one exact and one a top-down hierarchical approach. Robustness to outliers is evaluated on a real-world task related to speech segmentation. Our algorithms outperform baseline segmentation algorithms