Outlier detection in time series via mixed-integer conic quadratic optimization

Abstract: We consider the problem of estimating the true values of a Wiener process given noisy observations corrupted by outliers. The problem considered is closely related to the Trimmed Least Squares estimation problem, a robust estimation procedure well-studied from a statistical standpoint but poorly understood from an optimization perspective. In this paper we show how to improve existing mixed-integer quadratic optimization formulations for this problem. Specifically, we convexify the existing formulations via lifting, deriving new mixed-integer conic quadratic reformulations. The proposed reformulations are stronger and substantially faster when used with current mixed-integer optimization solvers. In our experiments, solution times are improved by at least two orders-of-magnitude.

optimization and control

Audience: researchers in the topic

Discrete Optimization Talks

Series comments: DOTs are virtual discrete optimization talks, organized by Aleksandr M. Kazachkov and Elias B. Khalil. To receive updates about upcoming DOTs, please join our mailing list. Topics of interest include theoretical, computational, and applied aspects of integer and combinatorial optimization.

The format is two thirty-minute talks and time for questions. Currently (January-April 2021), the seminars are scheduled on end-of-the-month Fridays at 1:00 p.m. ET. A special feature of DOTs is a social component. After a usual talk, you might grab a tea/coffee and chat with other attendees. Why not here too? Join us for some informal discussion after each DOT and throughout the week on our Discord channel.