Outlier Detection in Time Series via Mixed-Integer Conic Quadratic Optimization

We consider the problem of estimating the true values of a Wiener process given noisy observations corrupted by outliers. 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.