Detecting changes in slope in a noisy signal observed over time.

What is it about?

Often we make measurements of a process over time -- as an example in this paper we consider measurements of the angular position of a bacteria. It is natural to view the data as a signal (the true angular position in our example) plus some observational noise. This paper looks at how to efficiently estimate the signal, if we assume that the signal changes linearly with time, but that at some time points (called chanegpoints) the "slope" of the signal changes. The main innovation is an efficient algorithm for searching over all possible time-points where the slope may change.

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Why is it important?

Detecting changes in time-series is a common problem -- this paper presents a solution to detecting a particular type of change, and has algorithmic ideas that could be applied in other settings. For the change-in-slope problem our method appears to be much more accurate at estimating when the slope changes than alternative approaches.