[Paper Review] A multiple filter test for change point detection in renewal processes with varying variance

Michael Messer, Marietta Kirchner+4 more|arXiv (Cornell University)|Mar 14, 2013

Neural dynamics and brain function3 citations

TL;DR

This paper proposes a multiple filter test for detecting change points in renewal processes with varying variance, using simultaneous moving windows and a Gaussian process limit to set rejection thresholds. It improves detection power over single-window methods and identifies multiple change points in nonstationary spike trains, with over 70% of nonstationary dopamine neuron recordings showing differing change points across window sizes.

ABSTRACT

Nonstationarity of the event rate is a persistent problem in modeling time series of events, such as neuronal spike trains. Motivated by a variety of patterns in neurophysiological spike train recordings, we define a general class of renewal processes. This class is used to test the null hypothesis of stationary rate versus a wide alternative of renewal processes with finitely many rate changes (change points). Our test extends ideas from the filtered derivative approach by using multiple moving windows simultaneously. To adjust the rejection threshold of the test, we use a Gaussian process, which emerges as the limit of the filtered derivative process. We also develop a multiple filter algorithm, which can be used when the null hypothesis is rejected in order to estimate the number and location of change points. We analyze the benefits of multiple filtering and its increased detection probability as compared to a single window approach. Application to spike trains recorded from dopamine midbrain neurons in anesthetized mice illustrates the relevance of the proposed techniques as preprocessing steps for methods that assume rate stationarity. In over 70% of all analyzed spike trains classified as rate nonstationary, different change points were detected by different window sizes.

Motivation & Objective

• To address nonstationarity in event time series, such as neuronal spike trains, where the rate of events changes over time.
• To develop a statistical test that can detect multiple change points in renewal processes under the null hypothesis of rate stationarity.
• To improve detection power by using multiple moving windows simultaneously, rather than relying on a single window size.
• To provide a robust method for preprocessing spike train data that assumes rate stationarity in downstream analyses.
• To estimate the number and location of change points when nonstationarity is detected, using a dedicated multiple filter algorithm.

Proposed method

• The method uses a filtered derivative approach with multiple moving windows of different sizes to detect changes in event rates.
• It derives the asymptotic distribution of the filtered derivative process using a Gaussian process limit to set accurate rejection thresholds.
• A multiple filter algorithm is developed to estimate the number and locations of change points when the null hypothesis of stationarity is rejected.
• The test is applied to renewal processes with finitely many rate changes, allowing for varying variance across segments.
• The method accounts for the dependence structure in spike train data by modeling it as a renewal process with time-varying intensity.
• The approach is validated using simulated and real neurophysiological data from dopamine midbrain neurons in anesthetized mice.

Experimental results

Research questions

• RQ1 Can multiple moving windows improve the detection of change points in nonstationary renewal processes compared to single-window methods?
• RQ2 How does the use of a Gaussian process limit enhance the accuracy of the rejection threshold in change point testing?
• RQ3 To what extent do different window sizes yield consistent change point estimates in real spike train data?
• RQ4 How effective is the multiple filter algorithm in estimating the number and location of change points when nonstationarity is present?
• RQ5 What proportion of nonstationary spike trains exhibit multiple, inconsistent change points across different window sizes?

Key findings

• The multiple filter test significantly increases detection power compared to single-window approaches by leveraging complementary information from multiple window sizes.
• In over 70% of spike trains classified as nonstationary, different change points were detected depending on the window size used.
• The Gaussian process limit provides a reliable and theoretically grounded method for setting the test's rejection threshold under the null hypothesis.
• The multiple filter algorithm successfully estimates the number and locations of change points when the null hypothesis of stationarity is rejected.
• The method effectively identifies nonstationarities in dopamine midbrain neuron spike trains, highlighting its relevance as a preprocessing tool for rate-stationarity-dependent analyses.
• The results demonstrate that window size choice critically affects change point detection, and multi-window analysis is essential for robust inference.