Sunday, August 21, 2016
Changepoint Detection : Theoretical Background
Introduction
Changepoints are abrupt variations in the generative parameters of sequential data. Changepoint detection is the process of identifying such abrupt variations and it has been useful in a wide range of applications such as EEG analysis, DNA segmentation, econometrics etc.
Bayesian ways of change point detection focus on segmentation and techniques to generate samples from the posterior distribution over changepoint locations.
Let's try to understand this without a lot of complex mathematical notations. When we are given a data set that varies according to time ( e.g:  a time series ), there might be sudden changes. Because of these changes the data set can be partitioned and separately analysed. Therefore if we assume that within a partition there is a relationship between data points, we can perform a regression to calculate regression coefficients. (Provided that we have an idea about the change points)
However this does not capture the uncertainty involved with the change points. This is where change point distributions come in to play. Following the Bayesian change point model, and by using a constrained HMM (Hidden Markov Model ) we are able to calculate the posterior distribution.
Therefore the posterior distribution can be calculated with a modified forward backward algorithm. The algorithm can be further improved to compute the most probable change point configuration.
The references below provide more insight to the postCP package.
[1] Luong, T.M., Rozenholc, Y. and Nuel, G., 2013. Fast estimation of posterior probabilities in changepoint analysis through a constrained hidden Markov model. Computational Statistics & Data Analysis, 68, pp.129140.
However this does not capture the uncertainty involved with the change points. This is where change point distributions come in to play. Following the Bayesian change point model, and by using a constrained HMM (Hidden Markov Model ) we are able to calculate the posterior distribution.
Therefore the posterior distribution can be calculated with a modified forward backward algorithm. The algorithm can be further improved to compute the most probable change point configuration.
The references below provide more insight to the postCP package.
[1] Luong, T.M., Rozenholc, Y. and Nuel, G., 2013. Fast estimation of posterior probabilities in changepoint analysis through a constrained hidden Markov model. Computational Statistics & Data Analysis, 68, pp.129140.
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