Detecting change-points in Markov chains

Ordinal Patterns, Entropy, and EEG

“…In order to identify such points we have introduced the CEofOP ("Conditional-Entropy-of-Ordinal-Patterns-based") statistic, which is based on eCE. For finding all relevant change-points, we have used the binary segmentation procedure [67] in combination with block bootstrapping [63,64]. After segmenting the time series as described, the obtained segments were clustered on the basis of their ordinal pattern distributions by means of a commonly-used cluster algorithm (k-means clustering with the squared Hellinger distance).…”

“…This is a classical problem of change-point detection (see Section 1.1.2.2 in [59]); to solve it, we compare the value of CEofOP( t * ; d) with a certain threshold h: if CEofOP( t * ; d) ≥ h then one decides that there is a change-point in t * , otherwise it is concluded that no change has occurred. We compute the threshold h using block bootstrapping from the sequence of ordinal patterns (see [63,64] for a comprehensive description of the block bootstrapping; since this approach is rather often used we do not go into details). The solution of Problem 1 using the CEofOP statistic is described in Algorithm 1 (Appendix A.1).…”

“…A time point where some characteristic of a time series changes is called a change-point. The detection of change-points is a typical problem of time series analysis [59,[61][62][63][64]; in particular it provides a segmentation of time series into stationary segments. In this section we suggest an ordinal-patterns-based method for change-point detection.…”

Bayesian Detection of Changepoints in Finite-State Markov Chains for Multiple Sequences

“…The geometric assumption can be relaxed by using a hidden semi-Markov approach for example (Guédon 2003), but this imposes computational restrictions, namely that the time complexity of inference (e.g., via the forward-backward algorithm, Rabiner (1989)) can scale as O(T 2 ) where T is the length of a sequence. Polansky (2007) proposed a likelihood-based framework for segmentation assuming a process that switches between different Markov chains with unknown parameters, but for the 3 case of a single sequence rather than multiple sequences. A restricted variant of the multiple sequence changepoint problem is the case where sequences are required to be of the same length and the changepoints are assumed to occur at the same location in each sequence, which can also be viewed as a single multivariate sequence (Lai and Xing 2011;Xing et al 2012;Fitzpatrick and Marchev 2013).…”

Change-Point Detection using the Conditional Entropy of Ordinal Patterns

“…On the contrary, the higher h, the higher the possibility of false rejection of the H A is. As it is usually done, we consider the threshold h as a function of the desired probability α of false alarm; for computing the threshold h(α) we use block bootstrapping from the sequence π d,L of ordinal patterns (bootstrapping is often used in change-point detection for computing a threshold, see [44,45] for a theoretical discussion and [46,47] for applications of bootstrapping with detailed and clear explanations). Namely we shuffle blocks of ordinal patterns from the original sequence, in order to create a new artificial sequence.…”