7 research outputs found
Fast likelihood-based change point detection
Change point detection plays a fundamental role in many real-world
applications, where the goal is to analyze and monitor the behaviour of a data
stream. In this paper, we study change detection in binary streams. To this
end, we use a likelihood ratio between two models as a measure for indicating
change. The first model is a single bernoulli variable while the second model
divides the stored data in two segments, and models each segment with its own
bernoulli variable. Finding the optimal split can be done in time, where
is the number of entries since the last change point. This is too expensive
for large . To combat this we propose an approximation scheme that yields
approximation in time. The
speed-up consists of several steps: First we reduce the number of possible
candidates by adopting a known result from segmentation problems. We then show
that for fixed bernoulli parameters we can find the optimal change point in
logarithmic time. Finally, we show how to construct a candidate list of size
for model parameters. We demonstrate empirically the
approximation quality and the running time of our algorithm, showing that we
can gain a significant speed-up with a minimal average loss in optimality
Fast Likelihood-Based Change Point Detection
Change point detection plays a fundamental role in many real-world applications, where the goal is to analyze and monitor the behaviour of a data stream. In this paper, we study change detection in binary streams. To this end, we use a likelihood ratio between two models as a measure for indicating change. The first model is a single bernoulli variable while the second model divides the stored data in two segments, and models each segment with its own bernoulli variable. Finding the optimal split can be done in O(n) time, where n is the number of entries since the last change point. This is too expensive for large n. To combat this we propose an approximation scheme that yields (1 - epsilon) approximation in O(epsilon(-1) log(2) n) time. The speed-up consists of several steps: First we reduce the number of possible candidates by adopting a known result from segmentation problems. We then show that for fixed bernoulli parameters we can find the optimal change point in logarithmic time. Finally, we show how to construct a candidate list of size O(epsilon(-1) log n) formodel parameters. We demonstrate empirically the approximation quality and the running time of our algorithm, showing that we can gain a significant speed-up with a minimal average loss in optimality.Peer reviewe