| Summary: | Change point problems are referred to detect heterogeneity in temporal or spatial
data. They have applications in many areas like DNA sequences, financial
time series, signal processing, etc. A large number of techniques have been
proposed to tackle the problems. One of the most difficult issues is estimating
the number of the change points. As in other examples of model selection, the
Bayesian approach is particularly appealing, since it automatically captures a
trade off between model complexity (the number of change points) and model
fit. It also allows one to express uncertainty about the number and location of
change points.
In a series of papers [13, 14, 16], Fearnhead developed efficient dynamic programming
algorithms for exactly computing the posterior over the number and
location of change points in one dimensional series. This improved upon earlier
approaches, such as [12], which relied on reversible jump MCMC.
We extend Fearnhead's algorithms to the case of multiple dimensional series.
This allows us to detect changes on correlation structures, as well as changes on
mean, variance, etc. We also model the correlation structures using Gaussian
graphical models. This allow us to estimate the changing topology of dependencies
among series, in addition to detecting change points. This is particularly
useful in high dimensional cases because of sparsity. === Science, Faculty of === Computer Science, Department of === Graduate
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