2 research outputs found
Mining Sub-Interval Relationships In Time Series Data
Time-series data is being increasingly collected and stud- ied in several
areas such as neuroscience, climate science, transportation, and social media.
Discovery of complex patterns of relationships between individual time-series,
using data-driven approaches can improve our understanding of real-world
systems. While traditional approaches typically study relationships between two
entire time series, many interesting relationships in real-world applications
exist in small sub-intervals of time while remaining absent or feeble during
other sub-intervals. In this paper, we define the notion of a sub-interval
relationship (SIR) to capture inter- actions between two time series that are
prominent only in certain sub-intervals of time. We propose a novel and
efficient approach to find most interesting SIR in a pair of time series. We
evaluate our proposed approach on two real-world datasets from climate science
and neuroscience domain and demonstrated the scalability and computational
efficiency of our proposed approach. We further evaluated our discovered SIRs
based on a randomization based procedure. Our results indicated the existence
of several such relationships that are statistically significant, some of which
were also found to have physical interpretation
Explicit-Duration Markov Switching Models
Markov switching models (MSMs) are probabilistic models that employ multiple
sets of parameters to describe different dynamic regimes that a time series may
exhibit at different periods of time. The switching mechanism between regimes
is controlled by unobserved random variables that form a first-order Markov
chain. Explicit-duration MSMs contain additional variables that explicitly
model the distribution of time spent in each regime. This allows to define
duration distributions of any form, but also to impose complex dependence
between the observations and to reset the dynamics to initial conditions.
Models that focus on the first two properties are most commonly known as hidden
semi-Markov models or segment models, whilst models that focus on the third
property are most commonly known as changepoint models or reset models. In this
monograph, we provide a description of explicit-duration modelling by
categorizing the different approaches into three groups, which differ in
encoding in the explicit-duration variables different information about regime
change/reset boundaries. The approaches are described using the formalism of
graphical models, which allows to graphically represent and assess statistical
dependence and therefore to easily describe the structure of complex models and
derive inference routines. The presentation is intended to be pedagogical,
focusing on providing a characterization of the three groups in terms of model
structure constraints and inference properties. The monograph is supplemented
with a software package that contains most of the models and examples
described. The material presented should be useful to both researchers wishing
to learn about these models and researchers wishing to develop them further