Use of Input-driven Hidden Markov Models with Application to Multi-site 
Precipitation Modeling

Sergey Kirshner, School of Information and Computer Science, UC Irvine
Padhraic J. Smyth, School of Information and Computer Science, UC Irvine
Andrew W. Robertson, Internation Research Institute for Climate
Prediction, The Earth Institute at Columbia University


[Note to organizers: our work falls in the class of input-output HMMs, or
non-homogeneous HMMs. We are not sure whether this work really fits within
the scope of the workshop - if not please feel free to let us know,
thanks.]


Abstract:
In this talk, we describe how input-driven HMMs, a special type of RNNs,
can be applied to simultaneously model rainfall occurrences for a number
of locations.  These input-driven HMMs, called non-homogeneous HMMs
(NHMMs), were first introduced by Hughes and Guttorp (1994), and a
variation of this model was independently developed by Bengio and Frasconi
(1995). An NHMM is a generalization of an HMM that allows the transition
between the hidden states to become non-stationary by making the value of 
the next state depend not only on the value of the previous state, but
also on the value of other observed variables.

Prediction and modeling of rainfall occurrences, an important problem in 
atmospheric sciences and agriculture, can be addressed by statistical 
learning methods since global circulation and climate change models are
too coarse and inaccurate to capture properties of precipitation for a
specific location.  What makes the statistical modeling problem
challenging is the variety of aspects of the data to be modeled.  Ideally,
the model should capture the spatial dependencies between the rain
stations, the temporal (e.g. run-length) distribution of the wet and dry
spell lengths as well as the interannual variability in the number of
rainy days per season.  The non-homogeneous HMM provides an interpretable
stochastic model capturing several desirable properties.  We demonstrate
the utility of this model for forecasting and simulation using historical
precipitation data from Brazil.