Modeling multiple time series?

[sdwfrost]

The current ESN allows one to model multiple correlated time series, but I was wondering if one had multiple independent time series (assumed to be generated under the same process) - perhaps of different lengths - how one would train an ESN from those using this framework.

[MartinuzziFrancesco]

This took me a little to get to since I wanted to double check a little of literature but there doesn't seem to be a lot that helps in this direction. The most complex aspect of it is definitely the different length of the time series. An interesting direction to look into could be using multiple reservoirs, I've been playing with it in the past couple of days but I still have to wrap my head around it.

[sdwfrost]

In the case of fixed length timeseries, this is just a minibatch problem, and is implemented e.g. in pytorch-esn: https://github.com/stefanonardo/pytorch-esn. I can write up a Python example (using a sine curve generator) based on the toy problem examined here if it helps.

The standard approach in RNNs/LSTMs to accommodate varying time series length is to pad an array to the longest time-series, but there's plenty of room for improvement here.

[MartinuzziFrancesco]

The example could be useful, you are very kind! I'll start working in this direction, I am sure this feature could be of great use

[sdwfrost]

Thanks for looking into this! I've updated my gist to illustrate both fixed and variable length patterns. It's a nice example as predicting a sine curve naively can be quite fiddly, but ESNs work well for the continuous case.