training for causal graph generation

[arunvellat]

Hello,
It seems that during training the network with each epoch, a single training sample (consisting of X as the tensor of all time series, with target time shifted, and Y as the target time series) is being used. Am I missing something, or is this how it was intended ?

[M-Nauta]

You are right, TCDF can currently only handle one training sample (consisting of multiple time series). This was intended, since this was suitable for the datasets we used. Section 5.1 in our paper describes the datasets we used in our experiments. However, we can imagine that there are temporal datasets with multiple instances. We might extend TCDF in the future to handle this, but this is currently not supported.

[ritchieng]

You can try a rolling fixed window by dividing the long time series into multiple samples, and leaving tiny gaps in between as embargoes specifically just for this case. This way you can observe if training from samples up to T - 100 D has similar out-of-sample performance (or slight deterioration, not a total breakdown) from T - 100 to T.

[arunvellat]

Suppose I have only one replication of N time series (i.e. a single csv file with N time series), on which I run the model. How would the approach that you take of considering a training sample consisting of full time series data, compare with that of breaking up the time series into smaller chunks, and learning from several training samples, for the prediction task (evaluate_prediction.py) ? Also, have you considered the case that the causal dependency graph could vary with time ?

[M-Nauta]

We have not yet considered the case where the causal graph changes over time. This is however an interesting (and probably challenging) topic for future work. However, a way to compare graphs over time is to break up all the time series in multiple chunks, and apply TCDF to each chunk (consisting of multiple time series) such that the resulting causal graphs can be compared (although the chunks should not be too short, since TCDF performs better on longer time series). This could give you an indication of the changing causal relationships. Regarding your question on prediction performance: this depends on the data. If the underlying causal relationships in the data are stable (i.e. one static underlying causal graph), I expect that TCDF will more accurately predict the time series when it is not chunked (thus using the whole dataset), simply because there is then more data to train on. However, if the causal relationships change over time, I expect that TCDF will predict more accurately when the data is divided into smaller chunks, since these chunks then contain the underlying causal relationships of that time period.