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Replace data generation with exact integration of linear SDEs #3

@tovrstra

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@tovrstra

The current times series are based on a spectral filter, which produces periodic sequences (of which currently only the first half is retained to mimic aperiodicity). It would be more realistic to generate aperiodic sequences.

Linear SDEs can be integrated exactly and sampled, as explained in the following reference (amongst others):

R. Zwanzig, nonequilibrium Statistical Mechanics (Oxford University Press, New York, 2001).

For each kernel used in ACID, the corresponding linear SDE is known. When linear combinations of kernels are used, we can also take linear combinations of timeseries generated with each kernel separately.

Practically, this requires the following changes:

  • In 1_dataset/lib/kernels.py the compute methods and function should get sibling sample methods and function.
  • In 1_dataset/scripts/generate.py, these sample functions should be called to generate data, instead of relying on STACIE.
  • Update the file 1_acid-dataset.typ to explain how SDEs are used to generate the data.

Once this is done, we can also remove the sequence generation from STACIE.

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