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Transfer entropy (TE) estimators

Common interface

We provide a common transferentropy(driver, response; kwargs...) function, which may be nice for initial exploration of your data.

Note: the common interface uses default values for estimator parameters that may not be suited for your data. For real applications, it is highly recommended to use the underlying estimators directly.

Documentation

# CausalityTools.te — Function.

te(driver, response;
    estimator = :tetogrid,
    E = nothing, v = nothing,
    ϵ = nothing, n_ϵ = 5, ν = 1, τ = 1, dim = 3,
    k1 = 2, k2 = 3, distance_metric = Chebyshev(),
    which_is_surr = :none,
    surr_func = aaft,
    min_numbins = nothing,
    max_numbins = nothing)

Compute transfer entropy from a driver time series to a response time series.

Method

method sets the transfer entropy estimator to use. There are two types of estimators: grid-based approaches, and nearest-neighbor based approaches.

Embedding instructions

Specify embedding and instructions for how to compute marginal entropies are with E::AbstractEmbedding and v::TEVars. If either is missing, the data is embedded using the provided forward prediction lag ν, with embedding dimension dim and embedding lag η.

Grid-based estimators

  • :transferentropy_transferoperator_grid, or :tetogrid. Grid-based transfer entropy estimator based on the transfer operator.
  • ::transferentropy_visitfreq, or :tefreq. Simple visitation frequency based estimator.

For the grid based TE estimators, ϵ sets the bin size. If ϵ == nothing, then the algorithm uses a bin size corresponding to a number of subdivisions N along each axis so that N ≦ npoints^(1/(dim+1)). Transfer entropy is then computed as an average over n_ϵ different bin sizes corresponding to N-1 to N subdivisions along each axis. If ϵ is specified and consists of multiple bin sizes, an average TE estimate over the bin sizes is returened. If ϵ is a single value, then TE is estimated for that bin size only.

Nearest neighbor based estimator.

  • :transferentropy_kraskov, :tekraskov, or :tekNN. A nearest-neighbor based estimator that computes transfer entropy as the sum of two mutual information terms. k1 and k2 sets the number of nearest neighbors used to estimate the mutual information terms. distance_metric sets the distance metric (must be an instance of a valid metric from Distances.jl).

Surrogate analysis

A surrogate analysis will be run if which_is_surr is set to :both, :driver, :response. Default is :none.

  • which_is_surr = :both will replace both time series with a surrogate.
  • which_is_surr = :driver will replace the driver time series with a surrogate.
  • which_is_surr = :response will replace the response time series with a surrogate.

The type of surrogate must be either randomshuffle, randomphases, randomamplitudes, aaft or iaaft.

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