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Transfer entropy estimators

Abstract types

# TransferEntropy.TransferEntropyEstimator — Type.

TransferEntropyEstimator

An abstract type for transfer entropy estimators. This type has several concrete subtypes that are accepted as inputs to the transferentropy methods.

• VisitationFrequency
• TransferOperatorGrid
• NearestNeighbourMI

# TransferEntropy.BinningTransferEntropyEstimator — Type.

BinningTransferEntropyEstimator <: TransferEntropyEstimator

An abstract type for transfer entropy estimators that works on a discretization of the reconstructed state space. Has the following concrete subtypes

• VisitationFrequency
• TransferOperatorGrid

Used by

Concrete subtypes are accepted as inputs by

• transferentropy (low-level method)
• VisitationFrequencyTest
• TransferOperatorGridTest,
• ExactSimplexIntersectionTest
• ApproximateSimplexIntersectionTest

Concrete types

# TransferEntropy.VisitationFrequency — Type.

VisitationFrequency(; b::Number = 2)

An transfer entropy estimator which computes transfer entropy over a dicretization of an appropriate delay reconstruction, using the logarithm to the base b. The invariant probabilities over the partition are computed using an approximation to the transfer (Perron-Frobenius) operator over the grid [1], which explicitly gives the transition probabilities between states.

Used by

This estimator is accepted as input by

• transferentropy (low-level method)
• VisitationFrequencyTest
• ExactSimplexIntersectionTest
• ApproximateSimplexIntersectionTest

References

[1] Diego, David, Kristian Agasøster Haaga, and Bjarte Hannisdal. "Transfer entropy computation using the Perron-Frobenius operator." Physical Review E 99.4 (2019): 042212.

source

# TransferEntropy.TransferOperatorGrid — Type.

TransferOperatorGrid(; b::Number = 2)

An transfer entropy estimator which computes transfer entropy over a dicretization of an appropriate delay reconstruction, using the logarithm to base b. Invariant probabilities over the partition are computed using an approximation to the transfer (Perron-Frobenius) operator over the grid [1], which explicitly gives the transition probabilities between states.

Fields

• b::Number = 2: The base of the logarithm, controlling the unit of the transfer entropy estimate (e.g. b = 2 will give the transfer entropy in bits).

Used by

This estimator is accepted as input by

• transferentropy (low-level method)
• TransferOperatorGridTest
• ExactSimplexIntersectionTest
• ApproximateSimplexIntersectionTest

References

[1] Diego, David, Kristian Agasøster Haaga, and Bjarte Hannisdal. "Transfer entropy computation using the Perron-Frobenius operator." Physical Review E 99.4 (2019): 042212.

source

# TransferEntropy.NearestNeighbourMI — Type.

NearestNeighbourMI(k1::Int = 2, k2::Int = 3, metric::Metric = Chebyshev, b::Number)

A transfer entropy estimator counting of nearest neighbours nearest neighbours to estimate mutual information over an appropriate custom delay reconstruction (the method from [1], as implemented in [2]).

Fields

• k1::Int = 2: The number of nearest neighbours for the highest-dimensional mutual information estimate. To minimize bias, choose $k_1 < k_2$ if $min(k_1, k_2) < 10$ (see fig. 16 in [1]). Beyond dimension 5, choosing $k_1 = k_2$ results in fairly low bias, and a low number of nearest neighbours, say k1 = k2 = 4, will suffice.
• k2::Int = 3: The number of nearest neighbours for the lowest-dimensional mutual information estimate. To minimize bias, choose $k_1 < k_2$ if if $min(k_1, k_2) < 10$ (see fig. 16 in [1]). Beyond dimension 5, choosing $k_1 = k_2$ results in fairly low bias, and a low number of nearest neighbours, say k1 = k2 = 4, will suffice.
• metric::Metric = Chebyshev(): The metric used for distance computations.
• b::Number = 2: The base of the logarithm, controlling the unit of the transfer entropy estimate (e.g. b = 2 will give the transfer entropy in bits).

Used by

This estimator is accepted as input by

• transferentropy (low level method),
• NearestNeighbourMITest

References

1. Kraskov, Alexander, Harald Stögbauer, and Peter Grassberger. "Estimating mutual information." Physical review E 69.6 (2004): 066138.
2. Diego, David, Kristian Agasøster Haaga, and Bjarte Hannisdal. "Transfer entropy computation using the Perron-Frobenius operator." Physical Review E 99.4 (2019): 042212.

source