Introduction to Trentool

Introduction to Trentool

The transfer entropy toolbox

Max Planck Institute
for Human Cognitive and Brain Sciences Leipzig, Germany

Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 9, SEPTEMBER 2004

The Basics

Functional Effective
Fig. 5. (
and multi
axes: amp
(B) dDTF
1504 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 9, SEPTEMBER 2004 Pattern of
Granger- direct flow

Coherency Geweke The a
surrogat
Causality diagona
see that
DTF va
Fig. 5. (A) Ordinary (graphs above diagonal), partial (graphs below diagonal), (A) Granger causality calculated pair-wise.marked above the column flows w
Fig. 3.
function describing transmission from the channel
Each graph represents the
(Bendat and Piersol, 1986)
and multiple coherences (graphs on the diagonal) for the simulation (Geweke, 1982; Bressler et al., of the row. Horizontal axis: frequency (
I. Vertical channel marked on the left 2007)
to the the orde
range). Vertical axis: Granger causality in arbitrary units. Graphs on test. Ho
axes: amplitude in range. Horizontal axes: frequency in range.
the diagonal contain power spectra. (B) Resulting flow scheme. Convention
In ord
(B) dDTFs for the simulated data (power spectra shown on the diagonal). (C) concerning drawing of arrows the same as in Fig. 2.
troduced
Pattern of direct connections estimated from partial coherences. (D) Pattern of partial c
direct flows estimated from dDTFs. tion fact
This kin
is small
The accuracy of the results can be estimated by means of the Partial the chan

Partial surrogate data test. The results are shown in Fig. 4(b). On the
to ch

Directed value at

Coherence diagonal of Fig. 4(b), the power spectra are illustrated; we can the prop

Coherence
a “dip”
see that they correspond well to the spectra from Fig. 3. The avoid th
face ele
DTF values from 2000) 4(a) corresponding to “leak(graphs (Baccalá and Sameshima, (graphs below diagonal),
Fig. Fig. 5. (A) Ordinary flows”—the above diagonal), partial 2001) specific
alculated pair-wise. Each graph represents the andFig. 5. 1986; Dalhaus, (graphs above diagonal), partialcoherences (graphs on the diagonal) for the simulation I. Vertical
(Bendat Piersol, (A) Ordinary (graphs below diagonal),
from the channel marked above the column flows which should (graphs on the diagonal) for oursimulation I. Vertical
and multiple coherences not exist according to the scheme—are of
and multiple The s
axes: amplitude in in range. Horizontal Nonnormalized multichannel DTFs for the simulation I (Fig. 1). ence—c
Fig. 4. (A) axes: frequency in range.
axes:order of the values obtained by means of the surrogaterange. organization similar to Fig. 3 (on the diagonal power spectra). (B) DTFs common
t of the row. Horizontal axis: frequency ( the amplitude in range. Horizontal axes: frequency data
Picture
anger causality in arbitrary units. Graphs on (B) dDTFs for the this is not the case for theshown onsimulated data obtained from surrogate data. (C) Resulting flow pattern. Plots A(C)B are in other si
test. However, simulated data (power spectra “cascade” diagonal). (power spectra shown on the diagonal). and
(B) dDTFs for the the (C)
flows. the samefrom arbitrary units. Horizontal axes:(D) Pattern of range). set of sig
Pattern of direct connections estimated scale in partial coherences. frequency (
Pattern of direct connections estimated from partial coherences. (D) Pattern of
ctra. (B) Resulting flow scheme. Convention
e same as in Fig. 2. direct flows estimated from dDTFs. flows, one can use the dDTF in-
In order to find only direct direct flows estimated from dDTFs. are illus
1/9 Inspecting Figs. 2 and 3, we observe that the channels, which coheren
troduced in [20]. This function is a combination of ffDTF and delayed than the others, became “sinks” of activity. herence
are more
Dominic Portain - 16.08.2012 partial coherence. In the definitionbe estimated by means of It iscanHuman for pair-wise means that the Sciences
The accuracy of the results can The Max Planck the results for be estimated by estimates of they show directly
of ffDTF (7), the Institute quite common Cognitive and Brain
accuracy of normaliza- the
sinks rather than sources of activity. This effect appears also in The r


The Basics

Functional Effective
Fig. 5. (
and multi
axes: amp
(B) dDTF
1504 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 9, SEPTEMBER 2004 Pattern of
Bivariate

Granger- direct flow

Coherency Geweke The a
surrogat
Causality diagona
see that
DTF va
Fig. 5. (A) Ordinary (graphs above diagonal), partial (graphs below diagonal), (A) Granger causality calculated pair-wise.marked above the column flows w
Fig. 3.
function describing transmission from the channel
Each graph represents the
(Bendat and Piersol, 1986)
and multiple coherences (graphs on the diagonal) for the simulation (Geweke, 1982; Bressler et al., of the row. Horizontal axis: frequency (
I. Vertical channel marked on the left 2007)
to the the orde
range). Vertical axis: Granger causality in arbitrary units. Graphs on test. Ho
axes: amplitude in range. Horizontal axes: frequency in range.
the diagonal contain power spectra. (B) Resulting flow scheme. Convention
In ord
(B) dDTFs for the simulated data (power spectra shown on the diagonal). (C) concerning drawing of arrows the same as in Fig. 2.
troduced
Pattern of direct connections estimated from partial coherences. (D) Pattern of partial c
direct flows estimated from dDTFs. tion fact
This kin
Multivariate

is small
The accuracy of the results can be estimated by means of the Partial the chan

Partial surrogate data test. The results are shown in Fig. 4(b). On the
to ch

Directed value at

Coherence diagonal of Fig. 4(b), the power spectra are illustrated; we can the prop

Coherence
a “dip”
see that they correspond well to the spectra from Fig. 3. The avoid th
face ele
DTF values from 2000) 4(a) corresponding to “leak(graphs (Baccalá and Sameshima, (graphs below diagonal),
Fig. Fig. 5. (A) Ordinary flows”—the above diagonal), partial 2001) specific
alculated pair-wise. Each graph represents the andFig. 5. 1986; Dalhaus, (graphs above diagonal), partialcoherences (graphs on the diagonal) for the simulation I. Vertical
(Bendat Piersol, (A) Ordinary (graphs below diagonal),
from the channel marked above the column flows which should (graphs on the diagonal) for oursimulation I. Vertical
and multiple coherences not exist according to the scheme—are of
and multiple The s
axes: amplitude in in range. Horizontal Nonnormalized multichannel DTFs for the simulation I (Fig. 1). ence—c
Fig. 4. (A) axes: frequency in range.
axes:order of the values obtained by means of the surrogaterange. organization similar to Fig. 3 (on the diagonal power spectra). (B) DTFs common
t of the row. Horizontal axis: frequency ( the amplitude in range. Horizontal axes: frequency data
Picture
anger causality in arbitrary units. Graphs on (B) dDTFs for the this is not the case for theshown onsimulated data obtained from surrogate data. (C) Resulting flow pattern. Plots A(C)B are in other si
test. However, simulated data (power spectra “cascade” diagonal). (power spectra shown on the diagonal). and
(B) dDTFs for the the (C)
flows. the samefrom arbitrary units. Horizontal axes:(D) Pattern of range). set of sig
Pattern of direct connections estimated scale in partial coherences. frequency (
Pattern of direct connections estimated from partial coherences. (D) Pattern of
ctra. (B) Resulting flow scheme. Convention
e same as in Fig. 2. direct flows estimated from dDTFs. flows, one can use the dDTF in-
In order to find only direct direct flows estimated from dDTFs. are illus
1/9 Inspecting Figs. 2 and 3, we observe that the channels, which coheren
troduced in [20]. This function is a combination of ffDTF and delayed than the others, became “sinks” of activity. herence
are more
Dominic Portain - 16.08.2012 partial coherence. In the definitionbe estimated by means of It iscanHuman for pair-wise means that the Sciences
The accuracy of the results can The Max Planck the results for be estimated by estimates of they show directly
of ffDTF (7), the Institute quite common Cognitive and Brain
accuracy of normaliza- the
sinks rather than sources of activity. This effect appears also in The r

Causality methods

Causal modeling linear data nonlinear data

Extended Granger
causality mapping
Bivariate Granger causality
Bilinear DCM

Partial directed Coherence
Multivariate Transfer Entropy
Directed Transfer function

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Entropy

Two signal streams: Entropy:

X H(X)

Y H(Y)

H(X) + H(Y) = H(Xt+1|Xt) + H(Yt+1|Yt) + I(X,Y)
Conditional Mutual
Entropy
Entropy Information
Schreiber 2000
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Conditional Entropy

Conditional Entropy: H(Xt+1|Xt)

X(t)

Using Xt to predict Xt+1
Transition probability: p(Xt+1|Xt)

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Mutual Information

Mutual Information: Entropy:

X H(X)

Y H(Y)

X|Y H(X|Y)

I(X,Y) = H(X) + H(Y) – H(X|Y)
“Transfer entropy”

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Conditional Transfer Entropy

Conditional Entropy: H(Xt+1|Xt)

transition probability

Mutual information: I(X,Y)
“Apparent Transfer entropy”

Conditional mutual information: I(X,Yt+1|Yt)
“Conditional transfer entropy”

predictive information: H(Xt+1) - H(Xt+1|Xt)
total uncertainty uncertainty
about the future about the future,
given the past
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Types of Transfer Entropy

apparent Transfer Entropy misses multivariate effects
• doesn't capture multivariate interactions, e.g., ( xor )
• doesn't distinguish:
• redundant information
• common causes

conditional TE conditions other possible information sources
• eliminates redundancy, respects causal pathways

complete Transfer Entropy involves all source information
• captures collective interactions
4/9

Melanoma series
6

4

2 Properties of Transfer Entropy
0

detrended melanoma series

Advantages
1

0.5

• 0 model-free, robust to noise
−0.5

• −1 inherently non-linear,1960 1965 1970 fast with linear data
1935 1940 1945 1950 1955
but works 1975
• weaker coupling -> better results!
year

Figure 1: Detrendedwith multivariate effects: .
• copes well Sunspot-Melanoma 1936-1972 Series
Melanoma & Sunspot: Standardized series
3
Melanoma
2 Sunspot

1

0

−1

−2
1935 1940 1945 1950 1955 1960 1965 1970 1975

Normalized cross−correlation function
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Properties of Transfer Entropy

Application in Neuroscience
• causal interactions occur at a fine temporal scale (<10ms)
• weaker coupling -> better causal results!
• Issues with complex networks
• Noise influence:
• good detection rate for SNR above 15db
• breaks down to 50% at 10db

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Properties of Transfer Entropy

Problems
• (predictable) estimation bias for non-infinite data sequences
• difficult to test for significance
• vulnerable to volume conduction

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Generalized Synchronization

• paradigm: delayed feedback (stable and predictable sync)
• model: delay-coupled lasers
– increasingly complex behavior
– identical synchronization is always unstable
– response is shifted by coupling time (a few nanoseconds)
– cross correlation shows strong peaks at the coupling time
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Trentool

Properties Requirements
built on robust Matlab
Transfer
Entropy Fieldtrip
detection of
volume
applicable conduction Open-
TSTOOL

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Workflow

Preparation Single Dataset
Input
in Fieldtrip
raw format

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Workflow

Input Input sanitation
in Fieldtrip and validation
raw format

Parameter
optimization

Cao Ragwitz

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Workflow

in Fieldtrip Permutation test
and validation
raw format

Parameter Calculate
optimization Transfer Entropy

Sample
Cao Ragwitz Shift

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Workflow

in Fieldtrip Permutation test Shift test
and validation
raw format

Parameter Calculate
optimization Transfer Entropy

Sample
Cao Ragwitz Shift

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Workflow

and validation
raw format

Parameter Calculate Permutation test
optimization Transfer Entropy between conditions

Sample
Cao Ragwitz Shift
Results

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Workflow

and validation
raw format

optimization Transfer Entropy between conditions

conditions
loop over
Sample
Cao Ragwitz Shift
Results

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Workflow

Preparation Multiple Datasets
and validation
raw format

optimization Transfer Entropy between datasets

datasets
loop over
Sample
Cao Ragwitz Shift
Results

7/9

Data analysis with Trentool

Example set: 35 trials of 3500x2 samples
Quadrilinear relationship, delay of 15 ms

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Significance and delay estimation

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8/9

Thanks

Questions?

9/9

Introduction to Trentool

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