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- 1. Introduction to Trentool The transfer entropy toolbox Max Planck Institute for Human Cognitive and Brain Sciences Leipzig, GermanyDominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 2. 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 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 9, SEPTEMBER 2004 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) specificalculated 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 Pictureanger 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 ofctra. (B) Resulting flow scheme. Conventione 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
- 3. 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 Bivariate IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 9, SEPTEMBER 2004 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) specificalculated 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 Pictureanger 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 ofctra. (B) Resulting flow scheme. Conventione 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
- 4. 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 function2/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 5. 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 20003/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 6. Conditional Entropy Conditional Entropy: H(Xt+1|Xt) X(t) Using Xt to predict Xt+1 Transition probability: p(Xt+1|Xt)3/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 7. 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”3/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 8. 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 past3/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 9. Types of Transfer Entropy apparent Transfer Entropy misses multivariate effects • doesnt capture multivariate interactions, e.g., ( xor ) • doesnt 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 interactions4/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 10. 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 function5/9 1Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 11. 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 10db5/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 12. Properties of Transfer Entropy Problems • (predictable) estimation bias for non-infinite data sequences • difficult to test for significance • vulnerable to volume conduction5/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 13. 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 time6/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 14. Trentool Properties Requirements built on robust Matlab Transfer Entropy Fieldtrip detection of volume applicable conduction Open- TSTOOL7/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 15. Workflow Preparation Single Dataset Input in Fieldtrip raw format7/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 16. Workflow Preparation Single Dataset Input Input sanitation in Fieldtrip and validation raw format Parameter optimization Cao Ragwitz7/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 17. Workflow Preparation Single Dataset Input Input sanitation in Fieldtrip Permutation test and validation raw format Parameter Calculate optimization Transfer Entropy Sample Cao Ragwitz Shift7/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 18. Workflow Preparation Single Dataset Input Input sanitation in Fieldtrip Permutation test Shift test and validation raw format Parameter Calculate optimization Transfer Entropy Sample Cao Ragwitz Shift7/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 19. Workflow Preparation Single Dataset Input Input sanitation in Fieldtrip Permutation test Shift test and validation raw format Parameter Calculate Permutation test optimization Transfer Entropy between conditions Sample Cao Ragwitz Shift Results7/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 20. Workflow Preparation Single Dataset Input Input sanitation in Fieldtrip Permutation test Shift test and validation raw format Parameter Calculate Permutation test optimization Transfer Entropy between conditions conditions loop over Sample Cao Ragwitz Shift Results7/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 21. Workflow Preparation Multiple Datasets Input Input sanitation in Fieldtrip Permutation test Shift test and validation raw format Parameter Calculate Permutation test optimization Transfer Entropy between datasets datasets loop over Sample Cao Ragwitz Shift Results7/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 22. Data analysis with Trentool Example set: 35 trials of 3500x2 samples Quadrilinear relationship, delay of 15 ms8/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 23. Data analysis with Trentool Significance and delay estimation8/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 24. Data analysis with Trentool Significance and delay estimation8/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 25. Data analysis with Trentool8/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences
- 26. Thanks Questions?9/9Dominic Portain - 16.08.2012 Max Planck Institute for Human Cognitive and Brain Sciences

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