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| """ | ||
| PID: Decomposing the information carried by pairs of brain regions | ||
| ================================================================== | ||
| This example illustrates how to decompose the information carried by pairs of | ||
| brain regions about a behavioral variable `y` (e.g. stimulus, outcome, learning | ||
| curve, etc.). Here, we use the Partial Information Decomposition (PID) that | ||
| leads four non-negative and exclusive atoms of information: | ||
| - The unique information carried by the first brain region about `y` | ||
| - The unique information carried by the second brain region about `y` | ||
| - The redundant information carried by both regions about `y` | ||
| - The synergistic r complementary information carried by both regions about `y` | ||
| """ | ||
| import numpy as np | ||
| import xarray as xr | ||
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| from frites.simulations import StimSpecAR | ||
| from frites.conn import conn_pid | ||
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| from frites import set_mpl_style | ||
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| import matplotlib.pyplot as plt | ||
| set_mpl_style() | ||
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| ############################################################################### | ||
| # Data simulation | ||
| # --------------- | ||
| # | ||
| # Let's simulate some data. Here, we use an auto-regressive simulating a gamma | ||
| # increase. The gamma increase is modulated according to two conditions. | ||
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| ar_type = 'hga' | ||
| n_stim = 2 | ||
| n_epochs = 300 | ||
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| ss = StimSpecAR() | ||
| ar = ss.fit(ar_type=ar_type, n_epochs=n_epochs, n_stim=n_stim) | ||
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| print(ar) | ||
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| plt.figure(figsize=(7, 8)) | ||
| ss.plot(cmap='bwr') | ||
| plt.tight_layout() | ||
| plt.show() | ||
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| ############################################################################### | ||
| # Compute Partial Information Decomposition | ||
| # ----------------------------------------- | ||
| # | ||
| # Now we can use the simulated data to estimate the PID. Here, we'll try to | ||
| # decompose at each time point, the information carried by pairs of brain | ||
| # regions about the two conditions. | ||
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| # compute the PID | ||
| infotot, unique, redundancy, synergy = conn_pid( | ||
| ar, 'trials', roi='roi', times='times', mi_type='cd', verbose=False | ||
| ) | ||
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| # plot the results | ||
| infotot.plot(color='C3', label=r"$Info_{Tot}$", linestyle='--') | ||
| redundancy.plot(color='C0', label=r"$Redundancy_{XY}$") | ||
| synergy.plot(color='C1', label=r"$Synergy_{XY}$") | ||
| unique.sel(roi='x').squeeze().plot(color='C4', label=r"$Unique_{X}$") | ||
| unique.sel(roi='y').squeeze().plot(color='C5', label=r"$Unique_{Y}$") | ||
| plt.legend() | ||
| plt.ylabel("Information [Bits]") | ||
| plt.axvline(0., color='C3', lw=2) | ||
| plt.title("Decomposition of the information carried by a pair of brain regions" | ||
| "\nabout a task-related variable", fontweight='bold') | ||
| plt.show() | ||
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| """ | ||
| from the plot above, we can see that: | ||
| 1. The total information carried by the pairs of regions (Info_{Tot}) | ||
| 2. At the beginning, a large portion of the information is carried by the first | ||
| brain region (Unique_{X}) | ||
| 3. Then we can see a superimposition of redundancy (Redundancy_{XY}) and | ||
| synergy (Synergy_{XY}) carried by both regions | ||
| 4. Finally, later in time most of the information is carried by the second | ||
| brain region Y (Unique_{X}) | ||
| """ |
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