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Partial information decomposition for discrete target and continuous source random variables

Barà, Chiara, Antonacci, Yuri, Iovino, Marta, Lazic, Ivan, Faes, Luca·2025·Physical Review E
DOI 10.1103/58bg-5n9s
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Figure 1 Schematic representation of the nearest-neighbor estimation of the specific MI (5) for a binary target variable Y and two continuous sources X 1 and X 2 . The estimation proceeds by computing the distance (here, the Chebyshev distance) between each reference sample x i (star symbol) and its k th neighbor (here, k = 2 ) counted among the samples with Y = i (black circles), and then counting the number of samples falling within this distance in the two-dimensional space ( m X 1 X 2 = 3 ) and in the projected one-dimensional spaces considering all samples ( m X 1 = 6 , m X 2 = 7 ) or only the samples for which { Y = i } ( m i X 1 = 3 , m i X 2 = 4 ).
Figure 1 Schematic representation of the nearest-neighbor estimation of the specific MI (5) for a binary target variable Y and two continuous sources X 1 and X 2 . The estimation proceeds by computing the distance (here, the Chebyshev distance) between each reference sample x i (star symbol) and its k th neighbor (here, k = 2 ) counted among the samples with Y = i (black circles), and then counting the number of samples falling within this distance in the two-dimensional space ( m X 1 X 2 = 3 ) and in the projected one-dimensional spaces considering all samples ( m X 1 = 6 , m X 2 = 7 ) or only the samples for which { Y = i } ( m i X 1 = 3 , m i X 2 = 4 ).CC-BY · From the PDF
Figure 2 Theoretical values (dotted lines) and estimated distributions (solid lines, mean ± std. dev. over 100 simulations) of the PID measures obtained for the XOR gate ( a ), and for the AND gates with 2 ( b ) or 3 sources ( c ).
Figure 2 Theoretical values (dotted lines) and estimated distributions (solid lines, mean ± std. dev. over 100 simulations) of the PID measures obtained for the XOR gate ( a ), and for the AND gates with 2 ( b ) or 3 sources ( c ).CC-BY · From the PDF
Figure 3 Boxplot distributions and individual values of the PID applied to the MI between the binary target variable Y measuring inspiration/expiration and the continuous source variables X 1 and X 2 measuring respectively heart period and systolic arterial pressure, computed in conditions of resting state and postural stress. *, p < 0 . 05 paired Student's t -test, REST vs. STRESS. The number of subjects for which each measure is statistically significant according to surrogate data analysis is shown below each boxplot.
Figure 3 Boxplot distributions and individual values of the PID applied to the MI between the binary target variable Y measuring inspiration/expiration and the continuous source variables X 1 and X 2 measuring respectively heart period and systolic arterial pressure, computed in conditions of resting state and postural stress. *, p < 0 . 05 paired Student's t -test, REST vs. STRESS. The number of subjects for which each measure is statistically significant according to surrogate data analysis is shown below each boxplot.CC-BY · From the PDF
Figure S.1. Redundancy lattices representing the PI atoms ordering (panels .1 ) and the PID components definition (panels .2 ) for the PID with two sources (panels a. ) and for the PID with three sources (panels b. ).
Figure S.1. Redundancy lattices representing the PI atoms ordering (panels .1 ) and the PID components definition (panels .2 ) for the PID with two sources (panels a. ) and for the PID with three sources (panels b. ).CC-BY · From the PDF
Figure S.2. Average estimation of the percentage bias in computing the measure I ( Y ; X ) on one-hundred realizations of the XOR-logic gate between two sources (panel a. ), of the AND-logic gate between two (panel b. ) and three (panel c. ) sources at varying the variable realizations length N fi xing k = 5 (panel .1 ) and the number of neighbors k fi xing N = 300 (panel .2 ).
Figure S.2. Average estimation of the percentage bias in computing the measure I ( Y ; X ) on one-hundred realizations of the XOR-logic gate between two sources (panel a. ), of the AND-logic gate between two (panel b. ) and three (panel c. ) sources at varying the variable realizations length N fi xing k = 5 (panel .1 ) and the number of neighbors k fi xing N = 300 (panel .2 ).CC-BY · From the PDF
Figure S.3. Standard deviation of the estimates of I ( Y ; X ) on one-hundred realizations of the XOR-logic gate between two sources (panel a. ), of the AND-logic gate between two (panel b. ) and three (panel c. ) sources at varying the variable realizations length N fi xing k = 5 (panel .1 ) and the number of neighbors k fi xing N = 300 (panel .2 ).
Figure S.3. Standard deviation of the estimates of I ( Y ; X ) on one-hundred realizations of the XOR-logic gate between two sources (panel a. ), of the AND-logic gate between two (panel b. ) and three (panel c. ) sources at varying the variable realizations length N fi xing k = 5 (panel .1 ) and the number of neighbors k fi xing N = 300 (panel .2 ).CC-BY · From the PDF
Figure S.4. Percentage of realizations for which PID measures are statistically significant according to surrogate data analysis on simulated logic XOR (panel a ) and AND (panel b ) gates with 2 sources, and logic AND gate with 3 sources (panel c ).
Figure S.4. Percentage of realizations for which PID measures are statistically significant according to surrogate data analysis on simulated logic XOR (panel a ) and AND (panel b ) gates with 2 sources, and logic AND gate with 3 sources (panel c ).CC-BY · From the PDF
Figure S.5. Schematic representation of the procedure for extracting the time series from the synchronously acquired respiratory (RESP), electrocardiographic (ECG) and arterial blood pressure (ABP) signals (panel a ), and resulting time series representative of respiratory phase ( ¯ R ), heart period ( H ) and systolic arterial pressure ( S ) physiological dynamics, respectively (panel b ).
Figure S.5. Schematic representation of the procedure for extracting the time series from the synchronously acquired respiratory (RESP), electrocardiographic (ECG) and arterial blood pressure (ABP) signals (panel a ), and resulting time series representative of respiratory phase ( ¯ R ), heart period ( H ) and systolic arterial pressure ( S ) physiological dynamics, respectively (panel b ).CC-BY · From the PDF

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Metadata

Authors
Barà, C., Antonacci, Y., Iovino, M., Lazic, I., & Faes, L.
Affiliations
  • University of Palermo
  • University of Novi Sad
ORCID
Venue
Physical Review E
Publisher
American Physical Society (APS)
Published
2025-07-23
Volume
112
Issue
1
ISSN
  • 2470-0045
  • 2470-0053
DOI
10.1103/58bg-5n9s
Cited by
6
References
0
Language
en
Licence
link.aps.org/licenses/aps-default-license (vor)
Funders
Ministero dell'Università e della Ricerca (B53D23003020006)

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Barà, C., Antonacci, Y., Iovino, M., Lazic, I., & Faes, L. (2025). Partial information decomposition for discrete target and continuous source random variables. Physical Review E. https://doi.org/10.1103/58bg-5n9s