TY - BOOK
T1 - Learning causal probabilistic graphical models and their application to the analysis of effective connectivity from functional near infrared spectroscopy
AU - Montero-Hernandez, Samuel
PY - 2019/1
Y1 - 2019/1
N2 - Learning the structure of causal probabilistic graphical models (CPGMs) remains an open problem with current solutions limited to specific conditions. In this dissertation, we address the learning of the structure of CPGMs from limited observational data, a problem for which full solutions only exist under specific assumptions which remain in conflict with many real domains. We propose a multistage pipelined solution with three critical innovations; (i) the incorporation of background knowledge in the form of conditioning elements contrasting with classical structural constraints (realised by the new algorithm called seed Fast Causal Inference -sFCI-), (ii) a heuristic to recovery a single solution from an equivalence class whereby orientation is chosen by assessing intervals of causal effects (realised by a new algorithm named structural learning with interval causal effect -SLICE-), and (iii) a marker (namely differential symmetry index -DSI-) to estimate shared information among networks. Evaluation over synthetic data showed the superiority of the sFCI over plain FCI in shrinking the cardinality of the equivalence class recovered from observational data alone, as well as increased scalability and wider applicability to other domains than methods for linear systems with errors having non-Gaussian distributions, a consequence of assumptions relaxation. Application to retrieval of brain effective connectivity from functional optical neuroimaging (fNIRS) recordings exhibited face and nomological validity in datasets involving naturalistic social tasks and controlled visuomotor stimulation. Additionally, DSI is further shown to increase scalability by alleviating the problem of complexity (from bivariate to univariate analysis), and its implications in fNIRS analysis are quantified. Solving for the limited observational data grows the family of available solutions to learn CPGMs. We have shown that through the integration of background knowledge and adequate heuristics, a full causal identification in previously unmet conditions is possible. Enabling the application of CPGMs to functional near infrared spectroscopy (fNIRS) affords a suitable analysis approach to study brain effective connectivity. Formalisation has been carefully made to be independent of the domain application, and hence the applicability of the solution potentially exceeds exemplification on neuroimaging.
AB - Learning the structure of causal probabilistic graphical models (CPGMs) remains an open problem with current solutions limited to specific conditions. In this dissertation, we address the learning of the structure of CPGMs from limited observational data, a problem for which full solutions only exist under specific assumptions which remain in conflict with many real domains. We propose a multistage pipelined solution with three critical innovations; (i) the incorporation of background knowledge in the form of conditioning elements contrasting with classical structural constraints (realised by the new algorithm called seed Fast Causal Inference -sFCI-), (ii) a heuristic to recovery a single solution from an equivalence class whereby orientation is chosen by assessing intervals of causal effects (realised by a new algorithm named structural learning with interval causal effect -SLICE-), and (iii) a marker (namely differential symmetry index -DSI-) to estimate shared information among networks. Evaluation over synthetic data showed the superiority of the sFCI over plain FCI in shrinking the cardinality of the equivalence class recovered from observational data alone, as well as increased scalability and wider applicability to other domains than methods for linear systems with errors having non-Gaussian distributions, a consequence of assumptions relaxation. Application to retrieval of brain effective connectivity from functional optical neuroimaging (fNIRS) recordings exhibited face and nomological validity in datasets involving naturalistic social tasks and controlled visuomotor stimulation. Additionally, DSI is further shown to increase scalability by alleviating the problem of complexity (from bivariate to univariate analysis), and its implications in fNIRS analysis are quantified. Solving for the limited observational data grows the family of available solutions to learn CPGMs. We have shown that through the integration of background knowledge and adequate heuristics, a full causal identification in previously unmet conditions is possible. Enabling the application of CPGMs to functional near infrared spectroscopy (fNIRS) affords a suitable analysis approach to study brain effective connectivity. Formalisation has been carefully made to be independent of the domain application, and hence the applicability of the solution potentially exceeds exemplification on neuroimaging.
M3 - Doctoral Thesis
ER -