Areas of Research … Causal Discovery Application Integration Robustness Application Causal Discovery Sofia Triantafillou Assistant Professor, Department of Biomedical Informatics, University of Pittsburgh email: sot16@upitt.edu phone: +1 773 403 8781 A B C D E A B D C E …

Integrative Causal Discovery Breast Cancer Protein C Contraceptives Thrombosis Protein Z Protein E Thrombosis Contraceptives Protein C Cancer Protein Y Protein Z Study 1 observational Yes No 10.5 … 0.01 Study 2 0.03 9.3 3.4 22.2 Study 3 RCT Protein C 0 (Control) 5.0 (Treat.) 8.9 Study 4 RCT contraceptives No (Ctrl) Yes(Treat) Same system, different studies -Different variables -Different experimental designs One (true, unknown) Causal Model -marginals/experiments can be modeled with causal graphs Integrative Causal Discovery: Find the causal graph(s) that simultaneously fit all studies

Integrative Causal Discovery How? -Measure conditional independencies in the data. -Constrain graph paths after modeling experiments. -Convert to SAT instance. -Solutions are graphs that fit all observed statistical constraints. Why? -Increase robustness of causal discovery by using all data. -Make novel inferences by combining different data. -e.g. Predict the association (+ correlation coefficient). between variables never measured together. -Predictions successfully validated in 30 public data sets. A B C D E … A B D C E A B D C E Data Causal graph(s) Paths [ E 𝐴→D ∨ E 𝐴→B ∧ E 𝐵→D ∨ E 𝐴→C ∧ E 𝐶→D ∨ ⋮ [ E 𝐴→C ∨ E 𝐴→B ∧ E 𝐵→C ∨ E 𝐴↔C ∧ E 𝐶→D ∨ (In)dependencies Logic formula

Robust Causal Discovery Breast Cancer Protein C Contraceptives Thrombosis Protein Z Protein E Breast Cancer Protein C Contraceptives Thrombosis Protein Z Protein E Breast Cancer Protein C Contraceptives Thrombosis Protein Z Protein E Breast Cancer Protein C Contraceptives Thrombosis Protein Z Protein E best fitting graph Close to best fitting graphs What is P(Contraceptives --> Thrombosis | Data)? How? -Compute the probability of a graph (not very easy when you have confounders). -Find the probability of causal features over all graphs -Efficiency? Why? -Many graphs fit the data (almost) equally well. -In low sample sizes, it is hard to distinguish. -Be conservative: Identify features that are present in most high-probability graphs.

Applied Causal Discovery Identify causal protein phosphorylation signaling relationships from mass cytometry data. Local Causal Discovery Predictions phosphoprotein A -> phosphoprotein B Reproducibility in independent data sets Mass cytometry data (Bendall et al, 2011)