1. Areas of Research … Causal Discovery Application Integration
Robustness
Application
Causal Discovery
Sofia Triantafillou
Assistant Professor,
Department of Biomedical Informatics,
University of Pittsburgh
phone: A B C D E A B D C E …

2. 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

3. 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

4. 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.

5. 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)