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Ancestral Causal Inference - WIML 2016 @ NIPS

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Ancestral Causal Inference (ACI) talk slides from WIML 2016 workshop at NIPS.

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Ancestral Causal Inference - WIML 2016 @ NIPS

  1. 1. Ancestral Causal Inference Sara Magliacane, Tom Claassen, Joris M. Mooij s.magliacane@uva.nl 5th December, 2016 Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 1 / 16
  2. 2. Part I Introduction Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 2 / 16
  3. 3. Causal inference: learning causal relations from data Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 3 / 16
  4. 4. Causal inference: learning causal relations from data Definition X causes Y (X Y ) = intervening upon (changing) X changes Y We can represent causal relations with a causal DAG (hidden vars): X Y E.g. X = Smoking, Y = Cancer Causal inference = structure learning of the causal DAG Traditionally, causal relations are inferred from interventions. Sometimes, interventions are unethical, unfeasible or too expensive Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 3 / 16
  5. 5. Causal inference from observational and experimental data Holy Grail of Causal Inference Learn as much causal structure as possible from observations, integrating background knowledge and experimental data. Constraint-based causal discovery: use statistical independences to express constraints over possible causal models Intuition: Under certain assumptions, independences in the data correspond with d-separations in a causal DAG Issues: 1 Vulnerability to errors in statistical independence tests 2 No estimation of confidence in the causal predictions Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 4 / 16
  6. 6. Causal inference as an optimization problem (e.g. HEJ) Weighted list of statistical independence results: I = {(ij , wj )}: E.g. I = { (Y ⊥⊥ Z | X, 0.2), (Y ⊥⊥ X, 0.1)} For any possible causal structure C, we define the loss function: Loss(C, I) := (ij ,wj )∈I: ij is not satisfied in C wj “ij is not satisfied in C” = defined by causal reasoning rules Causal inference = Find causal structure minimizing loss function C∗ = arg min C∈C Loss(C, I) Problem: Scalability HEJ [Hyttinen et al., 2014] Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 5 / 16
  7. 7. Part II Ancestral Causal Inference Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 6 / 16
  8. 8. A more coarse grained representation Can we improve scalability of the most accurate state-of-the-art method (HEJ)? Ancestral Causal Inference: Main Idea Instead of representing direct causal relations use a more coarse-grained representation of causal information, e.g., an ancestral structure (a set of “indirect” causal relations). X Y Z Ancestral structures reduce drastically search space For 7 variables: 2.3 × 1015 → 6 × 106 Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 7 / 16
  9. 9. Causal inference as an optimization problem (Reprise) Weighted list of inputs: I = {(ij , wj )}: E.g. I = { (Y ⊥⊥ Z | X, 0.2), (Y ⊥⊥ X, 0.1)}, (U Z, 0.8) } Any consistent weighting scheme, e.g. frequentist, Bayesian For any possible ancestral structure C, we define the loss function: Loss(C, I) := (ij ,wj )∈I: ij is not satisfied in C wj Here: “ij is not satisfied in C” = defined by ancestral reasoning rules Causal inference = Find ancestral structure minimizing loss function C∗ = arg min C∈C Loss(C, I) Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 8 / 16
  10. 10. Ancestral reasoning rules: Example ACI rules: 7 ancestral reasoning rules that given (in)dependences constrain possible (non) ancestral relations Example For X, Y , W disjoint (sets of) variables: (X ⊥⊥ Y | W ) ∧ (X W ) =⇒ X Y X ⊥⊥ Y | W = “X is independent of Y given a set of variables W ” ∧ “and” X W = “X does not cause any variable in the set W ” =⇒ = “then” X Y = “X does not cause Y ” Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 9 / 16
  11. 11. A method for scoring causal predictions Score the confidence in a predicted statement s (e.g. X Y ) as: C(f ) = min C∈C Loss(C, I + (¬s, ∞)) − min C∈C Loss(C, I + (s, ∞)) ≈ MAP approximation of the log-odds ratio of s Asymptotically consistent, when consistent input weights Can be used with any method that solves an optimization problem Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 10 / 16
  12. 12. Part III Evaluation Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 11 / 16
  13. 13. Simulated data accuracy: example Precision Recall curve Recall 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Precision 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 HEJ (c=1) ACI (c=1) CFCI FCI ACI is as accurate as HEJ + our scoring method Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 12 / 16
  14. 14. Simulated data execution time ACI is orders of magnitude faster than HEJ The difference grows exponentially in the number of variables HEJ is not feasible for more than 8 variables Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 13 / 16
  15. 15. Application: Reconstructing a Protein Signalling Network Raf Mek Erk Akt JNK PIP3 PLCg PIP2 PKC PKA p38 Black edges = overlap Consistent with score-based method [Mooij and Heskes, 2013] Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 14 / 16
  16. 16. Conclusion Ancestral Causal Discovery (ACI), a causal discovery method as accurate as the state-of-the-art but much more scalable A method for scoring causal relations by confidence Source code: http://github.com/caus-am/aci Paper: [Magliacane et al., 2016] Poster: WIML, 1.30pm - 2.30pm, poster 3 Poster: NIPS, Tuesday 6pm - 9.30pm, poster 81 Talk on extensions of ACI at “What If?” NIPS workshop, Saturday Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 15 / 16
  17. 17. References I Hyttinen, A., Eberhardt, F., and J¨arvisalo, M. (2014). Constraint-based causal discovery: Conflict resolution with Answer Set Programming. In UAI. Magliacane, S., Claassen, T., and Mooij, J. M. (2016). Ancestral causal inference. In NIPS. Mooij, J. M. and Heskes, T. (2013). Cyclic causal discovery from continuous equilibrium data. In Nicholson, A. and Smyth, P., editors, UAI, pages 431–439. AUAI Press. Sara Magliacane (VU, UvA) Ancestral Causal Inference 5-12-2016 16 / 16

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