Identification and Estimation of Causal Effects from Dependent Data
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1 Identification and Estimation of Causal Effects from Dependent Data Eli Sherman with Ilya Shpitser Johns Hopkins Computer Science 12/6/2018 Eli Sherman Identification and Estimation of Causal Effects from Dependent Data 1 / 9
2 Causal Inference Problems in Networks Goal: learn about causality from data on interacting agents: Online social networks, cluster randomized trials of villages or households, infectious diseases Major difficulty: units are dependent Example (Shalizi and Thomas 1 ): If your friend Sam jumped off a bridge Shalizi and Thomas Shutterfly ID Eli Sherman Identification and Estimation of Causal Effects from Dependent Data 2 / 9
3 Causal Inference Problems in Networks Goal: learn about causality from data on interacting agents: Online social networks, cluster randomized trials of villages or households, infectious diseases Major difficulty: units are dependent Example (Shalizi and Thomas 1 ): If your friend Sam jumped off a bridge would you jump too? 1 Shalizi and Thomas Shutterfly ID Eli Sherman Identification and Estimation of Causal Effects from Dependent Data 2 / 9
4 Causal Inference Problems in Networks Example (Shalizi and Thomas 3 ): If your friend Sam jumped off a bridge, would you jump too? yes: want to imitate Sam because they re cool (social contagion) yes: Sam infected you with a judgement-suppressing parasite (physical contagion) yes: known shared interest in dangerous hobbies (observed homophily) yes: unknown to analyst, both you and Sam are daredevils (latent homophily) yes: you and Sam were both on the bridge as it started collapsing (external causation) In general, not possible to disentangle these 3 Shalizi and Thomas Eli Sherman Identification and Estimation of Causal Effects from Dependent Data 3 / 9
5 Causal Inference Problems in Networks Example (Shalizi and Thomas 3 ): If your friend Sam jumped off a bridge, would you jump too? yes: want to imitate Sam because they re cool (social contagion) yes: Sam infected you with a judgement-suppressing parasite (physical contagion) yes: known shared interest in dangerous hobbies (observed homophily) yes: unknown to analyst, both you and Sam are daredevils (latent homophily) yes: you and Sam were both on the bridge as it started collapsing (external causation) In general, not possible to disentangle these Nevertheless, under some assumptions causal inference is possible! 3 Shalizi and Thomas Eli Sherman Identification and Estimation of Causal Effects from Dependent Data 3 / 9
6 A Motivating Social Networking Example Subject i spends time online A i, leading to purchasing behavior Y i This is mediated by participation in a social network M i - entangled with participation of i s friends j Personal characteristics C i act as confounders; unobserved confounding by H i Counterfactual: if we artificially set i s online time, how would this influence j s behavior? H i C i A i M i C j A j M j H j This counterfactual query is complicated by: Interference via A i M j, A i Y j Symmetric dependence via M i M j edge; all Ms marginally correlated so we have one sample Y i and A i confounded by H i ( ) Y i Y j Eli Sherman Identification and Estimation of Causal Effects from Dependent Data 4 / 9
7 A Light Intro to Causal Inference 5 Wish to simulate randomized control trials Compare hypothetical cases (A 1) and controls (A 0) Often interested in mean difference β = E[Y (1)] E[Y (0)] Identification: is parameter β a function of observations? Fundamental problem of causal inference: - only observe assigned treatment for each unit 4 Sometimes identification is possible, for example: E[Y (1)] E[Y (0)] = E[E[Y A = 1, W ] E[Y A = 0, W ]] Identified if W is observed and encapsulates all confounders of A and Y Non-identification = ill-posed problem, even as n Need models and assumptions for identification; we use graphical models 4 Rubin Pearl Eli Sherman Identification and Estimation of Causal Effects from Dependent Data 5 / 9
8 Chain Graphs and their Segregated Projections 7 A 1 A 2 A 1 A 2 H 1 M 1 M 2 H 2 M 1 M 2 Y 1 Y 2 Y 1 Y 2 Chain graphs represent models with A B - directed causal relationship from A to B A B - feedback process at equilibrium between A and B Segregated graphs represent chain graph with latent variables A B - unmeasured confounding between A and B Complete identification algorithm IN: segregated graph; OUT: estimable functional or failure Above demonstrates non-id; can t disentangle effect A i Y i from confounding A i Y i. Algorithm extends ID algorithm for LV-DAGs 6 6 Tian and Pearl 2002; Shpitser and Pearl Lauritzen and Richardson 2002; Shpitser Eli Sherman Identification and Estimation of Causal Effects from Dependent Data 6 / 9
9 Contributions Complete identification algorithm Causal influence of i s online time on behavior of friend j identified: {C 1,C 2,M 1,M 2 } [ [ ] ] p(m 1, M 2 a 1, a 2, C 1, C 2 ) p(y 2 a 1, A 2, M 2, C 2 )p(a 2 C 2 )p(c 1 )p(c 2 ) A 2 Failure means β is not identifiable in the model by any method Single sample inference with hidden variables Gibbs sampling-based algorithm, Auto-G Computation 8 Experiments demonstrate consistency under correctly specified model The devil is in the details! Come see our poster in 10 minutes: 10:45 AM - 12:45 PM in Room 210 & 230 AB #13 Read the paper: Identification and Estimation of Causal Effects from Dependent Data 8 Tchetgen Tchetgen, Fulcher, and Shpitser Eli Sherman Identification and Estimation of Causal Effects from Dependent Data 7 / 9
10 Works Cited I Lauritzen, Steffen L. and Thomas S. Richardson (2002). Chain graph models and their causal interpretations (with discussion). In: Journal of the Royal Statistical Society: Series B 64, pp Pearl, Judea (2009). Causality: Models, Reasoning, and Inference. 2nd ed. Cambridge University Press. isbn: Rubin, D. B. (1976). Causal Inference and Missing Data (with discussion). In: Biometrika 63, pp Shalizi, Cosma Rohilla and Andrew C Thomas (2011). Homophily and contagion are generically confounded in observational social network studies. In: Sociological methods & research 40.2, pp Shpitser, Ilya (2015). Segregated Graphs and Marginals of Chain Graph Models. In: Advances in Neural Information Processing Systems 28. Curran Associates, Inc. Eli Sherman Identification and Estimation of Causal Effects from Dependent Data 8 / 9
11 Works Cited II Shpitser, Ilya and Judea Pearl (2006). Identification of Joint Interventional Distributions in Recursive Semi-Markovian Causal Models. In: Proceedings of the Twenty-First National Conference on Artificial Intelligence (AAAI-06). AAAI Press, Palo Alto. Tchetgen Tchetgen, Eric J., Isabel Fulcher, and Ilya Shpitser (2017). Auto-G-Computation of Causal Effects on a Network. hhttps://arxiv.org/abs/ Working paper. Tian, Jin and Judea Pearl (2002). A General Identification Condition for Causal Effects. In: Eighteenth National Conference on Artificial Intelligence, pp isbn: Eli Sherman Identification and Estimation of Causal Effects from Dependent Data 9 / 9
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