Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs
By Alain Hauser, Peter Buhlmann. 2013
106 citations recorded by the source corpus.
In many applications we have both observational and (randomized) interventional data. We propose a Gaussian likelihood framework for joint modelling of such different data types, based on global parameters consisting of a directed acyclic graph and corresponding edge weights and error variances. Thanks to the global nature of the parameters, maximum likelihood estimation is reasonable with only one or few data points per intervention. We prove consistency of the Bayesian information criterion for estimating the interventional Markov equivalence class of directed acyclic graphs which is smaller than the observational analogue owing to increased partial identifiability from interventional data. Such an improvement in identifiability has immediate implications for tighter bounds for inferring causal effects. Besides methodology and theoretical derivations, we present empirical results from real and simulated data.
Subfields: Artificial Intelligence, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Bernhard Schölkopf
- Jan Peters
- Peter Buhlmann
- Nicolai Meinshausen
- Yoshua Bengio
- Mathias Drton
- Caroline Uhler
- Sergey Levine
In Statistics and Probability
- Peter Buhlmann
- Jan Peters
- Bernhard Schölkopf
- Mathias Drton
- Nicolai Meinshausen
- Marloes H. Maathuis
- Sara A. van de Geer
- Dominik Rothenhausler
Citations in the corpus
- Causal inference by using invariant prediction: identification and confidence intervals (2015, methodology): “We also compare with IDA based on greedy interventional equivalence search (GIES) [Hauser and B¨uhlmann, 2015] and a correlation-based method that ranks pairs according to correlation on the pooled observational and interventional data.”
- Algebraic problems in structural equation modeling (2016, background): “Interested readers may find discussions of the problem in [43, 49, 57].”
- Permutation-based Causal Inference Algorithms with Interventions (2017, methodology): “For this dataset we compared the GIES results reported in [9] with Algorithm 2 using both, a linear Gaussian and a kernel-based independence criterium [6, 24].”
- A Survey of Learning Causality with Data (2018, background): “Although interventional data and a mixture of interventional and observational data are used in the literature [61, 79, 143, 161], we focus on observational data in this survey to take advantage of pervasive big data.”
- DiBS: Differentiable Bayesian Structure Learning (2021, methodology): “Moreover, we extend the bootstrap methods by taking the closed-form maximum likelihood estimate [57] as the posterior parameter sample for a given graph inferred using the BGe score (BPC∗ and BGES∗), an approach taken in, e.”
- Causal Dantzig: Fast inference in linear structural equation models with hidden variables under additive interventions (2017, background): “Hauser and B¨uhlmann [2015], for example, modify the greedy equivalence search of Chicker-ing [2002] to such a scenario.”
- Partition MCMC for Inference on Acyclic Digraphs (2015, background): “…and interventional data may however help to distinguish between the models of an equivalence class (Cooper andYoo 1999; Eaton and Murphy 2007a; Hauser and Bühlmann 2015; see also Friedman et al. 2000 for a concise discussion about the discovery of causal patterns from observational data).”
- Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions (2018, methodology): “Testing for invariance: To test whether a (conditional) distribution f (Xi|XS) is invariant, we used a method proposed by Heinze-Deml et al. (2017) that we found to work well in practice.”