Towards a Learning Theory of Cause-Effect Inference

David Lopez-Paz, Krikamol Muandet, Bernhard Schölkopf, Iliya Tolstikhin
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1452-1461, 2015.

Abstract

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection {(S_i,l_i)}_i=1^n, where each S_i is a sample drawn from the probability distribution of X_i \times Y_i, and l_i is a binary label indicating whether “X_i \to Y_i” or “X_i ←Y_i”. Given these data, we build a causal inference rule in two steps. First, we featurize each S_i using the kernel mean embedding associated with some characteristic kernel. Second, we train a binary classifier on such embeddings to distinguish between causal directions. We present generalization bounds showing the statistical consistency and learning rates of the proposed approach, and provide a simple implementation that achieves state-of-the-art cause-effect inference. Furthermore, we extend our ideas to infer causal relationships between more than two variables.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-lopez-paz15, title = {Towards a Learning Theory of Cause-Effect Inference}, author = {Lopez-Paz, David and Muandet, Krikamol and Schölkopf, Bernhard and Tolstikhin, Iliya}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {1452--1461}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/lopez-paz15.pdf}, url = {https://proceedings.mlr.press/v37/lopez-paz15.html}, abstract = {We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection {(S_i,l_i)}_i=1^n, where each S_i is a sample drawn from the probability distribution of X_i \times Y_i, and l_i is a binary label indicating whether “X_i \to Y_i” or “X_i ←Y_i”. Given these data, we build a causal inference rule in two steps. First, we featurize each S_i using the kernel mean embedding associated with some characteristic kernel. Second, we train a binary classifier on such embeddings to distinguish between causal directions. We present generalization bounds showing the statistical consistency and learning rates of the proposed approach, and provide a simple implementation that achieves state-of-the-art cause-effect inference. Furthermore, we extend our ideas to infer causal relationships between more than two variables.} }
Endnote
%0 Conference Paper %T Towards a Learning Theory of Cause-Effect Inference %A David Lopez-Paz %A Krikamol Muandet %A Bernhard Schölkopf %A Iliya Tolstikhin %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-lopez-paz15 %I PMLR %P 1452--1461 %U https://proceedings.mlr.press/v37/lopez-paz15.html %V 37 %X We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection {(S_i,l_i)}_i=1^n, where each S_i is a sample drawn from the probability distribution of X_i \times Y_i, and l_i is a binary label indicating whether “X_i \to Y_i” or “X_i ←Y_i”. Given these data, we build a causal inference rule in two steps. First, we featurize each S_i using the kernel mean embedding associated with some characteristic kernel. Second, we train a binary classifier on such embeddings to distinguish between causal directions. We present generalization bounds showing the statistical consistency and learning rates of the proposed approach, and provide a simple implementation that achieves state-of-the-art cause-effect inference. Furthermore, we extend our ideas to infer causal relationships between more than two variables.
RIS
TY - CPAPER TI - Towards a Learning Theory of Cause-Effect Inference AU - David Lopez-Paz AU - Krikamol Muandet AU - Bernhard Schölkopf AU - Iliya Tolstikhin BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-lopez-paz15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 1452 EP - 1461 L1 - http://proceedings.mlr.press/v37/lopez-paz15.pdf UR - https://proceedings.mlr.press/v37/lopez-paz15.html AB - We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection {(S_i,l_i)}_i=1^n, where each S_i is a sample drawn from the probability distribution of X_i \times Y_i, and l_i is a binary label indicating whether “X_i \to Y_i” or “X_i ←Y_i”. Given these data, we build a causal inference rule in two steps. First, we featurize each S_i using the kernel mean embedding associated with some characteristic kernel. Second, we train a binary classifier on such embeddings to distinguish between causal directions. We present generalization bounds showing the statistical consistency and learning rates of the proposed approach, and provide a simple implementation that achieves state-of-the-art cause-effect inference. Furthermore, we extend our ideas to infer causal relationships between more than two variables. ER -
APA
Lopez-Paz, D., Muandet, K., Schölkopf, B. & Tolstikhin, I.. (2015). Towards a Learning Theory of Cause-Effect Inference. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:1452-1461 Available from https://proceedings.mlr.press/v37/lopez-paz15.html.

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