Add instrumental variables example

[eb8680]

As in the other examples, the easiest way to approach this is probably to pick a single paper and reproduce its model and results.

Some candidate papers:

• Mendelian randomization
• Deep instrumental variables

[qinqian]

@eb8680, one quick question, shall we use pyro or causal_pyro to implement this and #21 examples? Is the causal_pyro ready with some basic get-started cases to use?

[eb8680]

@qinqian you should be able to get started along the same lines as the other examples (e.g. slc.ipynb) by creating a new notebook with the following sections:

1. a background section setting up an example problem and dataset taken from one of the papers above or a similar one
2. a section with a Pyro program corresponding to the causal model from the paper
3. a section with a causal query formulated as an expanded Pyro model
4. a section where the query is evaluated using SVI and an autoguide, or another standard Pyro inference algorithm
5. a section where the results of the query are visualized and found to reproduce the results from the source paper

If you get stuck with these at any point, feel free to put up a draft pull request and ask for help or feedback. The existing examples currently have steps 1-3 completed, and we're working on finishing steps 4-5 (e.g. #59).

[qinqian]

Thanks @eb8680!

[qinqian]

A relevant about the Mendelian randomization: https://www.nature.com/articles/s41467-023-41394-4.

[dimkab]

Published version of the Deep IV paper:

J. Hartford, G. Lewis, K. Leyton-Brown, and M. Taddy, “Deep IV: A Flexible Approach for Counterfactual Prediction,” in Proceedings of the 34th International Conference on Machine Learning, PMLR, Jul. 2017, pp. 1414–1423. Available: https://proceedings.mlr.press/v70/hartford17a.html