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We focus on a challenging distribution-shift setting in which the causal and anticausal variables of the target are unobserved. Leaning on information theory, we develop feature selection and engineering techniques for the observed downstream variables that act as proxies. We identify model-stabilizing proxies and moreover utilize auxiliary training tasks to answer counterfactual questions that stabilize our models.

The first known algorithm for $k$-MixBND.

We develop the “method of synthetic bits” for solving discretem mixtures of product distributions, giving a exponential time complexity improvement (in the number of sources). The algorithm involves a reduction to the $k$-MixIID case.

Nontransitivite properties of the voting systems are also possible in networks of experts and machine learning models.

Importance weighting via probability density function estimation is unstable and requires parameter tuning. We demonstrate that reweighting according to cumulative distirbution functions is stable without parameter tuning.