For a continuous random variable $Z$, testing conditional independence $X\indep Y|Z$ is known to be a particularly hard problem. It constitutes a key ingredient of many constraint-based causal discovery algorithms. These algorithms are often applied to datasets containing binary variables, which indicate the ‘context’ of the observations, e.g. a control or treatment group within an experiment. In these settings, conditional independence testing with $X$ or $Y$ binary (and the other continuous) is paramount to the performance of the causal discovery algorithm. To our knowledge no nonparametric ‘mixed’ conditional independence test currently exists, and in practice tests that assume all variables to be continuous are used instead. In this paper we aim to fill this gap, as we combine elements of Holmes et al. (2015) and Teymur and Filippi (2020) to propose a novel Bayesian nonparametric conditional two-sample test. Applied to the Local Causal Discovery algorithm, we investigate its performance on both synthetic and real-world data, and compare with state-of-the-art conditional independence tests.


A Bayesian Nonparametric Conditional Two-sample Test with an Application to Local Causal Discovery

One of the core assumptions in causal discovery is the faithfulness assumption---i.e. assuming that independencies found in the data are due to separations in the true causal graph. This assumption can, however, be violated in many ways, including xor connections, deterministic functions or cancelling paths. In this work, we propose a weaker assumption that we call 2-adjacency faithfulness. In contrast to adjacency faithfulness, which assumes that there is no conditional independence between each pair of variables that are connected in the causal graph, we only require no conditional independence between a node and a subset of its Markov blanket that can contain up to two nodes. Equivalently, we adapt orientation faithfulness to this setting.

A Weaker Faithfulness Assumption based on Triple Interactions

**Session Chair**: James Cussens
 **ID // Presenter // Live Discussant** 
8 // Tom Ryder // James Cussens 
227 // George De Ath // Alexander Alemi 
389 // Anders Kirk Uhrenholt // Yingzhen Li 
601 // Philip Boeken // Noa Malem-Shinitski

Bayesian Methods

technical paper

The Conference on Uncertainty in Artificial Intelligence (UAI) is one of the premier international conferences on research related to knowledge representation, learning, and reasoning in the presence of uncertainty. It is supported by the [Association for Uncertainty in Artificial Intelligence (AUAI).](https://www.auai.org/)

The 37th Conference on Uncertainty in Artificial Intelligence (UAI 2021) is held fully online. We have an exciting program consisting of keynote talks by [Susan Murphy](https://www.auai.org/uai2021/program?block=A), [Eric Horvitz](https://www.auai.org/uai2021/program?block=B), [Lenka Zdeborová](https://www.auai.org/uai2021/program?block=C), [Judea Pearl](https://www.auai.org/uai2021/program?block=D) and [Ankur Moitra](https://www.auai.org/uai2021/program?block=E), a town hall meeting, peer-reviewed papers, and three workshops. The main conference is single-track and each paper is show-cased with a live component (either a live discussion and Q&A, or a live lightning talk). All papers are also featured in video presentations and in poster sessions in gather.town. The three parallel workshops on Friday allow for smaller meetings on current topics.

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 Cassio de Campos and Marloes Maathuis
 UAI 2021 Program Chairs
 uai2021programchairs@gmail.com

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UAI 2021

The Conference on Uncertainty in Artificial Intelligence (UAI) is one of the premier international conferences on research related to knowledge representation, learning, and reasoning in the presence of uncertainty. It is supported by the [Association for Uncertainty in Artificial Intelligence (AUAI).](https://www.auai.org/)

Joris M. Mooij

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A Bayesian Nonparametric Conditional Two-sample Test with an Application to Local Causal Discovery

A Weaker Faithfulness Assumption based on Triple Interactions

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