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## Abstract

In recent years, there has been an increasing interest in studying causality-related properties in machine learning models generally, and in generative models in particular. While that is well motivated, it inherits the fundamental computational hardness of probabilistic inference, making exact reasoning intractable. Probabilistic tractable models have also recently emerged, which guarantee that conditional marginals can be computed in time linear in the size of the model, where the model is usually learned from data. Although initially limited to low treewidth models, recent tractable models such as sum product networks (SPNs) and probabilistic sentential decision diagrams (PSDDs) exploit efficient function representations and also capture high tree-width models.

In this paper, we ask the following technical question: can we use the distributions represented or learned by these models to perform causal queries, such as reasoning about interventions and counterfactuals? We answer in the negative. We show that when transforming SPNs to a causal graph interventional reasoning reduces to computing marginal distributions; in other words, only trivial causal reasoning is possible. For PSDDs the situation is only slightly better. We first provide an algorithm for constructing a causal graph from a PSDD, which introduces augmented variables. Intervening on the original variables, once again, reduces to marginal distributions, but when intervening on the augmented variables, a deterministic but nonetheless “causal-semantics” can be provided for PSDDs.

In this paper, we ask the following technical question: can we use the distributions represented or learned by these models to perform causal queries, such as reasoning about interventions and counterfactuals? We answer in the negative. We show that when transforming SPNs to a causal graph interventional reasoning reduces to computing marginal distributions; in other words, only trivial causal reasoning is possible. For PSDDs the situation is only slightly better. We first provide an algorithm for constructing a causal graph from a PSDD, which introduces augmented variables. Intervening on the original variables, once again, reduces to marginal distributions, but when intervening on the augmented variables, a deterministic but nonetheless “causal-semantics” can be provided for PSDDs.

Original language | English |
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Number of pages | 13 |

Publication status | Published - 13 Dec 2019 |

Event | Knowledge Representation & Reasoning Meets Machine Learning: Workshop at NeurIPS'19 - Vancouver, Canada Duration: 13 Dec 2019 → 13 Dec 2019 https://kr2ml.github.io/2019/ |

### Workshop

Workshop | Knowledge Representation & Reasoning Meets Machine Learning |
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Abbreviated title | KR2ML |

Country | Canada |

City | Vancouver |

Period | 13/12/19 → 13/12/19 |

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## Projects

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