Interventions and Counterfactuals in Tractable Probabilistic Models:
  Limitations of Contemporary Transformations
  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 tree-width 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? By appealing to some
existing ideas on transforming such models to Bayesian networks, we answer
mostly 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.
