Causal normalizing flows enable analysis despite missing data
Learning Causal Normalizing Flows from Incomplete Data via Observed-Data Likelihood
Machine Learning
Summary
Incomplete data often causes trouble for understanding cause and effect because many methods need all data to be fully observed. The authors present MissCNF, a method that can learn the causal relationships directly from data even when parts are missing, without guessing or discarding incomplete records. This approach uses knowledge about the cause-and-effect structure to efficiently deal with missing pieces. They test their method on various datasets with different missing patterns and show it often outperforms common ways of handling missing data, especially when data is complex and missing not at random.
What this means in practice
- •For healthcare data teams: Analyze incomplete patient records for causal insights without needing fully filled datasets or imputation steps.
- •For financial risk analysts: Model causal relationships in financial data with missing entries to improve risk predictions without discarding incomplete transactions.
Tested on simulated data.
Authors
Trung-Dung Hoang, Alceu Bissoto, Tim Flühmann, David Herzig, Christos Nakas, Lia Bally, Lisa M. Koch
Abstract
Causal Normalizing Flows (CNFs) enable causal inference from observational data given the causal structure, but they assume fully observed training data. We introduce MissCNF, which trains CNFs directly on incomplete data by maximizing the marginal likelihood of each partially observed sample, without discarding rows or constructing a completed dataset. Thanks to the causal structure encoded in the autoregressive factorization of CNFs, only missing variables in the ancestral closure of the observed set are integrated out, while the others are dropped without computation. We further establish the conditions under which MissCNF recovers the true joint distribution, and introduce \emph{causal-family positivity}, where identification is possible even when no record in the dataset is ever complete. We compare MissCNF with two common strategies for handling missing data: listwise deletion and impute-then-fit pipelines. Across eight synthetic causal benchmarks, three missingness mechanisms, and missing rates up to $90\%$, MissCNF achieves the lowest KL divergence in 23 of 24 nonlinear MCAR and MAR settings and in all nonlinear MNAR settings, as well as the lowest counterfactual error in 20 of 24 settings. On linear SCMs, where linear imputation performs best, MissCNF ranks in the top two in 22 of 24 settings.