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Differentiable Structure Learning and Causal Discovery for General Binary Data

NeurIPS 2025 · Probabilistic and scientific modeling › Causal discovery · approach: Interventional causal discovery · 0 citations (OpenAlex)

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Proposes a general differentiable structure learning framework for binary/discrete data based on the multivariate Bernoulli distribution with higher-order interaction terms, proves non-identifiability and Markov-equivalence identifiability under SMR, and introduces the two-stage BiNOTEARS method.

Problem

Causal discovery (DAG structure learning) for discrete binary data without assuming a specific structural equation model, while capturing arbitrary (including higher-order) dependencies among variables.

Approach

Represents any binary distribution as a multivariate Bernoulli with all interaction features, induces a weighted adjacency matrix from squared interaction coefficients, and solves a single differentiable program with a quasi-MCP sparsity penalty and an acyclicity constraint to recover the sparsest DAG up to Markov equivalence.

Key results

• On the real protein dataset (n=7,466, d=11), BiNOTEARS achieves SHD 13 versus 16 for NOTEARS-MLP and 22 for NOTEARS.
• On small synthetic graphs with second-order interactions, DAGMA (first-order only) shows markedly poor recovery while BiNOTEARS remains competitive.
• BiNOTEARS attains performance on par with existing baselines (PC, FGES, DAGMA) on larger synthetic graphs.

Measured effects reported in the paper

Surprising findings

• The general multivariate Bernoulli model is non-identifiable: for every topological order there is a distinct graph-parameter pair reproducing the same distribution.

Limitations

• Exact method scales exponentially in the number of nodes because the feature map has 2^p terms; BiNOTEARS is a heuristic without theoretical guarantees.
• Theoretical guarantees are population-level and rely on positivity of the distribution and the SMR or faithfulness assumption.
• Experiments are limited to small or moderate graphs (d up to around 11 for real data).

Experimental setup

Datasets: synthetic binary data from SEMs with higher-order interactions protein-signaling flow cytometry dataset (n=7,466, d=11)

Benchmarks: synthetic binary graphs (d<10 and larger graphs) protein-signaling real dataset (d=11)

Metrics: structural Hamming distance (SHD) number of edges

Baselines: DAGMA PC FGES NOTEARS NOTEARS-MLP

Builds on: NOTEARS DAGMA NOTEARS-MLP minimax concave penalty

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