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Consistency of Neural Causal Partial Identification

NeurIPS 2024 · Probabilistic and scientific modeling › Causal discovery · approach: Causal effect identification · 0 citations (OpenAlex)

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Proves consistency of max/min partial identification of causal effects via neural causal models (NCMs) for general SCMs with continuous and categorical variables, showing Lipschitz regularization is needed.

Problem

Partial identification of causal effects via optimization over neural causal models lacked consistency guarantees for general (continuous/mixed) SCMs; prior proofs covered only discrete or linear models.

Approach

Approximates any Lipschitz SCM by an NCM with ReLU networks for structural functions and push-forward networks (with a Gumbel-Softmax mixture layer over connected support components) for latent distributions, and proves the empirical max/min estimator with Lipschitz-truncated networks is asymptotically consistent, with a counterexample showing necessity of Lipschitz regularization.

Key results

• On the continuous IV model (n=5000), NCM gives average bound [2.49,3.24] vs AutoBounds [1.40,3.48] with 50/50 coverage of true ATE=3.
• On the discrete binary IV example, NCM bound [-0.49,0.05] vs AutoBounds [-0.45,-0.05] versus optimal [-0.45,-0.04]; both cover true value -0.31 in all runs.
• Theorem gives almost-sure asymptotic inclusion of limit points of the NCM estimator in [sharp lower bound with slightly larger Lipschitz constant, F_*].

Measured effects reported in the paper

Surprising findings

• Without Lipschitz regularization, an identifiable SCM can yield observationally close models whose ATE differs by a constant regardless of sample size, so the estimator may be inconsistent.
• On the continuous IV experiment, the NCM bounds are wider than AutoBounds' on the discrete-approximated problem in the binary case, and the AutoBounds average bound fails to cover the optimal bound in the discrete example.

Limitations

• Finite-sample guarantees are not established for the general case; only a special no-confounding case gets a rate.
• The estimator's limit set lies in [sharp lower bound at slightly larger Lipschitz constant, F_*] rather than converging to the sharp bound in general.
• Experiments are small-scale on two simple IV models and rely on discretization for the baseline.

Experimental setup

Datasets: synthetic SCMs (binary IV, continuous IV)

Benchmarks: binary IV example from Balke-Pearl setting continuous IV model

Metrics: bound width coverage of true value success rate

Baselines: AutoBounds

Builds on: Neural Causal Models (Xia et al.) AutoBounds Gumbel-Softmax

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