tramdag — Interpretable Neural Causal Models (TRAM-DAGs) in PyTorch

TRAM-DAGs model each variable of a structural causal model with a (transformation-model) flow: one triangular normalizing flow from iid standard-logistic latents to the observed variables, whose Jacobian sparsity is exactly your causal DAG. Fit it once on observational data and answer all three rungs of Pearl's causal hierarchy — observational (L1), interventional (L2, the do-operator), and counterfactual (L3, Pearl abduction) — while keeping interpretable effects: every linear-shift coefficient is a log-odds ratio, exactly as in classical proportional-odds models.

Beate Sick & Oliver Dürr, Interpretable Neural Causal Models with TRAM-DAGs, CLeaR 2025 (arXiv:2503.16206). This repo is the reference implementation (PyTorch, built on zuko); all of the paper's experiments are replicated here with pinned tests.

5-minute showcase: the Colab badge above fits the paper's bimodal benchmark live (GPU-ready) and walks L1 → L2 → L3, every answer checked against analytic ground truth. Didactic walkthrough of the model: notebooks/intro_tram_dag.py.

Install

pip install tramdag            # PyPI
uv sync                        # or: dev setup from a clone (tests, experiments)

30 seconds of API

import tramdag as td
from tramdag import CausalFlowDAG, ContinuousNode, OrdinalNode

spec = {                                  # the spec IS the labelled DAG
    "Age":     ContinuousNode(),
    "mRS_pre": OrdinalNode(levels=6, parents={"Age": "ci"}),
    "NIHSSa":  ContinuousNode(parents={"Age": "ci", "mRS_pre": "ls"}),
    "T":       OrdinalNode(levels=2,
                           parents={"Age": "ci", "mRS_pre": "ls", "NIHSSa": "cs"}),
    "mRS_3m":  OrdinalNode(levels=7,
                           parents={"Age": "ci", "mRS_pre": "ls",
                                    "NIHSSa": "cs", "T": "ls"}),
}
flow = CausalFlowDAG(spec)                # validates acyclicity, builds the flow

# self-stopping training: per-node plateau lr decay + freezing of converged
# nodes (exact, since the per-node NLLs have independent gradients);
# see docs/training-speed.md for benchmarks and the classic two-phase recipe
flow.fit(train_df, val_df, epochs=4000, learning_rate=1e-2,
         schedule="plateau", plateau_patience=30, freeze_patience=120)

flow.log_prob(df)                          # L1: joint log-likelihood per row
flow.sample(1000)                          # L1: observational sampling
flow.sample(1000, do={"T": 1})             # L2: interventional (graph mutilation)
flow.pmf(df, node="mRS_3m", do={"T": 1})   # L2: analytic interventional PMF

u  = flow.abduct(df)                       # L3 step 1: latents from observations
cf = flow.sample(do={"T": 1}, u=u)         # L3 steps 2+3: counterfactuals

flow.save("flow.pt"); flow = CausalFlowDAG.load("flow.pt")

td.simulations.REGISTRY                    # synthetic DGPs with known ground truth

The model in one table

Per node, the transformation is additive on the latent (log-odds) scale — u = h(x; θ) + Σ β·x_pa + Σ g(x_pa) — and each parent edge declares how it enters:

Continuous nodes carry a monotone 1-D transform (bernstein — TRAM-faithful default, spline, affine; ContinuousNode(transform=..., transform_kwargs=...)); ordinal nodes an ordered-logit head P(x ≤ k) = σ(θ_k − shift). Abduction is exact for continuous nodes and truncated-logistic for ordinal ones, so flow.sample(u=flow.abduct(df)) reproduces df exactly / level-exactly.

Validation (all pinned by tests)

• Paper replication — every experiment of the CLeaR paper is a registry family (numpy-only SCM + frozen CSVs + replication script):

  family	paper	demonstrates
  triangle (linear,atan,sin)	§6.1	LS coefficient recovery (β = 2, −0.2, +0.3), CS curve ≡ −f(x₂), non-monotone f
  triangle-mixed (linear,exp)	§6.2	mixed data L1/L2 + the C.4 odds-ratio check (OR ≈ 7.4)
  vaca	§5.1–5.2	the bimodal L1 case a default CNF misses; L2 p(x₃ | do(x₂))
  carefl	§5.3	L3 counterfactual curves vs analytic truth

  cd experiments && uv run python paper_triangle.py atan cs   # etc., see paper_*.py
  

  Sign note: ordinal shifts are subtracted here but added in the paper, so fitted ordinal weights are the paper's with flipped sign (truth.json records both conventions per family).

• Exact classical equivalence — an all-ls flow trained to convergence is the proportional-odds MLE: coefficients match statsmodels and R MASS::polr to ~4 decimals (experiments/validate_ls.py, R reference committed under data/magic-mrclean/*/ref_ls/).

• Training speed — schedules, per-node freezing, LBFGS and device benchmarks: docs/training-speed.md.

Case study: individualized treatment effects in stroke

The method's flagship application estimates individualized thrombectomy effects from the observational MAGIC cohort with external validation against the MR CLEAN trial:

Dürr, Herzog, Bühler, Wegener & Sick, Estimating Individualized Treatment Effects in Acute Ischemic Stroke with Causal Transformation Models (TRAM-DAG) (arXiv:2606.12623).

The clinical data is private and never part of this repo. Its public stand-in is data/magic-mrclean/ — a fully synthetic cohort with the same schema and known ground truth (true ATE, true individual counterfactuals), including an nl variant where an all-ls model is provably misspecified:

Full storyline, clinical-data context, R cross-check and reading notes: docs/stroke-case-study.md.

Layout

src/tramdag/            spec.py transforms.py conditioners.py flow.py
                        simulations/   (magic_mrclean, triangle, vaca, carefl + CLIs)
data/                   frozen synthetic CSVs + truth.json — a test contract
experiments/            stroke pipeline, paper replications, training benchmark
notebooks/              intro (didactic) + Colab demo   (jupytext .py — see README there)
tests/                  66 tests: unit, known-truth recovery, R regression
docs/                   training-speed.md, stroke-case-study.md

Implementation conventions (latent-scale signs, raw/one-hot parent encoding, log-space ordinal likelihood, seeding) are documented in CLAUDE.md and pinned by tests.

Citation

If you use tramdag, please cite the method paper:

@inproceedings{sick2025tramdag,
  title     = {Interpretable Neural Causal Models with TRAM-DAGs},
  author    = {Sick, Beate and D{\"u}rr, Oliver},
  booktitle = {Proceedings of the 4th Conference on Causal Learning and Reasoning (CLeaR)},
  series    = {Proceedings of Machine Learning Research},
  volume    = {275},
  year      = {2025},
}

For the stroke application (and the magic-mrclean cohort design) additionally:

@article{duerr2026stroke,
  title  = {Estimating Individualized Treatment Effects in Acute Ischemic Stroke
            with Causal Transformation Models (TRAM-DAG): A Multi-Centre
            Observational Study with External RCT Validation},
  author = {D{\"u}rr, Oliver and Herzog, Lisa and B{\"u}hler, Pascal and
            Wegener, Susanne and Sick, Beate},
  journal = {arXiv preprint arXiv:2606.12623},
  year   = {2026},
}