Information-Theoretic Causal Bounds under Unmeasured Confounding

This repo implements the method in "Information-Theoretic Causal Bounds under Unmeasured Confounding (Jung & Kang, 2026)." It provides lower and upper bounds on causal estimands under unmeasured confounding without bounded outcomes, sensitivity parameters, instruments/proxies, or full SCM specification.

Target estimands (paper notation):

θ(a, x) = E_{Q_{a,x}}[φ(Y)],  Q_{a,x} = P(Y | do(A=a), X=x)
θ(a)    = E_{Q_a}[φ(Y)]

Install (PyPI-first)

For most users, install directly from PyPI:

1) Create and activate a clean virtual environment (recommended)

python -m venv .venv
source .venv/bin/activate  # macOS/Linux

On Windows (PowerShell):

.venv\\Scripts\\Activate.ps1

On Windows (cmd.exe):

.venv\\Scripts\\activate.bat

2) Upgrade pip

python -m pip install --upgrade pip

3) Install from PyPI

python -m pip install itbound

4) Quick sanity check

itbound --help

If you see the CLI help output, the installation worked.

5) Optional extras for figure reproduction

python -m pip install 'itbound[experiments]'

Install from Source (development)

If you want editable installs and local code iteration:

git clone https://github.com/yonghanjung/Information-Theretic-Bounds.git
cd Information-Theretic-Bounds
python -m venv .venv
source .venv/bin/activate
python -m pip install --upgrade pip
python -m pip install -e .
python -m pip install -e '.[experiments]'

10-Minute Quickstart (Opt-in Wrapper)

quick is an opt-in wrapper around itbound.fit(...); default math remains paper-equivalent (mode=paper-default).

python -m venv .venv && source .venv/bin/activate
python -m pip install --upgrade pip
python -m pip install itbound
itbound example --out /tmp/itbound_example.csv
itbound quick --data /tmp/itbound_example.csv --treatment a --outcome y --covariates x1,x2 --outdir /tmp/itbound_quick

What the outputs mean:

• lower/upper: robust causal bound endpoints, not a single identified point estimate.
• width = upper - lower: interval uncertainty under the allowed confounding set.
• valid_interval: whether each row has a finite valid interval after domain/validity checks.

Artifact location:

• All quick outputs are written under --outdir (for example /tmp/itbound_quick).
• Expected files: summary.txt, results.json, claims.json, claims.md, plots/, optional report.html.
• Details: docs/quickstart.md, docs/artifact_contract.md, schema docs/results_schema_v0.md.

Python API

New wrapper (recommended):

import itbound

Standard-library function:

from itbound.standard import run_standard_bounds

result = run_standard_bounds(
    csv_path="/tmp/itbound_toy.csv",
    outcome_col="y",
    treatment_col="a",
    covariate_cols=["x1", "x2"],
    divergences=["KL", "JS", "Hellinger", "TV", "Chi2"],
    aggregation_mode="paper_adaptive_k",
    outdir="/tmp/itbound_standard",
    write_html=True,
)

Legacy import (still supported):

import fbound

CLI

Run bounds from config

itbound run --config docs/cli-config.example.yaml

You can override output path:

itbound run --config docs/cli-config.example.yaml --out /tmp/itbound_bounds.csv

Run a quick synthetic example

itbound example --out /tmp/itbound_example.csv

Reproduce arXiv plots

itbound reproduce --dry-run

Notes:

• reproduce expects the final-arxiv JSON summaries under experiments/final-arxiv.
• If you installed the package, run itbound reproduce from the repo root so the data files are found.
• Install extras first:
  • PyPI install: python -m pip install 'itbound[experiments]'
  • Source/editable install: python -m pip install -e '.[experiments]'

Standard-library run (CSV -> bounds + claims JSON + plots + optional HTML)

itbound standard \
  --csv /tmp/itbound_toy.csv \
  --y-col y \
  --a-col a \
  --x-cols x1,x2 \
  --outdir /tmp/itbound_standard \
  --divergences KL,JS,Hellinger,TV,Chi2 \
  --aggregation-mode paper_adaptive_k \
  --html

Aggregation modes:

• paper_adaptive_k (default): increase endpoint-k until feasible interval is found.
• fixed_k_endpoint: use exactly --fixed-k for both endpoints.
• tight_kth: experiment-style tight-kth aggregation (starts from large k, relaxes down).
  • default divergences for this mode are the same built-in 5: KL,JS,Hellinger,TV,Chi2.
  • you can override to a subset with --divergences (for example KL,TV).

Ground-truth plot overlay options (visualization only; math unchanged):

• --ground-truth-col <col>: draw per-row truth values from a column.
• --ground-truth-effect <float>: draw a scalar horizontal truth line.
• --no-ground-truth-auto: disable auto detection from mu1-mu0.
• default behavior auto-detects mu1-mu0 when available.

Example (tight_kth):

itbound standard \
  --csv /tmp/itbound_toy.csv \
  --y-col y \
  --a-col a \
  --x-cols x1,x2 \
  --outdir /tmp/itbound_standard_tight \
  --aggregation-mode tight_kth

Example (tight_kth subset override + explicit truth column):

itbound standard \
  --csv /tmp/itbound_toy.csv \
  --y-col y \
  --a-col a \
  --x-cols x1,x2 \
  --outdir /tmp/itbound_standard_tight_kltv \
  --divergences KL,TV \
  --aggregation-mode tight_kth \
  --ground-truth-col tau_true

Artifacts written to --outdir:

• bounds.csv
• summary.json (claims + diagnostics + run config)
• plot PNGs when matplotlib is available
• report.html when --html is enabled

If matplotlib is missing, plotting is skipped with a warning and other artifacts are still produced. See also: docs/aggregation_modes.md

Artifact Contract Run (schema-versioned results.json)

itbound artifacts \
  --csv /tmp/itbound_toy.csv \
  --y-col y \
  --a-col a \
  --x-cols x1,x2 \
  --outdir /tmp/itbound_artifacts \
  --divergences KL

This opt-in command writes a fixed folder contract:

• summary.txt
• results.json (schema versioned; see docs/results_schema_v0.md)
• claims.json
• claims.md
• plots/
• report.html (optional with --html)

Quick Wrapper Run (itbound.fit via CLI)

itbound quick \
  --data /tmp/itbound_toy.csv \
  --treatment a \
  --outcome y \
  --covariates x1,x2 \
  --outdir /tmp/itbound_quick

quick is an opt-in wrapper around itbound.fit(...) with default mode=paper-default, and writes the same artifact contract (summary.txt, results.json, claims.json, claims.md, plots/).

Live Demo (Toy + Benchmark)

IHDP scenario preview (GIF rendered from the actual CLI run):

Run a fast IHDP demo with explicit KL + truth-coverage envelope:

itbound demo --scenario ihdp --divergence KL --enforce-truth-coverage --eval-points 240 --rounds 5 --n-folds 5 --outdir /tmp/itbound_live_demo --batch-size 8

Run on a benchmark-style IHDP CSV:

itbound demo --scenario ihdp --ihdp-data /path/to/ihdp_npci_1.csv --divergence KL --enforce-truth-coverage --eval-points 240 --rounds 5 --n-folds 5 --outdir /tmp/itbound_live_demo --batch-size 8

Run both in one command:

itbound demo --scenario both --toy-n 1000 --divergence KL --enforce-truth-coverage --eval-points 240 --rounds 5 --n-folds 5 --outdir /tmp/itbound_live_demo --batch-size 8

The demo writes per-scenario artifact folders (toy/, ihdp/) plus live_demo_summary.md under --outdir. By default, IHDP plots use a demo-only truth-aware envelope so every point satisfies lower < truth < upper visually. Use --no-enforce-truth-coverage to disable this visualization aid. Use --eval-points (e.g., 240) to render fewer evaluation points for smoother, less spiky demo plots.

To regenerate the GIF:

bash scripts/demo/make_quick_demo.sh

Good Example (End-to-End)

Install, run a quick example, and verify the output columns:

python -m pip install itbound
itbound example --out /tmp/itbound_example.csv

python - <<'PY'
import pandas as pd
df = pd.read_csv("/tmp/itbound_example.csv")
print(df.columns.tolist())
PY

Expected columns include lower and upper.

Example Diagram

flowchart LR
    A[Config YAML/JSON] --> B[Data Loader]
    B --> C[Bound Estimator]
    C --> D[Bounds CSV]
    B --> E[Diagnostics]
    C --> E

Example Plot

Config schema (CLI)

The config must be YAML or JSON and include:

• data: one of synthetic, npz_path, or csv_path
• divergence
• propensity_model
• m_model
• dual_net_config
• fit_config
• seed

Optional:

• phi (default: identity)
• output_path (default: itbound_bounds.csv)

See docs/cli-config.example.yaml for a complete example.

For a full field-by-field explanation, see docs/config.md.

Toy CSV example

Create a toy CSV and run:

python - <<'PY'
import numpy as np
import pandas as pd

rng = np.random.default_rng(0)
n = 50
x1 = rng.normal(size=n)
x2 = rng.normal(size=n)
a = (x1 + rng.normal(scale=0.5, size=n) > 0).astype(int)
y = 1.0 + 0.5 * a + 0.3 * x1 - 0.2 * x2 + rng.normal(scale=0.1, size=n)

df = pd.DataFrame({"y": y, "a": a, "x1": x1, "x2": x2})
df.to_csv("/tmp/itbound_toy.csv", index=False)
print("/tmp/itbound_toy.csv")
PY

cat <<'YAML' > /tmp/itbound_toy.yaml
data:
  csv_path: /tmp/itbound_toy.csv
  y_col: y
  a_col: a
  x_cols: [x1, x2]
divergence: KL
phi: identity
propensity_model: logistic
m_model: linear
dual_net_config:
  hidden_sizes: [8, 8]
  activation: relu
  dropout: 0.0
  h_clip: 10.0
  device: cpu
fit_config:
  n_folds: 2
  num_epochs: 2
  batch_size: 16
  lr: 0.005
  weight_decay: 0.0
  max_grad_norm: 5.0
  eps_propensity: 0.001
  deterministic_torch: true
  train_m_on_fold: true
  propensity_config:
    C: 1.0
    max_iter: 200
    penalty: l2
    solver: lbfgs
    n_jobs: 1
  m_config:
    alpha: 1.0
  verbose: false
  log_every: 1
seed: 123
YAML

itbound run --config /tmp/itbound_toy.yaml --out /tmp/itbound_toy_bounds.csv

Agent Skill

Agent-friendly usage is documented in docs/agent/SKILL.md.

Theory at a glance (ITB.pdf)

Divergence bound from propensity (Theorem 1)

For any action a and covariates x with P(a|x) > 0:

D_f(P_{a,x} || Q_{a,x}) <= B_f(e_a(x)),  B_f(e) = e f(1/e) + (1-e) f(0)

This upper bound depends only on the propensity score, making the divergence radius fully propensity-score-based.

Specializations used in the code:

• KL: D_KL(P||Q) <= -log e
• Hellinger: D_H(P||Q) <= 1 - sqrt(e)
• Chi2: D_chi2(P||Q) <= (1-e)/(2e)
• TV: D_TV(P||Q) <= 1 - e
• JS: D_JS(P||Q) <= B_fJS(e) (closed form in the paper)

Dual causal bound (Theorem 2)

Define g(s)=s f(1/s) and its convex conjugate g*(t). The upper bound solves:

θ_up(a,x) = inf_{λ>0, u in R} { λ η_f(a,x) + u + λ E_{P_{a,x}}[g*((φ(Y)-u)/λ)] }

Debiased semiparametric estimator (Section 5)

The code minimizes the paper's risk function (Definition 4) with cross-fitting and a Neyman-orthogonal correction, using:

• PyTorch dual nets for h(a,x) and u(a,x) with λ(a,x)=exp(h(a,x))
• sklearn propensity + outcome regressors for nuisances

Diagnostics (AGENTS P0)

Endpoint-wise aggregation reports per-point diagnostics:

• n_eff_up, n_eff_lo: effective candidate counts after filtering.
• k_used_up, k_used_lo: order-statistic index used (default 1).
• invalid_up, invalid_lo, nonfinite_upper, nonfinite_lower, inverted_filtered: rejection counts.

Run example outputs include validity masks and these diagnostics in the saved tables.