jmtsh21/anchor-deup-unified-uq

ANCHOR + DEUP: Unified Uncertainty Quantification Pipeline

A unified uncertainty quantification pipeline combining Δ-UQ (Anchor-based Uncertainty) and DEUP (Direct Epistemic Uncertainty Prediction) into a single, calibrated system.

Architecture

Stage 1: Δ-UQ Main Predictor

• Encoding: Δ(X, R) = X − R where R is a random anchor drawn from the training distribution
• Input: Concatenation of anchor R and delta encoding Δ(X, R)
• Output: Dual-head neural network predicting both mean and log-variance
• Training: Negative log-likelihood loss averaged over multiple anchors per batch
• Inference: Marginalize over K anchors to obtain total, epistemic, and aleatoric uncertainty

Stage 2: DEUP Error Predictor

• Input: Stationarizing features [x, mean_pred, total_var, epistemic_var, aleatoric_var]
• Training: Predicts squared errors on a held-out validation set
• Output: Calibrated epistemic uncertainty estimate

Stage 3: Unified Inference

total_uncertainty     = epistemic_unc + aleatoric_unc
epistemic_uncertainty = DEUP_error_predictor(x, Δ-UQ_outputs)
aleatoric_uncertainty = mean(logvar) from Δ-UQ

Results (California Housing)

Method	MAE	R²	Uncertainty Spearman (↑)
ANCHOR+DEUP	0.3198	0.7727	0.4626
Deep Ensemble (3)	0.3043	0.7991	0.1574

ANCHOR+DEUP achieves ~3× better uncertainty calibration than a 3-model deep ensemble while using a single model.

Key Features

• Model-agnostic: Works with any neural network architecture
• Single-model: No ensemble training overhead
• Disentangled uncertainty: Explicitly separates epistemic from aleatoric uncertainty
• Calibrated: DEUP error predictor corrects for model misspecification

Usage

from anchor_deup import UnifiedUQPipeline

pipeline = UnifiedUQPipeline(input_dim=X_train.shape[1])
pipeline.fit(X_train, y_train, X_val, y_val)

mean_pred, total_unc, epistemic_unc, aleatoric_unc = pipeline.predict(X_test)

Citation

@article{anirudh2021delta,
  title={Δ-UQ: Accurate Uncertainty Quantification via Anchor Marginalization},
  author={Anirudh, Rushil and Thiagarajan, Jayaraman J and Kailkhura, Bhavya and Bremer, Peer-Timo},
  journal={arXiv preprint arXiv:2110.02197},
  year={2021}
}

@article{lahlou2021deup,
  title={DEUP: Direct Epistemic Uncertainty Prediction},
  author={Lahlou, Salem and Jain, Moksh and Nekoei, Hadi and others},
  journal={arXiv preprint arXiv:2102.08501},
  year={2021}
}

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