deep-ensemble-uq

name	deep_ensemble_uq
description	Constructing Gaussian output neural networks and training deep ensembles to quantify aleatoric and epistemic uncertainty.

Deep Ensembles Uncertainty Quantification (UQ)

Use this skill when deploying models for drug discovery screening or active learning loops. This allows the system to recognize out-of-distribution molecules or noisy measurements and compute prediction confidence.

Conceptual Framework

Uncertainty Categories

1. Aleatoric Uncertainty: Inherent noise in the experimental measurements (e.g., assay noise). Irreducible.
2. Epistemic Uncertainty: Model's lack of knowledge due to sparse training data in that chemical region. Reducible by collecting more data.

Math Formulation

Each model in the ensemble outputs both the predicted mean $\mu(x)$ and variance $\sigma^2(x)$ via a Gaussian output layer. The loss function minimized is the Negative Log-Likelihood (NLL): $$\text{NLL} = \frac{1}{2} \sum_{k=1}^{N} \left( \ln(\sigma^2(x_k)) + \frac{(y_k - \mu(x_k))^2}{\sigma^2(x_k)} \right)$$

For a query molecule $x$, the total uncertainty is decomposed using $M$ models: $$\sigma_{\text{total}}^2 = \underbrace{\frac{1}{M} \sum_{m=1}^{M} \sigma_m^2(x)}{\text{Aleatoric (Inherent Noise)}} + \underbrace{\frac{1}{M} \sum{m=1}^{M} (\mu_m(x) - \bar{\mu}(x))^2}_{\text{Epistemic (Model Disagreement)}}$$

Execution

Run the script deep_ensemble_uq.py to train an ensemble of Gaussian networks:

python scripts/deep_ensemble_uq.py --ensemble_size 5 --epochs 20

This trains multiple models and decomposes predictive uncertainty for high-error/OOD domains.