| 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
- Aleatoric Uncertainty: Inherent noise in the experimental measurements (e.g., assay noise). Irreducible.
- 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.
