Deep ensembles: predictive uncertainty and shared blind spots

Definition

A deep ensemble combines the predictions of several neural networks trained separately. Different random initializations and training orders can produce different fitted models even when they use the same dataset. Averaging their predictions can improve predictive uncertainty estimates, but agreement among members is not a certificate of correctness. [1]

How it works

For classification, average the members’ class probabilities rather than simply counting winning labels. For probabilistic regression, each member may predict a mean mu_m and variance v_m. The mixture mean is the average of mu_m; its variance is the average of (v_m + mu_m squared) minus the ensemble mean squared.

This separates average within-model variance from variation between predicted means. The original deep-ensemble method can train each member on the full dataset; bootstrap resampling is not required. [1]

Practical workflow

1. Choose the number of members according to a measured training, memory and latency budget.
2. Train members separately with recorded random seeds and a shared, versioned data protocol.
3. Save the member artifacts and the aggregation rule as one deployable version.
4. Evaluate the combined predictions on untouched data and plausible deployment shifts; compare with a single-model baseline.

For classification, inspect log loss, Brier score and reliability. For regression, assess residual behaviour and any claimed interval coverage. If uncertainty controls abstention, measure errors against the fraction of cases retained. Treat this as an operational evaluation plan, not an automatic property of ensembling.

Illustrative example

Illustrative calculation, not a trained result: three regression members predict means 10, 12 and 14 units, each with variance 4 units squared. The ensemble mean is 12. Average within-model variance is 4, while variance between member means is (4 + 0 + 4) / 3 = 8/3. Total mixture variance is therefore 20/3, approximately 6.67 units squared.

This uses the variance of the finite mixture, not the sample-variance estimator with denominator two. The calculation alone does not establish a calibrated prediction interval.

Limitations and evaluation

Members can share the same missing features, training biases or blind spots. Their disagreement reflects only the variation represented by the chosen ensemble, not all uncertainty. Independent training runs do not make the shared training observations independent.

The cited shift benchmark found useful ensemble performance, but uncertainty quality still degraded as shifts increased. [2] Assess each deployment rather than assuming that low disagreement means familiar or safe input. Account for the additional compute and storage, and document any reduced ensemble used in production. No local training or benchmark result is claimed.

Sources

[1] Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles [2] Can you trust your model’s uncertainty? Evaluating predictive uncertainty under dataset shift