Uncertainty Quantification

A class of neural networks that place a probability distribution over the model's weights instead of learning fixed point estimates. By performing inference over these weight distributions, BNNs naturally output a predictive posterior distribution that captures epistemic uncertainty. Key mechanisms:

• Variational Inference: Approximates the true posterior with a simpler distribution by minimizing KL divergence.
• Monte Carlo Dropout: A practical approximation where dropout is applied at inference time to generate multiple stochastic forward passes.
• Weight Uncertainty: High uncertainty in weight values for a given input indicates the model has not seen sufficient similar training data.

A frequentist, non-Bayesian method for uncertainty estimation that trains multiple independent models with different random initializations on the same dataset. The variance across the ensemble's predictions serves as a robust proxy for epistemic uncertainty. Distinguishing characteristics:

• Functional Diversity: Random initialization and stochastic optimization trajectories cause each ensemble member to converge to a different local minimum in the loss landscape.
• Decomposition: Total predictive uncertainty is split into aleatoric (average individual model variance) and epistemic (variance across ensemble means) components.
• Calibration: Often requires post-hoc temperature scaling on a validation set to ensure predicted confidence intervals align with empirical accuracy.

A non-parametric, kernel-based Bayesian method that defines a prior distribution over functions directly. A GP is fully specified by a mean function and a covariance kernel (e.g., Radial Basis Function, Matérn). Advantages for molecular data:

• Closed-Form Uncertainty: Provides analytically tractable posterior variance for every prediction point.
• Kernel Engineering: Custom kernels can encode chemical similarity, such as Tanimoto similarity between molecular fingerprints, directly into the prior.
• Limitations: Standard GPs scale cubically O(n³) with the number of data points, making them impractical for large-scale virtual screening without sparse approximation methods like inducing points.

A model-agnostic, distribution-free framework that wraps around any pre-trained predictor to produce prediction sets with a rigorous, finite-sample coverage guarantee. Instead of outputting a single value, it outputs a set (e.g., a range for regression or multiple labels for classification) that contains the true value with a user-specified probability (e.g., 90%). Core workflow:

• Calibration Set: A held-out dataset is used to compute nonconformity scores, which measure how 'strange' a prediction is relative to the true label.
• Validity Guarantee: The marginal coverage guarantee holds regardless of the underlying model or data distribution, assuming exchangeability of the calibration and test points.
• Mondrian Conformal Prediction: A variant that provides conditional coverage guarantees for specific subgroups, such as distinct chemical scaffolds, preventing biased performance.

A statistical technique that estimates the conditional median or other quantiles of a response variable, directly modeling the prediction interval without assuming a specific parametric distribution. Implementation in deep learning:

• Pinball Loss Function: The standard loss function for quantile regression, which asymmetrically penalizes overestimation and underestimation to target a specific quantile (e.g., 0.05 for the lower bound, 0.95 for the upper bound).
• Simultaneous Quantile Modeling: A multi-headed neural network architecture can output multiple quantiles (e.g., 10th, 50th, 90th percentiles) simultaneously, forming a sharp prediction interval.
• Aleatoric Focus: This method primarily captures aleatoric uncertainty inherent in the data, as it models the spread of the target variable conditional on the input features.

A method that trains a neural network to output the parameters of a higher-order evidential distribution (e.g., a Normal-Inverse-Gamma distribution for regression) placed directly over the likelihood function. This allows the model to learn to predict its own uncertainty in a single forward pass. Key concepts:

• Prior over Likelihood: Instead of predicting a single mean and variance, the network predicts hyperparameters (γ, ν, α, β) that govern a distribution over possible means and variances.
• Regularization: The loss function maximizes the evidence for correct predictions while penalizing incorrect evidence, effectively increasing uncertainty on out-of-distribution samples.
• Computational Efficiency: Unlike ensembles or BNNs, evidential methods require only a single deterministic forward pass, making them highly suitable for high-throughput virtual screening pipelines.