Composite Loss Function for Aleatoric and Epistemic Error Correlation
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Solution Overview
Problem
Existing methods for correlating aleatoric and epistemic uncertainties in neural networks with absolute prediction errors are inadequate, leading to questionable reliance on these uncertainties.
Innovation Solution
A custom loss function for neural networks that incorporates three terms to capture both epistemic and aleatoric uncertainties, explicitly correlating them with prediction bias or error, using a regularization parameter to balance accuracy and correlation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional loss functions are used in neural networks, then training is simpler, but the correlation between predicted uncertainties and actual errors is poor
Solution Approach 1:
The patent modifies the loss function by adding a third term that explicitly correlates uncertainty with absolute error. The custom loss function L(θ) = L1(θ) + L2(θ) + L3(θ) changes the parameterization by incorporating the correlation term L3(θ) = Σα|y_i - f_θ(x_i)|σ_i, where α is a weighting parameter. This parameter change enables the network to learn uncertainties that are correlated with actual errors while maintaining a structured approach to loss function design.
Solution Approach 2:
The patent creates a composite loss function by combining three distinct loss terms: L1(θ) for mean squared error, L2(θ) for log-likelihood with aleatoric uncertainty, and L3(θ) for uncertainty-error correlation. This composite structure integrates multiple objectives into a unified training framework, allowing the neural network to simultaneously optimize prediction accuracy, aleatoric uncertainty estimation, and the correlation between epistemic uncertainty and actual errors.
2Reliability
If dropout-based Bayesian inference is used, then epistemic uncertainty is estimated, but the total uncertainty is not well correlated to absolute error
Solution Approach 1:
The patent introduces a feedback mechanism through the L3(θ) term that explicitly uses the absolute error |y_i - f_θ(x_i)| to adjust the epistemic uncertainty σ_i. During training, the loss function provides feedback by penalizing discrepancies between the predicted uncertainty and the actual error magnitude, enabling the network to learn uncertainties that are calibrated to the true error distribution.
Solution Approach 2:
The patent segments the uncertainty estimation into two distinct components: aleatoric uncertainty (σ_i from data) and epistemic uncertainty (from model parameters). By separately modeling these components and adding a dedicated correlation term L3(θ) that specifically addresses epistemic uncertainty's relationship with error, the patent enables precise control and optimization of each uncertainty type's contribution to the total uncertainty.
3Reliability
If log-likelihood loss function is used, then aleatoric uncertainty is incorporated, but epistemic uncertainty correlation with error is insufficient
Solution Approach 1:
The patent merges multiple loss function objectives into a unified custom loss function L(θ) that simultaneously optimizes: (1) prediction accuracy via L1(θ), (2) aleatoric uncertainty estimation via L2(θ), and (3) epistemic uncertainty-error correlation via L3(θ). This merging allows the neural network to learn all three objectives in a single training process, with the regularization parameter α controlling the balance between correlation and accuracy.
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AI summary
A method and a non-transitory computer readable medium for performing a calculation in a neural network comprise: accepting a data set into the neural network; performing a calculations with the neural network using the data set, wherein the calculations use a loss function and provide an aleatoric and epistemic uncertainty that is correlated to a value; and displaying results of the calculations performed.