Bayesian Neural Network Training for Uncertainty-Aware Control
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Solution Overview
Problem
Existing methods for training Bayesian neural networks (BNNs) are prone to inaccurate posterior distribution approximations, especially in deep architectures, and require computationally costly inference-time sampling, which is prohibitive for deep BNNs.
Innovation Solution
Training BNNs using marginal likelihood maximization, which integrates out the weights to obtain a marginal likelihood function, allowing for more accurate posterior distribution approximations without the need for inference-time sampling, and incorporating prior knowledge through a regularization term to improve training stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Bayesian neural networks are trained using existing methods (Monte Carlo Dropout or variational inference), then inference uncertainty can be quantified, but the training results in inaccurate posterior distribution approximations especially in deep architectures
Solution Approach 1:
The patent changes the training objective from approximate inference methods to direct marginal likelihood maximization. By reformulating the training process to optimize the marginal likelihood function p(D|θ) directly through gradient ascent, the method achieves accurate posterior distributions without relying on approximate inference techniques like Monte Carlo Dropout or variational inference, thereby resolving the contradiction between computational feasibility and accuracy.
2Measurement precision
If inference-time sampling is used to quantify uncertainty in BNNs, then uncertainty can be measured, but the computational cost is prohibitive for deep BNNs
Solution Approach 1:
The patent performs preliminary action by computing and storing the Hessian matrix and its inverse during the training phase. This pre-computation allows the system to efficiently estimate posterior variance and quantify uncertainty during inference without performing costly sampling operations, thereby resolving the contradiction between accurate uncertainty measurement and computational efficiency.
3Reliability
If the trained model is applied to out-of-distribution inputs or corrupted data, then the model may produce unreliable inferences, but detecting such cases is challenging
Solution Approach 1:
The patent implements feedback by using the quantified uncertainty as a signal to detect out-of-distribution inputs. When the model encounters inputs that differ from the training distribution, the posterior variance increases, providing a natural feedback mechanism that flags unreliable predictions. This resolves the contradiction by making uncertainty detection automatic and integrated into the inference process.
Data Source
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AI summary
Physical systems are increasingly controlled based on inferences which are obtained from machine learned ('trained') models. Examples of such physical systems include computer-controlled systems such as robots, vehicles, domestic appliances, power tools, manufacturing machines, access control systems, building heating systems and the like. A trained model is described in the form of a Bayesian neural network (BNN) which provides a quantification of its inference uncertainty during use and which is trained using marginal likelihood maximization. A Probably Approximately Correct (PAC) bound may be used in the training to incorporate prior knowledge and to improve training stability even when the network architecture is deep. Thereby, a more accurate trained model is obtained, enabling the physical system to be more accurately controlled and monitored.