In the context of industrially mass-manufactured products, quality management is based on physically inspecting a small sample from a large batch and reasoning about the batch's quality conformance. When complementing physical inspections with predictions from machine learning models, it is crucial that the uncertainty of the prediction is known. Otherwise, the application of established quality management concepts is not legitimate. Deterministic (machine learning) models lack quantification of their predictive uncertainty and are therefore unsuitable. Probabilistic (machine learning) models provide a predictive uncertainty along with the prediction. However, a concise relationship is missing between the measurement uncertainty of physical inspections and the predictive uncertainty of probabilistic models in their application in quality management. Here, we show how the predictive uncertainty of probabilistic (machine learning) models is related to the measurement uncertainty of physical inspections. This enables the use of probabilistic models for virtual inspections and integrates them into existing quality management concepts. Thus, we can provide a virtual measurement for any quality characteristic based on the process data and achieve a 100 percent inspection rate. In the field of Predictive Quality, the virtual measurement is of great interest. Based on our results, physical inspections with a low sampling rate can be accompanied by virtual measurements that allow an inspection rate of 100 percent. We add substantial value, especially to complex process chains, as faulty products/parts are identified promptly and upcoming process steps can be aborted.

Machine learning models can be improved by adapting them to respect existing background knowledge. In this paper we consider multitask Gaussian processes, with background knowledge in the form of constraints that require a specific sum of the outputs to be constant. This is achieved by conditioning the prior distribution on the constraint fulfillment. The approach allows for both linear and nonlinear constraints. We demonstrate that the constraints are fulfilled with high precision and that the construction can improve the overall prediction accuracy as compared to the standard Gaussian process.

There is significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware neural networks (NNs), based on learning evidential distributions for aleatoric and epistemic uncertainties, shows promise over traditional deterministic methods and typical Bayesian NNs, yet several important gaps in the theory and implementation of these networks remain. We discuss three issues with a proposed solution to extract aleatoric and epistemic uncertainties from regression-based neural networks. The approach derives a technique by placing evidential priors over the original Gaussian likelihood function and training the NN to infer the hyperparameters of the evidential distribution. Doing so allows for the simultaneous extraction of both uncertainties without sampling or utilization of out-of-distribution data for univariate regression tasks. We describe the outstanding issues in detail, provide a possible solution, and generalize the deep evidential regression technique for multivariate cases.