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Semiconductors are widely used in various applications and critical infrastructures. These devices have specified lifetimes and quality targets that manufacturers must achieve. Lifetime estimation is conducted through accelerated stress tests. Electrical parameters are measured at multiple times during a stress test procedure. The change in these Electrical parameters is called lifetime drift. Data from these tests can be used to develop a statistical model predicting the lifetime behavior of the electrical parameters in real devices. These models can provide early warnings in production processes, identify critical parameter drift, and detect outliers. While models for continuous electrical parameters exists, there may be bias when estimating the lifetime of discrete parameters. To address this, we propose a semi-parametric model for degradation trajectories based on longitudinal stress test data. This model optimizes guard bands, or quality guaranteeing tighter limits, for discrete electrical parameters at production testing. It is scalable, data-driven, and explainable, offering improvements over existing methods for continuous underlying data, such as faster calculations, arbitrary non-parametric conditional distribution modeling, and a natural extension of optimization algorithms to the discrete case using Markov transition matrices.

Feature selection represents a measure to reduce the complexity of high-dimensional datasets and gain insights into the systematic variation in the data. This aspect is of specific importance in domains that rely on model interpretability, such as life sciences. We propose UBayFS, an ensemble feature selection technique embedded in a Bayesian statistical framework. Our approach considers two sources of information: data and domain knowledge. We build a meta-model from an ensemble of elementary feature selectors and aggregate this information in a multinomial likelihood. The user guides UBayFS by weighting features and penalizing specific feature blocks or combinations, implemented via a Dirichlet-type prior distribution and a regularization term. In a quantitative evaluation, we demonstrate that our framework (a) allows for a balanced trade-off between user knowledge and data observations, and (b) achieves competitive performance with state-of-the-art methods.

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as scalable approximations of classical Gaussian processes. Variable selection is achieved by conditioning the process mean and covariance function on a random set that represents the indices of contributing variables. A priori beliefs regarding this set control the variable selection, while reference priors are assigned to the remaining model parameters, ensuring numerical robustness in the process covariance matrix. We propose a Metropolis-Within-Gibbs algorithm for model inference. Evaluation using simulated data, a computer experiment approximation, and two real-world data sets demonstrate the effectiveness of our approach.

The 3D modelling of indoor environments and the generation of process simulations play an important role in factory and assembly planning. In brownfield planning cases existing data are often outdated and incomplete especially for older plants, which were mostly planned in 2D. Thus, current environment models cannot be generated directly on the basis of existing data and a holistic approach on how to build such a factory model in a highly automated fashion is mostly non-existent. Major steps in generating an environment model in a production plant include data collection and pre-processing, object identification as well as pose estimation. In this work, we elaborate a methodical workflow, which starts with the digitalization of large-scale indoor environments and ends with the generation of a static environment or simulation model. The object identification step is realized using a Bayesian neural network capable of point cloud segmentation. We elaborate how the information on network uncertainty generated by a Bayesian segmentation framework can be used in order to build up a more accurate environment model. The steps of data collection and point cloud segmentation as well as the resulting model accuracy are evaluated on a real-world data set collected at the assembly line of a large-scale automotive production plant. The segmentation network is further evaluated on the publicly available Stanford Large-Scale 3D Indoor Spaces data set. The Bayesian segmentation network clearly surpasses the performance of the frequentist baseline and allows us to increase the accuracy of the model placement in a simulation scene considerably., Comment: Submitted to MDPI Entropy for Review

The digital factory provides undoubtedly a great potential for future production systems in terms of efficiency and effectivity. A key aspect on the way to realize the digital copy of a real factory is the understanding of complex indoor environments on the basis of 3D data. In order to generate an accurate factory model including the major components, i.e. building parts, product assets and process details, the 3D data collected during digitalization can be processed with advanced methods of deep learning. In this work, we propose a fully Bayesian and an approximate Bayesian neural network for point cloud segmentation. This allows us to analyze how different ways of estimating uncertainty in these networks improve segmentation results on raw 3D point clouds. We achieve superior model performance for both, the Bayesian and the approximate Bayesian model compared to the frequentist one. This performance difference becomes even more striking when incorporating the networks' uncertainty in their predictions. For evaluation we use the scientific data set S3DIS as well as a data set, which was collected by the authors at a German automotive production plant. The methods proposed in this work lead to more accurate segmentation results and the incorporation of uncertainty information makes this approach especially applicable to safety critical applications., Comment: 17 pages, 5 figures, submitted to MDPI Modelling journal for review

Accurate demand forecasting is one of the key aspects for successfully managing restaurants and staff canteens. In particular, properly predicting future sales of menu items allows a precise ordering of food stock. From an environmental point of view, this ensures maintaining a low level of pre-consumer food waste, while from the managerial point of view, this is critical to guarantee the profitability of the restaurant. Hence, we are interested in predicting future values of the daily sold quantities of given menu items. The corresponding time series show multiple strong seasonalities, trend changes, data gaps, and outliers. We propose a forecasting approach that is solely based on the data retrieved from Point of Sales systems and allows for a straightforward human interpretation. Therefore, we propose two generalized additive models for predicting the future sales. In an extensive evaluation, we consider two data sets collected at a casual restaurant and a large staff canteen consisting of multiple time series, that cover a period of 20 months, respectively. We show that the proposed models fit the features of the considered restaurant data. Moreover, we compare the predictive performance of our method against the performance of other well-established forecasting approaches.

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are commonly the two main problems classical, i.e. non-Bayesian, architectures have to struggle with. The proposed approach applies variational inference in order to approximate the intractable posterior distribution. In particular, the variational distribution is defined as product of multiple multivariate normal distributions with tridiagonal covariance matrices. Each single normal distribution belongs either to the weights, or to the biases corresponding to one network layer. The layer-wise a posteriori variances are defined based on the corresponding expectation values and further the correlations are assumed to be identical. Therefore, only a few additional parameters need to be optimized compared to non-Bayesian settings. The novel approach is successfully evaluated on basis of the popular benchmark datasets MNIST and CIFAR-10.

We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of nonzero regression coefficients as well as a specification of beliefs that given coefficients are nonzero. To guarantee numerical stability, we adopt a $g$-prior with an additional ridge parameter for the unknown regression coefficients. In order to simulate from the joint posterior distribution an intelligent random walk Metropolis-Hastings algorithm which is able to switch between different models is proposed. Testing our algorithm on real and simulated data illustrates that it performs at least on par and often even better than other well-established methods. Finally, we prove that under some nominal assumptions, the presented approach is consistent in terms of model selection.

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic. First, model uncertainty cannot be measured thus limiting the use of deep learning in many fields of application and second, training of deep neural networks is often hampered by overfitting. The proposed approach uses variational inference to approximate the intractable a posteriori distribution on basis of a normal prior. The variational density is designed in such a way that the a posteriori uncertainty of the network parameters is represented per network layer and depending on the estimated parameter expectation values. This way, only a few additional parameters need to be optimized compared to a non-Bayesian network. We apply this Bayesian approach to train and test the LeNet architecture on the MNIST dataset. Compared to classical deep learning, the test error is reduced by 15%. In addition, the trained model contains information about the parameter uncertainty in each layer. We show that this information can be used to calculate credible intervals for the prediction and to optimize the network architecture for a given training data set.

The interest in "Physically Unclonable Function"-devices has increased rapidly over the last few years, as they have several interesting properties for system security related applications like, for example, the management of cryptographic keys. Unfortunately, the output provided by these devices is noisy and needs to be corrected for these applications. Related error correcting mechanisms are typically constructed on the basis of an equal error probability for each output bit. This assumption does not hold for Physically Unclonable Functions, where varying error probabilities can be observed. This results in a generalized binomial distribution for the number of errors in the output. The intention of this paper is to discuss a novel Bayesian statistical model for the noise of an especially wide-spread class of Physically Unclonable Functions, which properly handles the varying output stability and also reflects the different noise behaviors observed in a collection of such devices. Furthermore, we compare several different methods for estimating the model parameters and apply the proposed model to concrete measurements obtained within the CODES research project in order to evaluate typical correction and stabilization approaches.