Training deep learning neural networks often requires massive amounts of computational ressources. We propose to sequentially monitor network predictions to trigger retraining only if the predictions are no longer valid. This can reduce drastically computational costs and opens a door to green deep learning. Our approach is based on the relationship to projected second moments monitoring, a problem also arising in other areas such as computational finance. Various open-end as well as closed-end monitoring rules are studied under mild assumptions on the training sample and the observations of the monitoring period. The results allow for high-dimensional non-stationary time series data and thus, especially, non-i.i.d. training data. Asymptotics is based on Gaussian approximations of projected partial sums allowing for an estimated projection vector. Estimation of projection vectors is studied both for classical non-$\ell_0$-sparsity as well as under sparsity. For the case that the optimal projection depends on the unknown covariance matrix, hard- and soft-thresholded estimators are studied. The method is analyzed by simulations and supported by synthetic data experiments.

Active learning of physical systems must commonly respect practical safety constraints, which restricts the exploration of the design space. Gaussian Processes (GPs) and their calibrated uncertainty estimations are widely used for this purpose. In many technical applications the design space is explored via continuous trajectories, along which the safety needs to be assessed. This is particularly challenging for strict safety requirements in GP methods, as it employs computationally expensive Monte Carlo sampling of high quantiles. We address these challenges by providing provable safety bounds based on the adaptively sampled median of the supremum of the posterior GP. Our method significantly reduces the number of samples required for estimating high safety probabilities, resulting in faster evaluation without sacrificing accuracy and exploration speed. The effectiveness of our safe active learning approach is demonstrated through extensive simulations and validated using a real-world engine example.

Abstract High resolution electroluminescence (EL) images captured in the infrared spectrum allow to visually and non-destructively inspect the quality of photovoltaic (PV) modules. Currently, however, such a visual inspection requires trained experts to discern different kinds of defects, which is time-consuming and expensive. Automated segmentation of cells is therefore a key step in automating the visual inspection workflow. In this work, we propose a robust automated segmentation method for extraction of individual solar cells from EL images of PV modules. This enables controlled studies on large amounts of data to understanding the effects of module degradation over time—a process not yet fully understood. The proposed method infers in several steps a high-level solar module representation from low-level ridge edge features. An important step in the algorithm is to formulate the segmentation problem in terms of lens calibration by exploiting the plumbline constraint. We evaluate our method on a dataset of various solar modules types containing a total of 408 solar cells with various defects. Our method robustly solves this task with a median weighted Jaccard index of $$94.47\%$$ 94.47% and an $$F_1$$ F1 score of $$97.62\%$$ 97.62% , both indicating a high sensitivity and a high similarity between automatically segmented and ground truth solar cell masks.

A nonparametric version of the sequential signal detection problem is studied. Our signal model includes a class of time-limited signals for which we collect data in the sequential fashion at discrete points in the presence of correlated noise. For such a setup we introduce a novel signal detection algorithm relying on the postfiltering smooth correction of the classical Whittaker–Shannon interpolation series. Given a finite frame of noisy samples of the signal, we design a detection algorithm being able to detect a departure from a reference signal as quickly as possible. Our detector is represented as a normalized partial-sum continuous time stochastic process, for which we obtain a functional central limit theorem under weak assumptions on the correlation structure of the noise. Particularly, our results allow for noise processes such as ARMA and general linear processes as well as$ \alpha $-mixing processes. The established limit theorems allow us to design monitoring algorithms with the desirable level of the probability of false alarm and able to detect a change with probability approaching one.

This paper examines a new method for sequential detection of a sudden and unobservable change in a sequence of independent observations with completely unspecified distribution functions. A nonparametric detection rule is proposed which relies on the concept of a moving vertically trimmed box. As such, it will be coined as the Vertical Box Control Chart (V-Box Chart). Its implementation requires merely to count the number of data points which fall into the box attached to the last available observation. Noa prioriknowledge of data distributions is required and proper tuning of the box size provides a quick detection technique. This is supported by establishing statistical properties of the method which explain the role of the tuning parameters used in the V-Box Chart. These theoretical results are verified by simulation studies which indicate that the V-Box Chart may provide quick detection with zero delay for jumps of moderate sizes. Its averaged run length to detection is more favorable than the one for the classical EWMA method. By comparison with the classical Shewhart chart, which was optimized for normal errors, our method provides comparable or better performance.