Lufthansa Technik Logistik Services (LTLS) began their digital transformation three years ago. LTLS, with revenues of almost 270 million Euros in 2017, provides logistics services, transport and warehousing for customers in the aviation industry. LTLS is a subsidiary of Lufthansa Technik. Lufhansa Technik in turn provides maintenance, completions, repair, and overhaul (MRO) services for aircraft, and MRO services for engines and components. LTLS has several material flows related to warehousing: they receive brand new spare parts from the manufacturers, they receive repaired parts from partners, and they receive unserviceable parts from airlines they will repair at Lufthansa Technik's own facilities.

In this paper, we introduce the first principled adaptive-sampling procedure for learning a convex function in the $L_\infty$ norm, a problem that arises often in economics, psychology, and the social sciences. We present a function-specific measure of complexity and use it to prove that our algorithm is information-theoretically near-optimal in a strong, function-specific sense. We also corroborate our theoretical contributions with extensive numerical experiments, finding that our method substantially outperforms passive, uniform sampling for favorable synthetic and data-derived functions in low-noise settings with large sampling budgets. Our results also suggest an idealized `oracle strategy', which we use to gauge the potential for deploying the adaptive-sampling strategy on any function in any particular setting.

The graph Laplacian is a standard tool in data science, machine learning, and image processing. The corresponding matrix inherits the complex structure of the underlying network and is in certain applications densely populated. This makes computations, in particular matrix-vector products, with the graph Laplacian a hard task. A typical application is the computation of a number of its eigenvalues and eigenvectors. Standard methods become infeasible as the number of nodes in the graph is too large. We propose the use of the fast summation based on the nonequispaced fast Fourier transform (NFFT) to perform the dense matrix-vector product with the graph Laplacian fast without ever forming the whole matrix. The enormous flexibility of the NFFT algorithm allows us to embed the accelerated multiplication into Lanczos-based eigenvalues routines or iterative linear system solvers. We illustrate the feasibility of our approach on a number of test problems from image segmentation to semi-supervised learning based on graph-based PDEs. In particular, we compare our approach with the Nystr\"om method. Moreover, we present and test an enhanced, hybrid version of the Nystr\"om method, which internally uses the NFFT.

Collaborative filtering is an important technique for recommendation. Whereas it has been repeatedly shown to be effective in previous work, its performance remains unsatisfactory in many real-world applications, especially those where the items or users are highly diverse. In this paper, we explore an ensemble-based framework to enhance the capability of a recommender in handling diverse data. Specifically, we formulate a probabilistic model which integrates the items, the users, as well as the associations between them into a generative process. On top of this formulation, we further derive a progressive algorithm to construct an ensemble of collaborative filters. In each iteration, a new filter is derived from re-weighted entries and incorporated into the ensemble. It is noteworthy that while the algorithmic procedure of our algorithm is apparently similar to boosting, it is derived from an essentially different formulation and thus differs in several key technical aspects. We tested the proposed method on three large datasets, and observed substantial improvement over the state of the art, including L2Boost, an effective method based on boosting.

Active learning stands for methods which increase classification quality by means of user feedback. An important subcategory is active learning for one-class classifiers, i.e., for imbalanced class distributions. While various methods in this category exist, selecting one for a given application scenario is difficult. This is because existing methods rely on different assumptions, have different objectives, and often are tailored to a specific use case. All this calls for a comprehensive comparison, the topic of this article. This article starts with a categorization of the various methods. We then propose ways to evaluate active learning results. Next, we run extensive experiments to compare existing methods, for a broad variety of scenarios. One result is that the practicality and the performance of an active learning method strongly depend on its category and on the assumptions behind it. Another observation is that there only is a small subset of our experiments where existing approaches outperform random baselines. Finally, we show that a well-laid-out categorization and a rigorous specification of assumptions can facilitate the selection of a good method for one-class classification.

Neural networks with ReLU activations have achieved great empirical success in various domains. However, existing results for learning ReLU networks either pose assumptions on the underlying data distribution being e.g. Gaussian, or require the network size and/or training size to be sufficiently large. In this context, the problem of learning a two-layer ReLU network is approached in a binary classification setting, where the data are linearly separable and a hinge loss criterion is adopted. Leveraging the power of random noise, this contribution presents a novel stochastic gradient descent (SGD) algorithm, which can provably train any single-hidden-layer ReLU network to attain global optimality, despite the presence of infinitely many bad local minima and saddle points in general. This result is the first of its kind, requiring no assumptions on the data distribution, training/network size, or initialization. Convergence of the resultant iterative algorithm to a global minimum is analyzed by establishing both an upper bound and a lower bound on the number of effective (non-zero) updates to be performed. Furthermore, generalization guarantees are developed for ReLU networks trained with the novel SGD. These guarantees highlight a fundamental difference (at least in the worst case) between learning a ReLU network as well as a leaky ReLU network in terms of sample complexity. Numerical tests using synthetic data and real images validate the effectiveness of the algorithm and the practical merits of the theory.

Long-term human motion can be represented as a series of motion modes---motion sequences that capture short-term temporal dynamics---with transitions between them. We leverage this structure and present a novel Motion Transformation Variational Auto-Encoders (MT-VAE) for learning motion sequence generation. Our model jointly learns a feature embedding for motion modes (that the motion sequence can be reconstructed from) and a feature transformation that represents the transition of one motion mode to the next motion mode. Our model is able to generate multiple diverse and plausible motion sequences in the future from the same input. We apply our approach to both facial and full body motion, and demonstrate applications like analogy-based motion transfer and video synthesis.

In recent years, probabilistic forecasts techniques were proposed in research as well as in applications to integrate volatile renewable energy resources into the electrical grid. These techniques allow decision makers to take the uncertainty of the prediction into account and, therefore, to devise optimal decisions, e.g., related to costs and risks in the electrical grid. However, it was yet not studied how the input, such as numerical weather predictions, affects the model output of forecasting models in detail. Therefore, we examine the potential influences with techniques from the field of sensitivity analysis on three different black-box models to obtain insights into differences and similarities of these probabilistic models. The analysis shows a considerable number of potential influences in those models depending on, e.g., the predicted probability and the type of model. These effects motivate the need to take various influences into account when models are tested, analyzed, or compared. Nevertheless, results of the sensitivity analysis will allow us to select a model with advantages in the practical application.

Several statistical and machine learning methods are proposed to estimate the type and intensity of physical load and accumulated fatigue . They are based on the statistical analysis of accumulated and moving window data subsets with construction of a kurtosis-skewness diagram. This approach was applied to the data gathered by the wearable heart monitor for various types and levels of physical activities, and for people with various physical conditions. The different levels of physical activities, loads, and fitness can be distinguished from the kurtosis-skewness diagram, and their evolution can be monitored. Several metrics for estimation of the instant effect and accumulated effect (physical fatigue) of physical loads were proposed. The data and results presented allow to extend application of these methods for modeling and characterization of complex human activity patterns, for example, to estimate the actual and accumulated physical load and fatigue, model the potential dangerous development, and give cautions and advice in real time.

As a promising area in artificial intelligence, a new learning paradigm, called Small Sample Learning (SSL), has been attracting prominent research attention in the recent years. In this paper, we aim to present a survey to comprehensively introduce the current techniques proposed on this topic. Specifically, current SSL techniques can be mainly divided into two categories. The first category of SSL approaches can be called "concept learning", which emphasizes learning new concepts from only few related observations. The purpose is mainly to simulate human learning behaviors like recognition, generation, imagination, synthesis and analysis. The second category is called "experience learning", which usually co-exists with the large sample learning manner of conventional machine learning. This category mainly focuses on learning with insufficient samples, and can also be called small data learning in some literatures. More extensive surveys on both categories of SSL techniques are introduced and some neuroscience evidences are provided to clarify the rationality of the entire SSL regime, and the relationship with human learning process. Some discussions on the main challenges and possible future research directions along this line are also presented.