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Black-box variational inference (BBVI) is a technique to approximate the posterior of Bayesian models by optimization. Similar to MCMC, the user only needs to specify the model; then, the inference procedure is done automatically. In contrast to MCMC, BBVI scales to many observations, is faster for some applications, and can take advantage of highly optimized deep learning frameworks since it can be formulated as a minimization task. In the case of complex posteriors, however, other state-of-the-art BBVI approaches often yield unsatisfactory posterior approximations. This paper presents Bernstein flow variational inference (BF-VI), a robust and easy-to-use method flexible enough to approximate complex multivariate posteriors. BF-VI combines ideas from normalizing flows and Bernstein polynomial-based transformation models. In benchmark experiments, we compare BF-VI solutions with exact posteriors, MCMC solutions, and state-of-the-art BBVI methods, including normalizing flow-based BBVI. We show for low-dimensional models that BF-VI accurately approximates the true posterior; in higher-dimensional models, BF-VI compares favorably against other BBVI methods. Further, using BF-VI, we develop a Bayesian model for the semi-structured melanoma challenge data, combining a CNN model part for image data with an interpretable model part for tabular data, and demonstrate, for the first time, the use of BBVI in semi-structured models.
Das Projekt eFlow, an dem unter anderem die HTWG Konstanz seit 2012 forscht, simuliert mit Hilfe einer mathematischen Simulation wie sich Menschenmassen verhalten, wenn sie ein vorgegebenes Gelände verlassen sollen. Die Simulation baut auf einen Ansatz der Finite Elemente Methode auf, in der mehrere gekoppelte Differenzialgleichungen berechnet werden müssen. Diese Berechnungen erweisen sich gerade bei komplexen Szenarien mit großem Gelände und vielen Personen als sehr rechenintensiv. Ziel dieser Bachelorarbeit ist es ein Surrogate Modell zu erstellen, welches basierend auf machine-learning Ansätzen im spezifischen auf Regressionsmethoden Ergebnisse der Simulation vorhersagen soll. Somit müssen Datensätze generiert werden. Diese entstehen durch wiederholte Durchläufe der Simulation, in der jeweils die Eingabeparameter, die in das Regressionsmodell einfließen sollen variiert werden und mit dem entsprechenden Ergebnis der Simulation verknüpft werden. Die Regressionsansätze werden dabei pro Durchlauf komplexer, in dem jeweils zusätzliche Eingabeparameter mit in die Datengenerierung aufgenommen werden. Es soll überprüft werden, ob diese Simulation mittels machine-learning Ansätzen reproduzierbar ist. Basierend auf diesen Surrogate Modellen soll es möglich gemacht werden, Situationen in Echtzeit zu überprüfen, ohne dabei den Weg der rechenaufwendigen Simulation zu gehen. Die Ergebnisse bestätigen, dass die mathematische Simulation mittels Regression reproduzierbar ist. Es erweist sich jedoch als sehr rechenaufwendig, Daten zu sammeln, um genügend Eingabeparameter mit in die Regressionsmethode einfließen zu lassen. Diese Arbeit gestaltet somit eine Vorstudie zur Umsetzung eines ausgereiften Surrogate Modells, welches jegliche Eingabeparameter der Simulation berücksichtigen kann.
Lidar sensors are widely used for environmental perception on autonomous robot vehicles (ARV). The field of view (FOV) of Lidar sensors can be reshaped by positioning plane mirrors in their vicinity. Mirror setups can especially improve the FOV for ground detection of ARVs with 2D-Lidar sensors. This paper presents an overview of several geometric designs and their strengths for certain vehicle types. Additionally, a new and easy-to-implement calibration procedure for setups of 2D-Lidar sensors with mirrors is presented to determine precise mirror orientations and positions, using a single flat calibration object with a pre-aligned simple fiducial marker. Measurement data from a prototype vehicle with a 2D-Lidar with a 2 m range using this new calibration procedure are presented. We show that the calibrated mirror orientations are accurate to less than 0.6° in this short range, which is a significant improvement over the orientation angles taken directly from the CAD. The accuracy of the point cloud data improved, and no significant decrease in distance noise was introduced. We deduced general guidelines for successful calibration setups using our method. In conclusion, a 2D-Lidar sensor and two plane mirrors calibrated with this method are a cost-effective and accurate way for robot engineers to improve the environmental perception of ARVs.
Image novelty detection is a repeating task in computer vision and describes the detection of anomalous images based on a training dataset consisting solely of normal reference data. It has been found that, in particular, neural networks are well-suited for the task. Our approach first transforms the training and test images into ensembles of patches, which enables the assessment of mean-shifts between normal data and outliers. As mean-shifts are only detectable when the outlier ensemble and inlier distribution are spatially separate from each other, a rich feature space, such as a pre-trained neural network, needs to be chosen to represent the extracted patches. For mean-shift estimation, the Hotelling T2 test is used. The size of the patches turned out to be a crucial hyperparameter that needs additional domain knowledge about the spatial size of the expected anomalies (local vs. global). This also affects model selection and the chosen feature space, as commonly used Convolutional Neural Networks or Vision Image Transformers have very different receptive field sizes. To showcase the state-of-the-art capabilities of our approach, we compare results with classical and deep learning methods on the popular dataset CIFAR-10, and demonstrate its real-world applicability in a large-scale industrial inspection scenario using the MVTec dataset. Because of the inexpensive design, our method can be implemented by a single additional 2D-convolution and pooling layer and allows particularly fast prediction times while being very data-efficient.
Die Frage „Wozu braucht man das?“ vonseiten der Studierenden oder Aussagen wie „Das habe ich im Beruf später nie mehr benötigt.“ von ehemaligen Studierenden ist den meisten Mathematikdozierenden sehr vertraut. Im Projekt BiLeSA wird dem Wunsch nach Integration von Praxisnähe im Mathematikunterricht mithilfe einer Smartphone-App, welche ausgewählte Themen in der Mathematik anhand von digitalen Bildern sichtbar macht, umgesetzt. Bei den ausgewählten Themen handelt es sich um (affin) lineare Abbildungen, Ableitungen in höheren Raumdimensionen und Potenzen von Komplexen Zahlen. Die Konzeptionierung des Lernobjekts erfolgte mit dem Design Based Research (DBR) Ansatz, welches im Basisprojekt des IBH-Labs „Seamless Learning“ konzipiert und entwickelt wurde.
Wer schon einmal dicht gedrängt vor der Konzertbühne stand kann sich die aussichtslose Lage, wenn die Stimmung kippt und Panik aufkommt, gut vorstellen. Es ist sehr wichtig, Räume und Events, die zeitweise von sehr vielen Menschen aufgesucht werden, so zu gestalten und zu planen, dass maximale Sicherheit gewährleistet ist. Damit eine öffentliche Veranstaltung reibungslos verläuft ist eine gründliche Planung, also ein qualitativ hochwertiges Crowd Management unabdingbar.
Interpretability and uncertainty modeling are important key factors for medical applications. Moreover, data in medicine are often available as a combination of unstructured data like images and structured predictors like patient’s metadata. While deep learning models are state-of-the-art for image classification, the models are often referred to as ’black-box’, caused by the lack of interpretability. Moreover, DL models are often yielding point predictions and are too confident about the parameter estimation and outcome predictions.
On the other side with statistical regression models, it is possible to obtain interpretable predictor effects and capture parameter and model uncertainty based on the Bayesian approach. In this thesis, a publicly available melanoma dataset, consisting of skin lesions and patient’s age, is used to predict the melanoma types by using a semi-structured model, while interpretable components and model uncertainty is quantified. For Bayesian models, transformation model-based variational inference (TM-VI) method is used to determine the posterior distribution of the parameter. Several model constellations consisting of patient’s age and/or skin lesion were implemented and evaluated. Predictive performance was shown to be best by using a combined model of image and patient’s age, while providing the interpretable posterior distribution of the regression coefficient is possible. In addition, integrating uncertainty in image and tabular parts results in larger variability of the outputs corresponding to high uncertainty of the single model components.
Forecasting is crucial for both system planning and operations in the energy sector. With increasing penetration of renewable energy sources, increasing fluctuations in the power generation need to be taken into account. Probabilistic load forecasting is a young, but emerging research topic focusing on the prediction of future uncertainties. However, the majority of publications so far focus on techniques like quantile regression, ensemble, or scenario-based methods, which generate discrete quantiles or sets of possible load curves. The conditioned probability distribution remains unknown and can only be estimated when the output is post-processed using a statistical method like kernel density estimation.
Instead, the proposed probabilistic deep learning model uses a cascade of transformation functions, known as normalizing flow, to model the conditioned density function from a smart meter dataset containing electricity demand information for over 4,000 buildings in Ireland. Since the whole probability density function is tractable, the parameters of the model can be obtained by minimizing the negative loglikelihood through the state of the art gradient descent. This leads to the model with the best representation of the data distribution.
Two different deep learning models have been compared, a simple three-layer fully connected neural network and a more advanced convolutional neural network for sequential data processing inspired by the WaveNet architecture. These models have been used to parametrize three different probabilistic models, a simple normal distribution, a Gaussian mixture model, and the normalizing flow model. The prediction horizon is set to one day with a resolution of 30 minutes, hence the models predict 48 conditioned probability distributions.
The normalizing flow model outperforms the two other variants for both architectures and proves its ability to capture the complex structures and dependencies causing the variations in the data. Understanding the stochastic nature of the task in such detail makes the methodology applicable for other use cases apart from forecasting. It is shown how it can be used to detect anomalies in the power grid or generate synthetic scenarios for grid planning.
We propose a novel end-to-end neural network architecture that, once trained, directly outputs a probabilistic clustering of a batch of input examples in one pass. It estimates a distribution over the number of clusters k, and for each 1≤k≤kmax, a distribution over the individual cluster assignment for each data point. The network is trained in advance in a supervised fashion on separate data to learn grouping by any perceptual similarity criterion based on pairwise labels (same/different group). It can then be applied to different data containing different groups. We demonstrate promising performance on high-dimensional data like images (COIL-100) and speech (TIMIT). We call this “learning to cluster” and show its conceptual difference to deep metric learning, semi-supervise clustering and other related approaches while having the advantage of performing learnable clustering fully end-to-end.