A U(1) Gauge Theory for Antisymmetric Tensor Fields

We show that a U(1) gauge theory defined in the configuration space for closed p-branes yields the gauge theory of a massless rank-(p+1) antisymmetric tensor field and the Stueckelberg formalism for a massive vector field.Comment: 8 pages, Te

Estimating Local Function Complexity via Mixture of Gaussian Processes

Real world data often exhibit inhomogeneity, e.g., the noise level, the sampling distribution or the complexity of the target function may change over the input space. In this paper, we try to isolate local function complexity in a practical, robust way. This is achieved by first estimating the locally optimal kernel bandwidth as a functional relationship. Specifically, we propose Spatially Adaptive Bandwidth Estimation in Regression (SABER), which employs the mixture of experts consisting of multinomial kernel logistic regression as a gate and Gaussian process regression models as experts. Using the locally optimal kernel bandwidths, we deduce an estimate to the local function complexity by drawing parallels to the theory of locally linear smoothing. We demonstrate the usefulness of local function complexity for model interpretation and active learning in quantum chemistry experiments and fluid dynamics simulations.Comment: 19 pages, 16 figure

Sparse Probit Linear Mixed Model

Linear Mixed Models (LMMs) are important tools in statistical genetics. When used for feature selection, they allow to find a sparse set of genetic traits that best predict a continuous phenotype of interest, while simultaneously correcting for various confounding factors such as age, ethnicity and population structure. Formulated as models for linear regression, LMMs have been restricted to continuous phenotypes. We introduce the Sparse Probit Linear Mixed Model (Probit-LMM), where we generalize the LMM modeling paradigm to binary phenotypes. As a technical challenge, the model no longer possesses a closed-form likelihood function. In this paper, we present a scalable approximate inference algorithm that lets us fit the model to high-dimensional data sets. We show on three real-world examples from different domains that in the setup of binary labels, our algorithm leads to better prediction accuracies and also selects features which show less correlation with the confounding factors.Comment: Published version, 21 pages, 6 figure

Self-Supervised Training with Autoencoders for Visual Anomaly Detection

Deep autoencoders provide an effective tool for learning non-linear dimensionality reduction in an unsupervised way. Recently, they have been used for the task of anomaly detection in the visual domain. By optimizing for the reconstruction error using anomaly-free examples, the common belief is that a corresponding network should fail to accurately reconstruct anomalous regions in the application phase. This goal is typically addressed by controlling the capacity of the network, either by reducing the size of the bottleneck layer or by enforcing sparsity constraints on the activations. However, neither of these techniques does explicitly penalize reconstruction of anomalous signals often resulting in poor detection. We tackle this problem by adapting a self-supervised learning regime that allows the use of discriminative information during training but focuses on the data manifold of normal examples. We emphasize that inference with our approach is very efficient during training and prediction requiring a single forward pass for each input image. Our experiments on the MVTec AD dataset demonstrate high detection and localization performance. On the texture-subset, in particular, our approach consistently outperforms recent anomaly detection methods by a significant margin