390 research outputs found
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
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