A probability density function generator based on neural networks

© 2019 Elsevier B.V. In order to generate a probability density function (PDF) for fitting the probability distributions of practical data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be utilised as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of the trained deep learning model can be used to estimate the PDF. Numerical experiments with single and mixed distributions are conducted to evaluate the performance of the proposed method. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method

Unsupervised learning architecture for classifying the transient noise of interferometric gravitational-wave detectors

Abstract: In the data obtained by laser interferometric gravitational wave detectors, transient noise with non-stationary and non-Gaussian features occurs at a high rate. This often results in problems such as detector instability and the hiding and/or imitation of gravitational-wave signals. This transient noise has various characteristics in the time–frequency representation, which is considered to be associated with environmental and instrumental origins. Classification of transient noise can offer clues for exploring its origin and improving the performance of the detector. One approach for accomplishing this is supervised learning. However, in general, supervised learning requires annotation of the training data, and there are issues with ensuring objectivity in the classification and its corresponding new classes. By contrast, unsupervised learning can reduce the annotation work for the training data and ensure objectivity in the classification and its corresponding new classes. In this study, we propose an unsupervised learning architecture for the classification of transient noise that combines a variational autoencoder and invariant information clustering. To evaluate the effectiveness of the proposed architecture, we used the dataset (time–frequency two-dimensional spectrogram images and labels) of the Laser Interferometer Gravitational-wave Observatory (LIGO) first observation run prepared by the Gravity Spy project. The classes provided by our proposed unsupervised learning architecture were consistent with the labels annotated by the Gravity Spy project, which manifests the potential for the existence of unrevealed classes