A recurrent neural network for classification of unevenly sampled variable stars

Astronomical surveys of celestial sources produce streams of noisy time series measuring flux versus time ("light curves"). Unlike in many other physical domains, however, large (and source-specific) temporal gaps in data arise naturally due to intranight cadence choices as well as diurnal and seasonal constraints. With nightly observations of millions of variable stars and transients from upcoming surveys, efficient and accurate discovery and classification techniques on noisy, irregularly sampled data must be employed with minimal human-in-the-loop involvement. Machine learning for inference tasks on such data traditionally requires the laborious hand-coding of domain-specific numerical summaries of raw data ("features"). Here we present a novel unsupervised autoencoding recurrent neural network (RNN) that makes explicit use of sampling times and known heteroskedastic noise properties. When trained on optical variable star catalogs, this network produces supervised classification models that rival other best-in-class approaches. We find that autoencoded features learned on one time-domain survey perform nearly as well when applied to another survey. These networks can continue to learn from new unlabeled observations and may be used in other unsupervised tasks such as forecasting and anomaly detection.Comment: 23 pages, 14 figures. The published version is at Nature Astronomy (https://www.nature.com/articles/s41550-017-0321-z). Source code for models, experiments, and figures at https://github.com/bnaul/IrregularTimeSeriesAutoencoderPaper (Zenodo Code DOI: 10.5281/zenodo.1045560

Group Iterative Spectrum Thresholding for Super-Resolution Sparse Spectral Selection

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods break down in presence of high coherence and large noise. We propose a new regularization approach to handle model collinearity and obtain parsimonious frequency selection simultaneously. It takes advantage of the pairing structure of sine and cosine atoms in the frequency dictionary. A probabilistic spectrum screening is also developed for fast computation in high dimensions. A data-resampling version of high-dimensional Bayesian Information Criterion is used to determine the regularization parameters. Experiments show the efficacy and efficiency of the proposed algorithms in challenging situations with small sample size, high frequency resolution, and low signal-to-noise ratio

Gap filling and noise reduction of unevenly sampled data by means of the Lomb-Scargle periodogram

International audienceThe Lomb-Scargle periodogram is widely used for the estimation of the power spectral density of unevenly sampled data. A small extension of the algorithm of the Lomb-Scargle periodogram permits the estimation of the phases of the spectral components. The amplitude and phase information is sufficient for the construction of a complex Fourier spectrum. The inverse Fourier transform can be applied to this Fourier spectrum and provides an evenly sampled series (Scargle, 1989). We are testing the proposed reconstruction method by means of artificial time series and real observations of mesospheric ozone, having data gaps and noise. For data gap filling and noise reduction, it is necessary to modify the Fourier spectrum before the inverse Fourier transform is done. The modification can be easily performed by selection of the relevant spectral components which are above a given confidence limit or within a certain frequency range. Examples with time series of lower mesospheric ozone show that the reconstruction method can reproduce steep ozone gradients around sunrise and sunset and superposed planetary wave-like oscillations observed by a ground-based microwave radiometer at Payerne

Analysis of surface atrial signals using spectral methods for time series with missing data

In this work, the analysis of atrial signals recorded during atrial fibrillation was pursued using two spectral estimators designed for series with missing data: the Lomb periodogram (LP) and the Iterative Singular Spectrum Analysis (ISSA). The main aim is to verify if subtraction ofthe ventricular activity might be avoided by performing spectral analysis on those ECG intervals where such activity is absent, (i.e. the T-Q intervals), at least to estimate the dominant atrial Fibrillatory Frequency (FF). Recordings coming from the 2004 Computers in Cardiology Termination Challenge Database were analyzed. Fibrillatory frequencies were then compared with those obtained from the analysis ofthe correspondent atrial signals extracted using a modified Average Beat Substraction (ABS) technique. We observed that the mean absolute difference was 0.42 \ub1 0.66 Hz for LP, (mean\ub1SD), and 0.39 \ub1 0.64 Hz for ISSA. We concluded that estimation of FF is feasible without applying QRS-T subtraction

Hierarchical Bayesian sparse image reconstruction with application to MRFM

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g. by maximizing the estimated posterior distribution. In our fully Bayesian approach the posteriors of all the parameters are available. Thus our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of our hierarchical Bayesian sparse reconstruction method is illustrated on synthetic and real data collected from a tobacco virus sample using a prototype MRFM instrument.Comment: v2: final version; IEEE Trans. Image Processing, 200

Surrogate time series

Before we apply nonlinear techniques, for example those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified "by the data". While many processes in nature seem very unlikely a priori to be linear, the possible nonlinear nature might not be evident in specific aspects of their dynamics. The method of surrogate data has become a very popular tool to address such a question. However, while it was meant to provide a statistically rigorous, foolproof framework, some limitations and caveats have shown up in its practical use. In this paper, recent efforts to understand the caveats, avoid the pitfalls, and to overcome some of the limitations, are reviewed and augmented by new material. In particular, we will discuss specific as well as more general approaches to constrained randomisation, providing a full range of examples. New algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains. The main limitation, which lies in the interpretability of the test results, will be illustrated through instructive case studies. We will also discuss some implementational aspects of the realisation of these methods in the TISEAN (http://www.mpipks-dresden.mpg.de/~tisean) software package.Comment: 28 pages, 23 figures, software at http://www.mpipks-dresden.mpg.de/~tisea

Laser diffraction particle sizing : sampling and inversion

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 13, 1987The inverse problem of obtaining particle size distributions from observations of the angular distribution of near forward scattered light is reexamined. Asymptotic analysis of the forward problem reveals the information content of the observations, and the sources of non-uniqueness and instability in inverting them. A sampling criterion, such that the observations uniquely specify the size distribution is derived, in terms of the largest particle size, and an angle above which the intensity is indistinguishable from an asymptote. The instability of inverting unevenly spaced data is compared to that of super-resolving Fourier spectra. Resolution is shown to be inversely proportional to the angular range of observations. The problem is rephrased so that the size weighted number density is sought from the intensity weighted by the scattering angle cubed. Algorithms which impose positivity and bounds on particle size improve the stability of inversions. The forward problem can be represented by an over-determined matrix equation by choosing a large integration increment in size dependent on the frequency content of the angular intensity, further improving stability. Experimental data obtained using a linear CCD array illustrates the theory, with standard polystyrene spheres as scatterers. The scattering from single and tri-modal distributions is successfully inverted.I was supported by a NASA Technology Transfer Traineeship grant (NGT-014-800, Supplement 5), and by the Joint Program in Oceanographic Engineering between the Woods Hole Oceanographic Institution and the Massachusetts Institute of Technology. The experimental work was funded by the Coastal Research Laboratory of the Woods Hole Oceanographic Institution, through the generosity of the Mellon Foundation