TRUFAS, a wavelet based algorithm for the rapid detection of planetary transits

Aims: We describe a fast, robust and automatic detection algorithm, TRUFAS, and apply it to data that are being expected from the CoRoT mission. Methods: The procedure proposed for the detection of planetary transits in light curves works in two steps: 1) a continuous wavelet transformation of the detrended light curve with posterior selection of the optimum scale for transit detection, and 2) a period search in that selected wavelet transformation. The detrending of the light curves are based on Fourier filtering or a discrete wavelet transformation. TRUFAS requires the presence of at least 3 transit events in the data. Results: The proposed algorithm is shown to identify reliably and quickly the transits that had been included in a standard set of 999 light curves that simulate CoRoT data. Variations in the pre-processing of the light curves and in the selection of the scale of the wavelet transform have only little effect on TRUFAS results. Conclusions: TRUFAS is a robust and quick transit detection algorithm, especially well suited for the analysis of very large volumes of data from space or ground-based experiments, with long enough durations for the target-planets to produce multiple transit events.

Comparing the performance of stellar variability filters for the detection of planetary transits

We have developed a new method to improve the transit detection of Earth-sized planets in front of solar-like stars by fitting stellar microvariability by means of a spot model. A large Monte Carlo numerical experiment has been designed to test the performance of our approach in comparison with other variability filters and fitting techniques for stars of different magnitudes and planets of different radius and orbital period, as observed by the space missions CoRoT and Kepler. Here we report on the results of this experiment.

A Survey for Planetary Transits in the Field of NGC 7789

We present results from 30 nights of observations of the open cluster NGC 7789 with the WFC camera on the INT telescope in La Palma. From ~900 epochs, we obtained lightcurves and Sloan r-i colours for ~33000 stars, with ~2400 stars with better than 1% precision. We expected to detect ~2 transiting hot Jupiter planets if 1% of stars host such a companion and that a typical hot Jupiter radius is ~1.2RJ. We find 24 transit candidates, 14 of which we can assign a period. We rule out the transiting planet model for 21 of these candidates using various robust arguments. For 2 candidates we are unable to decide on their nature, although it seems most likely that they are eclipsing binaries as well. We have one candidate exhibiting a single eclipse for which we derive a radius of 1.81+0.09-0.00RJ. Three candidates remain that require follow-up observations in order to determine their nature.

Efficient Optimization of Echo State Networks for Time Series Datasets

Echo State Networks (ESNs) are recurrent neural networks that only train their output layer, thereby precluding the need to backpropagate gradients through time, which leads to significant computational gains. Nevertheless, a common issue in ESNs is determining its hyperparameters, which are crucial in instantiating a well performing reservoir, but are often set manually or using heuristics. In this work we optimize the ESN hyperparameters using Bayesian optimization which, given a limited budget of function evaluations, outperforms a grid search strategy. In the context of large volumes of time series data, such as light curves in the field of astronomy, we can further reduce the optimization cost of ESNs. In particular, we wish to avoid tuning hyperparameters per individual time series as this is costly; instead, we want to find ESNs with hyperparameters that perform well not just on individual time series but rather on groups of similar time series without sacrificing predictive performance significantly. This naturally leads to a notion of clusters, where each cluster is represented by an ESN tuned to model a group of time series of similar temporal behavior. We demonstrate this approach both on synthetic datasets and real world light curves from the MACHO survey. We show that our approach results in a significant reduction in the number of ESN models required to model a whole dataset, while retaining predictive performance for the series in each cluster.

Random Warping Series: A Random Features Method for Time-Series Embedding

Time series data analytics has been a problem of substantial interests for decades, and Dynamic Time Warping (DTW) has been the most widely adopted technique to measure dissimilarity between time series. A number of global-alignment kernels have since been proposed in the spirit of DTW to extend its use to kernel-based estimation method such as support vector machine. However, those kernels suffer from diagonal dominance of the Gram matrix and a quadratic complexity w.r.t. the sample size. In this work, we study a family of alignment-aware positive definite (p.d.) kernels, with its feature embedding given by a distribution of emph{Random Warping Series (RWS)}. The proposed kernel does not suffer from the issue of diagonal dominance while naturally enjoys a emph{Random Features} (RF) approximation, which reduces the computational complexity of existing DTW-based techniques from quadratic to linear in terms of both the number and the length of time-series. We also study the convergence of the RF approximation for the domain of time series of unbounded length. Our extensive experiments on 16 benchmark datasets demonstrate that RWS outperforms or matches state-of-the-art classification and clustering methods in both accuracy and computational time. Our code and data is available at { url{https://github.com/IBM/RandomWarpingSeries}}.