T-CGAN: Conditional Generative Adversarial Network for Data Augmentation in Noisy Time Series with Irregular Sampling

In this paper we propose a data augmentation method for time series with irregular sampling, Time-Conditional Generative Adversarial Network (T-CGAN). Our approach is based on Conditional Generative Adversarial Networks (CGAN), where the generative step is implemented by a deconvolutional NN and the discriminative step by a convolutional NN. Both the generator and the discriminator are conditioned on the sampling timestamps, to learn the hidden relationship between data and timestamps, and consequently to generate new time series. We evaluate our model with synthetic and real-world datasets. For the synthetic data, we compare the performance of a classifier trained with T-CGAN-generated data, against the performance of the same classifier trained on the original data. Results show that classifiers trained on T-CGAN-generated data perform the same as classifiers trained on real data, even with very short time series and small training sets. For the real world datasets, we compare our method with other techniques of data augmentation for time series, such as time slicing and time warping, over a classification problem with unbalanced datasets. Results show that our method always outperforms the other approaches, both in case of regularly sampled and irregularly sampled time series. We achieve particularly good performance in case with a small training set and short, noisy, irregularly-sampled time series.

Clustering Based Feature Learning on Variable Stars

The success of automatic classification of variable stars strongly depends on the lightcurve representation. Usually, lightcurves are represented as a vector of many statistical descriptors designed by astronomers called features. These descriptors commonly demand significant computational power to calculate, require substantial research effort to develop and do not guarantee good performance on the final classification task. Today, lightcurve representation is not entirely automatic; algorithms that extract lightcurve features are designed by humans and must be manually tuned up for every survey. The vast amounts of data that will be generated in future surveys like LSST mean astronomers must develop analysis pipelines that are both scalable and automated. Recently, substantial efforts have been made in the machine learning community to develop methods that prescind from expert-designed and manually tuned features for features that are automatically learned from data. In this work we present what is, to our knowledge, the first unsupervised feature learning algorithm designed for variable stars. Our method first extracts a large number of lightcurve subsequences from a given set of photometric data, which are then clustered to find common local patterns in the time series. Representatives of these patterns, called exemplars, are then used to transform lightcurves of a labeled set into a new representation that can then be used to train an automatic classifier. The proposed algorithm learns the features from both labeled and unlabeled lightcurves, overcoming the bias generated when the learning process is done only with labeled data. We test our method on MACHO and OGLE datasets; the results show that the classification performance we achieve is as good and in some cases better than the performance achieved using traditional features, while the computational cost is significantly lower.

Computational Intelligence Challenges and Applications on Large-Scale Astronomical Time Series Databases

Time-domain astronomy (TDA) is facing a paradigm shift caused by the exponential growth of the sample size, data complexity and data generation rates of new astronomical sky surveys. For example, the Large Synoptic Survey Telescope (LSST), which will begin operations in northern Chile in 2022, will generate a nearly 150 Petabyte imaging dataset of the southern hemisphere sky. The LSST will stream data at rates of 2 Terabytes per hour, effectively capturing an unprecedented movie of the sky. The LSST is expected not only to improve our understanding of time-varying astrophysical objects, but also to reveal a plethora of yet unknown faint and fast-varying phenomena. To cope with a change of paradigm to data-driven astronomy, the fields of astroinformatics and astrostatistics have been created recently. The new data-oriented paradigms for astronomy combine statistics, data mining, knowledge discovery, machine learning and computational intelligence, in order to provide the automated and robust methods needed for the rapid detection and classification of known astrophysical objects as well as the unsupervised characterization of novel phenomena. In this article we present an overview of machine learning and computational intelligence applications to TDA. Future big data challenges and new lines of research in TDA, focusing on the LSST, are identified and discussed from the viewpoint of computational intelligence/machine learning. Interdisciplinary collaboration will be required to cope with the challenges posed by the deluge of astronomical data coming from the LSST.

Supervised detection of anomalous light-curves in massive astronomical catalogs

The development of synoptic sky surveys has led to a massive amount of data for which resources needed for analysis are beyond human capabilities. To process this information and to extract all possible knowledge, machine learning techniques become necessary. Here we present a new method to automatically discover unknown variable objects in large astronomical catalogs. With the aim of taking full advantage of all the information we have about known objects, our method is based on a supervised algorithm. In particular, we train a random forest classifier using known variability classes of objects and obtain votes for each of the objects in the training set. We then model this voting distribution with a Bayesian network and obtain the joint voting distribution among the training objects. Consequently, an unknown object is considered as an outlier insofar it has a low joint probability. Our method is suitable for exploring massive datasets given that the training process is performed offline. We tested our algorithm on 20 millions light-curves from the MACHO catalog and generated a list of anomalous candidates. We divided the candidates into two main classes of outliers: artifacts and intrinsic outliers. Artifacts were principally due to air mass variation, seasonal variation, bad calibration or instrumental errors and were consequently removed from our outlier list and added to the training set. After retraining, we selected about 4000 objects, which we passed to a post analysis stage by perfoming a cross-match with all publicly available catalogs. Within these candidates we identified certain known but rare objects such as eclipsing Cepheids, blue variables, cataclysmic variables and X-ray sources. For some outliers there were no additional information. Among them we identified three unknown variability types and few individual outliers that will be followed up for a deeper analysis.

Fast and optimal nonparametric sequential design for astronomical observations

The spectral energy distribution (SED) is a relatively easy way for astronomers to distinguish between different astronomical objects such as galaxies, black holes, and stellar objects. By comparing the observations from a source at different frequencies with template models, astronomers are able to infer the type of this observed object. In this paper, we take a Bayesian model averaging perspective to learn astronomical objects, employing a Bayesian nonparametric approach to accommodate the deviation from convex combinations of known log-SEDs. To effectively use telescope time for observations, we then study Bayesian nonparametric sequential experimental design without conjugacy, in which we use sequential Monte Carlo as an efficient tool to maximize the volume of information stored in the posterior distribution of the parameters of interest. A new technique for performing inferences in log-Gaussian Cox processes called the Poisson log-normal approximation is also proposed. Simulations show the speed, accuracy, and usefulness of our method. While the strategy we propose in this paper is brand new in the astronomy literature, the inferential techniques developed apply to more general nonparametric sequential experimental design problems.

Automatic Classification of Variable Stars in Catalogs with missing data

We present an automatic classification method for astronomical catalogs with missing data. We use Bayesian networks, a probabilistic graphical model, that allows us to perform inference to pre- dict missing values given observed data and dependency relationships between variables. To learn a Bayesian network from incomplete data, we use an iterative algorithm that utilises sampling methods and expectation maximization to estimate the distributions and probabilistic dependencies of variables from data with missing values. To test our model we use three catalogs with missing data (SAGE, 2MASS and UBVI) and one complete catalog (MACHO). We examine how classification accuracy changes when information from missing data catalogs is included, how our method compares to traditional missing data approaches and at what computational cost. Integrating these catalogs with missing data we find that classification of variable objects improves by few percent and by 15% for quasar detection while keeping the computational cost the same.

Infinite Shift-invariant Grouped Multi-task Learning for Gaussian Processes

Multi-task learning leverages shared information among data sets to improve the learning performance of individual tasks. The paper applies this framework for data where each task is a phase-shifted periodic time series. In particular, we develop a novel Bayesian nonparametric model capturing a mixture of Gaussian processes where each task is a sum of a group-specific function and a component capturing individual variation, in addition to each task being phase shifted. We develop an efficient \textsc{em} algorithm to learn the parameters of the model. As a special case we obtain the Gaussian mixture model and \textsc{em} algorithm for phased-shifted periodic time series. Furthermore, we extend the proposed model by using a Dirichlet Process prior and thereby leading to an infinite mixture model that is capable of doing automatic model selection. A Variational Bayesian approach is developed for inference in this model. Experiments in regression, classification and class discovery demonstrate the performance of the proposed models using both synthetic data and real-world time series data from astrophysics. Our methods are particularly useful when the time series are sparsely and non-synchronously sampled.

An improved quasar detection method in EROS-2 and MACHO LMC datasets

We present a new classification method for quasar identification in the EROS-2 and MACHO datasets based on a boosted version of Random Forest classifier. We use a set of variability features including parameters of a continuous auto regressive model. We prove that continuous auto regressive parameters are very important discriminators in the classification process. We create two training sets (one for EROS-2 and one for MACHO datasets) using known quasars found in the LMC. Our model's accuracy in both EROS-2 and MACHO training sets is about 90% precision and 86% recall, improving the state of the art models accuracy in quasar detection. We apply the model on the complete, including 28 million objects, EROS-2 and MACHO LMC datasets, finding 1160 and 2551 candidates respectively. To further validate our list of candidates, we crossmatched our list with a previous 663 known strong candidates, getting 74% of matches for MACHO and 40% in EROS-2. The main difference on matching level is because EROS-2 is a slightly shallower survey which translates to significantly lower signal-to-noise ratio lightcurves.

Nonparametric Bayesian Estimation of Periodic Functions

Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the problem of identifying the period: estimating the period of a periodic function based on noisy observations made at irregularly spaced time points. This problem is still a difficult challenge despite extensive study in different disciplines. The paper makes several contributions toward solving this problem. First, we present a nonparametric Bayesian model for period finding, based on Gaussian Processes (GP), that does not make strong assumptions on the shape of the periodic function. As our experiments demonstrate, the new model leads to significantly better results in period estimation when the target function is non-sinusoidal. Second, we develop a new algorithm for parameter optimization for GP which is useful when the likelihood function is very sensitive to the setting of the hyper-parameters with numerous local minima, as in the case of period estimation. The algorithm combines gradient optimization with grid search and incorporates several mechanisms to overcome the high complexity of inference with GP. Third, we develop a novel approach for using domain knowledge, in the form of a probabilistic generative model, and incorporate it into the period estimation algorithm. Experimental results on astrophysics data validate our approach showing significant improvement over the state of the art in this domain.

Period Estimation in Astronomical Time Series Using Slotted Correntropy

In this letter, we propose a method for period estimation in light curves from periodic variable stars using correntropy. Light curves are astronomical time series of stellar brightness over time, and are characterized as being noisy and unevenly sampled. We propose to use slotted time lags in order to estimate correntropy directly from irregularly sampled time series. A new information theoretic metric is proposed for discriminating among the peaks of the correntropy spectral density. The slotted correntropy method outperformed slotted correlation, string length, VarTools (Lomb-Scargle periodogram and Analysis of Variance), and SigSpec applications on a set of light curves drawn from the MACHO survey.