# On the Quality of Deep Representations for Kepler Light Curves Using Variational Auto-Encoders
## 1 Introduction  
New instrumentation technologies, such as the Legacy Survey of Space and Time (LSST) at the Vera C. Rubin Observatory [1], the Transiting Exoplanet Survey Satellite (TESS, [2]), and future space-based telescopes and ground-based observatories have motivated the use of automatic techniques to process and analyze the large amount of data that is being and will be generated. In the exoplanet domain, advances in instrumentation and data analysis have allowed the discovery of thousands of exoplanets. NASA has reported (last updated 12 October2021: [[https://exoplanets.nasa.gov](https://exoplanets.nasa.gov)]([https://exoplanets.nasa.gov](https://exoplanets.nasa.gov)) accessed on 13 October 2021) more than 4500 exoplanets detected using different techniques, despite the fact that planets emit or reflect very faint light compared to their host star and that their orbital distance is very small relative to observational distance. The analysis of light curves has been the main source of candidate objects. These series are photometric observations of light intensity as a function of time, where the observed star luminosity varies through time as a result of intrinsic processes or due to external influences, such as an orbiting planet passing between the star and the observer. The latter phenomenon is called a transit and has been used as an effective method ([[http://exoplanetarchive.ipac.caltech.edu/docs/counts_detail.html](http://exoplanetarchive.ipac.caltech.edu/docs/counts_detail.html)]([http://exoplanetarchive.ipac.caltech.edu/docs/counts_detail.html](http://exoplanetarchive.ipac.caltech.edu/docs/counts_detail.html)) accessed on 12 October 2021) method to study candidate orbiting objects. A transit light curve can be mathematically modeled as a natural phenomenon of an orbiting object, and algorithms such as the well-known Mandel-Aglol method [3] can be used to fit such models. Unfortunately, the diversity of planetary systems (and their corresponding astrophysical scenarios) prevents unique model selection due to the unknown number of transits and complex dynamics, such as eclipsing binary systems, very faint observation, or the microvariability of the star [4]. The application of task-based learning models to solve specific tasks (e.g., exoplanet search) has been the common approach to reduce human effort [5; 6; 7; 8]. These are methods that learn representations and model parameters based on a specific learning task and a particular objective function, usually based on the available labels. On the other hand, learning models to build self-generated representations of light curves have been largely unexplored. Task-free methods, such as those in [9; 10; 11], learn the key features (representation) for detecting candidate exoplanets from data instead of imposing a model without the correct capacity to learn the task (i.e., excessively simple or complex for the observed data). These methods learn pattern structures from the data without the need for labels (i.e., unsupervised learning), having the advantage of using all the available data. A major challenge of working with time series in astronomy is that they are usually noisy, meaning that values are missing for several timestamps or that the measurements are not uniform throughout the series. Different approaches have been proposed to solve this representation issue such as binning the light curve based on a previous folding of the periodic behavior [6], extracting specialized features based on subsets of data points [12], or explicitly modeling the time dependencies [13]. Based on the latter, some approaches have included the time information in the input representation of the learning model, showing improved results [10; 14; 15]. Motivated by the success of deep learning techniques [16] in different research fields, we focused on using the auto-encoder models. In this paper, we propose using variational (stochastic) models as dimensionality reduction techniques in order to learn a quality deep representation for Kepler light curves.