Theoretical Validation of Potential Habitability via Analytical and Boosted Tree Methods: An Optimistic Study on Recently Discovered Exoplanets

Seven Earth-sized planets, TRAPPIST-1 system, were discovered in February 2017. Three of these planets are in the habitable zone (HZ) of their star, making them potentially habitable planets a mere 40 light years away. Discovery of the closest potentially habitable planet to us just a year before -- Proxima~b, and a realization that Earth-type planets in HZ are a common occurrence provides the impetus to the pursuit for life outside the Solar System. The search for life has two goals: Earth similarity and habitability. An index was recently proposed, Cobb-Douglas Habitability Score (CDHS), based on Cobb-Douglas production function, which computes the habitability score by using measured and estimated planetary parameters like radius, density, escape velocity and surface temperature of a planet. The proposed metric with exponents accounting for metric elasticity, is endowed with analytical properties that ensure global optima and can be scaled to accommodate a finite number of input parameters. We show that the model is elastic, and the conditions on elasticity to ensure global maxima can scale as the number of predictor parameters increase. K-Nearest Neighbour classification algorithm, embellished with probabilistic herding and thresholding restriction, utilizes CDHS scores and labels exoplanets to appropriate classes via feature-learning methods. The algorithm works on top of a decision-theoretical model using the power of convex optimization and machine learning. A second approach, based on a novel feature-learning and tree-building method classifies the same planets without computing the CDHS of the planets and produces a similar outcome. The convergence of the two different approaches indicates the strength of the proposed scheme and the likelihood of the potential habitability of the recent discoveries.