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Seven Earth-sized planets, TRAPPIST-1 system, were discovered in February2017. Three of these planets are in the habitable zone (HZ) of their star,making them potentially habitable planets a mere 40 light years away. Discoveryof the closest potentially habitable planet to us just a year before --Proxima~b, and a realization that Earth-type planets in HZ are a commonoccurrence provides the impetus to the pursuit for life outside the SolarSystem. The search for life has two goals: Earth similarity and habitability.An index was recently proposed, Cobb-Douglas Habitability Score (CDHS), basedon Cobb-Douglas production function, which computes the habitability score byusing measured and estimated planetary parameters like radius, density, escapevelocity and surface temperature of a planet. The proposed metric withexponents accounting for metric elasticity, is endowed with analyticalproperties that ensure global optima and can be scaled to accommodate a finitenumber of input parameters. We show that the model is elastic, and theconditions on elasticity to ensure global maxima can scale as the number ofpredictor parameters increase. K-Nearest Neighbour classification algorithm,embellished with probabilistic herding and thresholding restriction, utilizesCDHS scores and labels exoplanets to appropriate classes via feature-learningmethods. The algorithm works on top of a decision-theoretical model using thepower of convex optimization and machine learning. A second approach, based ona novel feature-learning and tree-building method classifies the same planetswithout computing the CDHS of the planets and produces a similar outcome. Theconvergence of the two different approaches indicates the strength of theproposed scheme and the likelihood of the potential habitability of the recentdiscoveries.

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