As for ML methods, I know for a fact that modern Bayesian inference techniques have been successfully applied in comparative linguistics and proto-language reconstruction.
I should have made this clearer, but the 'question' I had in mind was not whether Basque is related to Georgian, but the more general one of whether it's related to anything at all.
In “Google’s Multilingual Neural Machine Translation System: Enabling Zero-Shot Translation”, we address this challenge by extending our previous GNMT system, allowing for a single system to translate between multiple languages. Our proposed architecture requires no change in the base GNMT system, but instead uses an additional “token” at the beginning of the input sentence to specify the required target language to translate to. In addition to improving translation quality, our method also enables “Zero-Shot Translation” — translation between language pairs never seen explicitly by the system.
https://research.googleblog.com/2016/11/zero-shot-translatio...
The related research paper: