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The maximum likelihood method is the best-known method for estimating theprobabilities behind the data. However, the conventional method obtains theprobability model closest to the empirical distribution, resulting inoverfitting. Then regularization methods prevent the model from beingexcessively close to the wrong probability, but little is known systematicallyabout their performance. The idea of regularization is similar toerror-correcting codes, which obtain optimal decoding by mixing suboptimalsolutions with an incorrectly received code. The optimal decoding inerror-correcting codes is achieved based on gauge symmetry. We propose atheoretically guaranteed regularization in the maximum likelihood method byfocusing on a gauge symmetry in Kullback -- Leibler divergence. In ourapproach, we obtain the optimal model without the need to search forhyperparameters frequently appearing in regularization.

Performance-guaranteed regularization in maximum likelihood method: Gauge symmetry in Kullback -- Leibler divergence