Empirical Localization of Homogeneous Divergences on Discrete Sample Spaces

Part of Advances in Neural Information Processing Systems 28 (NIPS 2015)

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Takashi Takenouchi, Takafumi Kanamori


In this paper, we propose a novel parameter estimator for probabilistic models on discrete space. The proposed estimator is derived from minimization of homogeneous divergence and can be constructed without calculation of the normalization constant, which is frequently infeasible for models in the discrete space. We investigate statistical properties of the proposed estimator such as consistency and asymptotic normality, and reveal a relationship with the alpha-divergence. Small experiments show that the proposed estimator attains comparable performance to the MLE with drastically lower computational cost.