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Empirical Localization of Homogeneous Divergences on Discrete Sample Spaces

Neural Information Processing Systems

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 information geometry. Some experiments show that the proposed estimator attains comparable performance to the maximum likelihood estimator with drastically lower computational cost.



Reply to Reviewer # 1

Neural Information Processing Systems

Q1: What other ways to generate fake sequences may be suitable for this problem? A1: That is a good question. GAN to generate some more difficult fake sequences to further improve the ability of the encoder. Q1: Comparison with other state-of-the-art deep clustering methods which are not designed for time-series. A1: Following your suggestion, we compare our method with two state-of-the-art deep clustering methods (i.e., DEC (Xie et al., Table 1: Comparisons on 36 time series datasets (The No. of datasets is consistent with the one in Table 2 in main text)Dataset DEC(RI) IDEC(RI) DTCR(RI) DTCR(NMI) DTCR(ACC) Dataset DEC(RI) IDEC(RI) DTCR(RI) DTCR(NMI) DTCR(ACC)1 0.5817 0.6210 0.6868(0.0026)