Unbiased Estimating Equation on Inverse Divergence and Its Conditions
<|reference_start|>Unbiased Estimating Equation on Inverse Divergence and Its Conditions: This paper focuses on the Bregman divergence defined by the reciprocal function, called the inverse divergence. For the loss function defined by the monotonically increasing function $f$ and inverse divergence, the conditions for the statistical model and function $f$ under which the estimating equation is unbiased are clarified. Specifically, we characterize two types of statistical models, an inverse Gaussian type and a mixture of generalized inverse Gaussian type distributions, to show that the conditions for the function $f$ are different for each model. We also define Bregman divergence as a linear sum over the dimensions of the inverse divergence and extend the results to the multi-dimensional case.<|reference_end|>
@article{kobayashi2024unbiased,
    title={Unbiased Estimating Equation on Inverse Divergence and Its Conditions},
    author={Masahiro Kobayashi, Kazuho Watanabe},
    journal={Proc. of the IEEE International Symposium on Information Theory
  (ISIT), 2024, pp.3618-3623},
    year={2024},
    doi={10.1109/ISIT57864.2024.10619262},
    archivePrefix={arXiv},
    eprint={2404.16519},
    primaryClass={cs.IT cs.LG math.IT math.ST stat.TH}
}