Parameter Estimation for Unnormalized Discrete Models via Empirically Localized Deformed Bregman Divergence
Abstract
Estimation of parameter of probabilistic models is an important task in the field of machine learning.For models of discrete variables, calculation of the normalization constant of model is sometimes difficult and a lot of researches have been done to avoid the calculation of the normalization constant. In this paper, we tackle with the difficulty by combining a technique of empirical localization and a deformed Bregman divergence.The technique of empirical localization makes it possible to drastically reduce computational cost of the calculation of the normalization constant, and in addition, appropriate choice of the deformation for the Bregman divergence can invest the proposed estimator with various kinds of favorable statistical properties, such as efficiency or robustness against outlier noise.
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BibTeX
@misc{takenouchi2026parameter,
title = {{Parameter Estimation for Unnormalized Discrete Models via Empirically Localized Deformed Bregman Divergence}},
author = {Takashi Takenouchi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30713},
eprint = {2609.30713},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30713},
}
RIS
TY - UNPB
TI - Parameter Estimation for Unnormalized Discrete Models via Empirically Localized Deformed Bregman Divergence
AU - Takashi Takenouchi
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30713
UR - https://arxiv.org/abs/2609.30713
AB - Estimation of parameter of probabilistic models is an important task in the field of machine learning.For models of discrete variables, calculation of the normalization constant of model is sometimes difficult and a lot of researches have been done to avoid the calculation of the normalization constant. In this paper, we tackle with the difficulty by combining a technique of empirical localization and a deformed Bregman divergence.The technique of empirical localization makes it possible to drastically reduce computational cost of the calculation of the normalization constant, and in addition, appropriate choice of the deformation for the Bregman divergence can invest the proposed estimator with various kinds of favorable statistical properties, such as efficiency or robustness against outlier noise.
ER -