تقرير
Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures
| العنوان: | Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures |
|---|---|
| المؤلفون: | Watanabe, Takumi, Watanabe, Sumio |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Mathematics - Statistics Theory |
| الوصف: | Multinomial mixtures are widely used in the information engineering field, however, their mathematical properties are not yet clarified because they are singular learning models. In fact, the models are non-identifiable and their Fisher information matrices are not positive definite. In recent years, the mathematical foundation of singular statistical models are clarified by using algebraic geometric methods. In this paper, we clarify the real log canonical thresholds and multiplicities of the multinomial mixtures and elucidate their asymptotic behaviors of generalization error and free energy. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2203.06884 |
| رقم الأكسشن: | edsarx.2203.06884 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |