Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures
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Abstract (arXiv)
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.
Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 2 of its 24 references that are in the map. First posted on arXiv 14 Mar 2022.
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2 of 24 references.
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Citing papers per year: 2022: 2; 2023: 3; 2024: 3; 2025: 0; 2026: 1.
9 papers.
- 2022Mathematical Theory of Bayesian Statistics for Unknown Information Sourcecited by 5
- 2022Recent Advances in Algebraic Geometry and Bayesian Statisticscited by 4
- 2023Bayesian Generalization Error in Linear Neural Networks with Concept Bottleneck Structure and Multitask Formulationcited by 3
- 2024Review and Prospect of Algebraic Research in Equivalent Framework between Statistical Mechanics and Machine Learning Theorycited by 2
- 2024Upper Bound of Bayesian Generalization Error in Partial Concept Bottleneck Model (CBM): Partial CBM outperforms naive CBMcited by 1
- 2026Upper Bounds for Local Learning Coefficients of Three-Layer Neural Networkscited by 1
- 2023Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inferencecited by 0
- 2023Blow-up Algorithm for Sum-of-Products Polynomials and Real Log Canonical Thresholdscited by 0
- 2024Statistical inference for quantum singular modelscited by 0
- 2026Upper Bounds for Local Learning Coefficients of Three-Layer Neural Networks13 Mar 2026
- 2024Statistical inference for quantum singular models25 Nov 2024
- 2024Review and Prospect of Algebraic Research in Equivalent Framework between Statistical Mechanics and Machine Learning Theory31 May 2024
- 2024Upper Bound of Bayesian Generalization Error in Partial Concept Bottleneck Model (CBM): Partial CBM outperforms naive CBM14 Mar 2024
- 2023Blow-up Algorithm for Sum-of-Products Polynomials and Real Log Canonical Thresholds21 Mar 2023
- 2023Bayesian Generalization Error in Linear Neural Networks with Concept Bottleneck Structure and Multitask Formulation16 Mar 2023
- 2023Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference10 Mar 2023
- 2022Recent Advances in Algebraic Geometry and Bayesian Statistics18 Nov 2022
- 2022Mathematical Theory of Bayesian Statistics for Unknown Information Source11 Jun 2022