Upper Bound of Bayesian Generalization Error in Non-negative Matrix Factorization
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Abstract (arXiv)
Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as it is not a regular statistical model, resulting that theoretical optimization method of NMF has not yet established. In this paper, we study the real log canonical threshold of NMF and give an upper bound of the generalization error in Bayesian learning. The results show that the generalization error of the matrix factorization can be made smaller than regular statistical models if Bayesian learning is applied.
Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Dec 2016.
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Citing papers per year: 2021: 1; 2022: 1; 2023: 3; 2024: 2; 2025: 1; 2026: 2.
10 papers.
- 2022Recent Advances in Algebraic Geometry and Bayesian Statisticscited by 4
- 2026A Basin-Selection Perspective on Grokking via Singular Learning Theorycited by 4
- 2021Tropical Support Vector Machines: Evaluations and Extension to Function Spacescited by 3
- 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
- 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
- 2025An Asymptotic Equation Linking WAIC and WBIC in Singular Modelscited by 0
- 2026Singularities of Non-negative Matrix Factorization and their application to Bayesian inferencecited by 0
- 2026Singularities of Non-negative Matrix Factorization and their application to Bayesian inference28 Sep 2026
- 2026A Basin-Selection Perspective on Grokking via Singular Learning Theory1 Mar 2026
- 2025An Asymptotic Equation Linking WAIC and WBIC in Singular Models20 May 2025
- 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
- 2021Tropical Support Vector Machines: Evaluations and Extension to Function Spaces27 Jan 2021