方法对比

	贝叶斯典型相关分析 (Bayesian CCA)	贝叶斯主成分分析 (BPCA)
领域	统计学	统计学
方法族	Latent structure	Latent structure
起源年份	2005-2013	1999
提出者	Francis Bach & Michael Jordan (probabilistic formulation, 2005); Klami, Virtanen & Kaski (fully Bayesian treatment, 2013)	Christopher M. Bishop
类型	Latent variable model / dimensionality reduction	Bayesian latent variable / dimension reduction
开创性文献	Bach, F. R. & Jordan, M. I. (2005). A probabilistic interpretation of canonical correlation analysis. Technical Report 688, Department of Statistics, University of California, Berkeley.	Bishop, C. M. (1999). Bayesian PCA. In M. S. Kearns, S. A. Solla & D. A. Cohn (Eds.), Advances in Neural Information Processing Systems 11 (pp. 382–388). MIT Press.
别名	Bayesian CCA, probabilistic CCA, BCCA	BPCA, Bayesian PCA, probabilistic PCA with Bayesian inference, variational Bayesian PCA
相关	5	2
摘要	Bayesian canonical correlation analysis is a probabilistic generative model that identifies shared latent structure between two or more sets of observed variables. It extends classical CCA by placing priors on model parameters, enabling principled uncertainty quantification, automatic determination of the number of shared dimensions, and robustness when sample sizes are small relative to dimensionality.	Bayesian principal component analysis embeds probabilistic PCA within a Bayesian framework, placing priors over the loading matrix so that irrelevant components are automatically pruned. It handles missing data naturally and provides principled uncertainty estimates for both the latent scores and the dimensionality of the representation.