Methoden vergleichen

	Bayessche kanonische Korrelationsanalyse (Bayesian CCA)	Bayesian Principal Component Analysis (BPCA)
Fachgebiet	Statistik	Statistik
Familie	Latent structure	Latent structure
Entstehungsjahr	2005-2013	1999
Urheber	Francis Bach & Michael Jordan (probabilistic formulation, 2005); Klami, Virtanen & Kaski (fully Bayesian treatment, 2013)	Christopher M. Bishop
Typ	Latent variable model / dimensionality reduction	Bayesian latent variable / dimension reduction
Wegweisende Quelle	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.
Aliasnamen	Bayesian CCA, probabilistic CCA, BCCA	BPCA, Bayesian PCA, probabilistic PCA with Bayesian inference, variational Bayesian PCA
Verwandt	5	2
Zusammenfassung	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.