A Probabilistic Interpretation of Canonical Correlation Analysis

By Francis R. Bach, Michael I. Jordan. 2005

534 citations recorded by the source corpus.

Subfields: Representation & Self-Supervised Learning, Probabilistic & Bayesian Methods

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Citations in the corpus

Beyond CCA: Moment Matching for Multi-View Models (2016, positive): “Bach & Jordan (2005) provide a probabilistic interpretation of CCA: they show that the maximum likelihood estimators of a particular Gaussian graphical model, which we refer to as Gaussian CCA, is equivalent to the classical CCA by Hotelling (1936).”
Composing graphical models with neural networks for structured representations and fast inference (2016, methodology): “For the synthetic 1D dot video data, we trained an LDS SVAE on 80 random image sequences each of length 50, using one sequence per update, and show the model’s future predictions given a prefix of a longer sequence.”
The Incomplete Rosetta Stone problem: Identifiability results for Multi-view Nonlinear ICA (2019, methodology): “CCA can be interpretated probabilistically [4] and is equivalent to maximum likelihood estimation in a graphical model which is a special case of that depicted in Figure 2.”
Deep Multimodal Feature Analysis for Action Recognition in RGB+D Videos (2016, methodology): “In our implementation of the CCA-RICA method (section 5) we used the provided codes by the authors of [4] for CCA and [28] for RICA.”
Bayesian group factor analysis with structured sparsity (2016, methodology): “The maximum likelihood estimates of the loading matrices in the classical CCA framework, Λ (1) and Λ (2) , are the first k canonical directions up to orthogonal transformations (Bach and Jordan, 2005).”
A Survey of Multi-View Representation Learning (2016, unknown): “Consequently, Bach and Jordan [65] provide a detailed connection between CCA and probabilistic CCA based on the result of the maximum likelihood estimation of Eq.”
Multi-view learning overview: Recent progress and new challenges (2017, background): “[70] F.R. Bach , M.I. Jordan , Kernel independent component analysis, J. Mach.”
Multi-view Super Vector for Action Recognition (2014, methodology): “Bach and Jordan [3] gave a probabilistic interpretation of CCA.”
Factorized Latent Spaces with Structured Sparsity (2010, methodology): “2(d), we show the results obtained with CCA.”
Tensor Canonical Correlation Analysis for Action Classification (2007, methodology): “We extend the classical canonical correlation analysis - a standard tool for inspecting linear relationships between two sets of vectors [9, 11] - into that of multi-dimensional data arrays (or high-order tensors) for analyzing the similarity of video data/space-time volumes.”
Canonical Correlation Analysis of Video Volume Tensors for Action Categorization and Detection (2009, background): “Keywords– Action categorization, gesture recognition, canonical correlation analysis, tensor, action detection, incremental subspace learning, spatiotemporal pattern classification.”
Sparse probabilistic projections (2008, methodology): “Hence, the probabilistic reformulations of PCA and CCA fit this probabilistic framework.”
On Deep Multi-View Representation Learning (2015, background): “The CCA objective has been studied extensively and has a number of useful properties and interpretations ( Borga, 2001; Bach and Jordan, 2002, 2005; Chechik et al., 2005), and the optimal linear projection mappings can be obtained by solving an eigenvalue system of a matrix whose dimensions equal…”
Probabilistic Linear Discriminant Analysis (2006, methodology): “It has long been known that LDA maximizes the likelihood of a Gaussian mixture model and is mathematically equivalent to linear regression of the class assignment labels [3, 4].”
Multi-View Intact Space Learning (2015, background): “A number of works exploit the shared latent subspace across diverse views, such as canonical correlation analysis (CCA) [28], [29], its kernel extension [30], its probabilistic interpretation [31], and its sparse formulation [32].”
Bayesian exponential family projections for coupled data sources (2010, methodology): “The probabilistic interpretation of CCA (Bach and Jordan, 2005) shows that the classical CCA implicitly assumes normal distribution.”