A classical problem in statistics is to study relationships between several blocks of variables. The goal is to find variables of one block directly related to variables of other blocks. The Regularized Generalized Canonical Correlation Analysis (RGCCA) is a very attractive framework to study such a kind of relationships between blocks. However, RGCCA captures linear relations between blocks an...

We present Deep Generalized Canonical Correlation Analysis (DGCCA) – a method for learning nonlinear transformations of arbitrarily many views of data, such that the resulting transformations are maximally informative of each other. While methods for nonlinear two-view representation learning (Deep CCA, (Andrew et al., 2013)) and linear many-view representation learning (Generalized CCA (Horst,...

Canonical correlation analysis (CCA) is a method for finding linear relations between two multidimensional random variables. This paper presents a generalization of the method to more than two variables. The approach is highly scalable, since it scales linearly with respect to the number of training examples and number of views (standard CCA implementations yield cubic complexity). The method i...

We present deep variational canonical correlation analysis (VCCA), a deep multiview learning model that extends the latent variable model interpretation of linear CCA (Bach and Jordan, 2005) to nonlinear observation models parameterized by deep neural networks (DNNs). Computing the marginal data likelihood, as well as inference of the latent variables, are intractable under this model. We deriv...

4 Knowledge of the relationship between model parameters and forecast quantities is 5 useful because it can aid in setting the values of the former for the purpose of having 6 a desired effect on the latter. Here, it is proposed that a well-established multivariate 7 statistical method known as Canonical Correlation Analysis can be formulated to gauge 8 the strength of that relationship. The me...

In generalized canonical correlation analysis several sets of variables are analyzed simultaneously. This makes the method suited for the analysis of various types of data. For example, in marketing research, subjects may be asked to rate a set of objects on a set of attributes. For each individual, a data matrix can then be constructed where the objects are represented row-wise and the attribu...

Partial canonical correlation analysis (partial CCA) is a statistical method that estimates a pair of linear projections onto a low dimensional space, where the correlation between two multidimensional variables is maximized after eliminating the influence of a third variable. Partial CCA is known to be closely related to a causality measure between two time series. However, partial CCA require...