$\ell_0$-based Sparse Canonical Correlation Analysis

Abstract

Canonical Correlation Analysis (CCA) models can extract informative correlated representations from multimodal unlabelled data. Despite their success, CCA models may break if the number of variables exceeds the number of samples. We propose Deep Gated-CCA, a method for learning correlated representations based on a sparse subset of variables from two observed modalities. The proposed procedure learns two non-linear transformations and simultaneously gates the input variables to identify a subset of most correlated variables. The non-linear transformations are learned by training two neural networks to maximize a shared correlation loss defined based on their outputs. Gating is obtained by adding an approximate 0 regularization term applied to the input variables. This approximation relies on a recently proposed continuous Gaussian based relaxation for Bernoulli variables which act as gates. We demonstrate the efficacy of the method using several synthetic and real examples. Most notably, the method outperforms other linear and non-linear CCA models.

Probabilistic Robust Autoencoders for Anomaly Detection

“…(2) the problem becomes intractable for a large number of samples. To overcome this limitation, following[40,25,26], we propose to replace the deterministic search over the values of the indicator vector b with a probabilistic counterpart.…”