Rate-Distortion Auto-Encoders
This work addresses regularization in auto-encoder training for deep learning applications, but it appears incremental as it builds on existing rate-distortion concepts with a new entropy measure.
The paper tackles the problem of learning regularized representations in auto-encoders by proposing a rate-distortion objective that minimizes mutual information between inputs and outputs while maintaining reconstruction fidelity, with experiments showing it can learn regularized mappings implicitly using over-complete bases.
A rekindled the interest in auto-encoder algorithms has been spurred by recent work on deep learning. Current efforts have been directed towards effective training of auto-encoder architectures with a large number of coding units. Here, we propose a learning algorithm for auto-encoders based on a rate-distortion objective that minimizes the mutual information between the inputs and the outputs of the auto-encoder subject to a fidelity constraint. The goal is to learn a representation that is minimally committed to the input data, but that is rich enough to reconstruct the inputs up to certain level of distortion. Minimizing the mutual information acts as a regularization term whereas the fidelity constraint can be understood as a risk functional in the conventional statistical learning setting. The proposed algorithm uses a recently introduced measure of entropy based on infinitely divisible matrices that avoids the plug in estimation of densities. Experiments using over-complete bases show that the rate-distortion auto-encoders can learn a regularized input-output mapping in an implicit manner.