Deep Component Analysis via Alternating Direction Neural Networks

TL;DR

DeepCA introduces a multilayer model with hierarchical constraints, using ADNNs for inference, bridging the gap between deep neural networks and component analysis, with improved performance on tasks like depth prediction.

Contribution

We propose Deep Component Analysis (DeepCA), a new multilayer model with hierarchical latent constraints, and a differentiable optimization algorithm using ADNNs for inference and learning.

Findings

Performance improvements on depth prediction tasks.

Effective incorporation of prior knowledge into deep models.

Theoretical insights into feed-forward network approximations.

Abstract

Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich intuition and theory, but smaller capacity often limits its usefulness. To bridge this gap, we introduce Deep Component Analysis (DeepCA), an expressive multilayer model formulation that enforces hierarchical structure through constraints on latent variables in each layer. For inference, we propose a differentiable optimization algorithm implemented using recurrent Alternating Direction Neural Networks (ADNNs) that enable parameter learning using standard backpropagation. By interpreting feed-forward networks as single-iteration approximations of inference in our model, we provide both a novel theoretical perspective for understanding them and a practical technique for constraining predictions with prior knowledge. Experimentally, we demonstrate performance improvements on a variety of tasks, including single-image depth prediction with sparse output constraints.