Deep forest

Current deep-learning models are mostly built upon neural networks, i.e. multiple layers of parameterized differentiable non-linear modules that can be trained by backpropagation. In this paper, we explore the possibility of building deep models based on non-differentiable modules such as decision trees. After a discussion about the mystery behind deep neural networks, particularly by contrasting them with shallow neural networks and traditional machine-learning techniques such as decision trees and boosting machines, we conjecture that the success of deep neural networks owes much to three characteristics, i.e. layer-by-layer processing, in-model feature transformation and sufficient model complexity. On one hand, our conjecture may offer inspiration for theoretical understanding of deep learning; on the other hand, to verify the conjecture, we propose an approach that generates deep forest holding these characteristics. This is a decision-tree ensemble approach, with fewer hyper-parameters than deep neural networks, and its model complexity can be automatically determined in a data-dependent way. Experiments show that its performance is quite robust to hyper-parameter settings, such that in most cases, even across different data from different domains, it is able to achieve excellent performance by using the same default setting. This study opens the door to deep learning based on non-differentiable modules without gradient-based adjustment, and exhibits the possibility of constructing deep models without backpropagation.