Deep forest is a non-differentiable deep model that has achieved impressive empirical success across a wide variety of applications, especially on categorical/symbolic or mixed modeling tasks. Many of the application fields prefer explainable models, such as random forests with feature contributions that can provide a local explanation for each prediction, and Mean Decrease Impurity (MDI) that can provide global feature importance. However, deep forest, as a cascade of random forests, possesses interpretability only at the first layer. From the second layer on, many of the tree splits occur on the new features generated by the previous layer, which makes existing explaining tools for random forests inapplicable. To disclose the impact of the original features in the deep layers, we design a calculation method with an estimation step followed by a calibration step for each layer, and propose our feature contribution and MDI feature importance calculation tools for deep forest. Experimental results on both simulated data and real-world data verify the effectiveness of our methods.

Recent studies on deep forests have shown that deep learning frameworks can be built on non-differentiable modules without a backpropagation training process. However, the feature representations of deep forests only consist of predicted class probabilities. The information these class probabilities deliver is very limited and lacks diversity, especially when the number of output labels is far less than the number of input features. Besides, the prediction-based representations require us to save multiple layers of random forests to use them during testing, which is high-memory and high-time cost. In this paper, we propose a novel deep forest model that utilizes high-order interactions of input features to generate more informative and diverse feature representations. Specifically, we design a generalized version of Random Intersection Trees (gRIT) to discover stable high-order interactions and apply Activated Linear Combination (ALC) to transform them into hierarchical distributed representations. These interaction-based representations obviate the need to store random forests in the front layers, thus greatly improving the computational efficiency. Our experiments show that our method achieves highly competitive predictive performance with significantly reduced time and memory cost.