Joints in Random Forests

TL;DR

This paper introduces a novel interpretation of decision trees and random forests as generative models, enabling them to handle missing data and detect outliers more effectively than traditional methods.

Contribution

It presents a new generative perspective on DTs and RFs, leading to the development of GeDTs and GeFs that can process missing features and identify outliers.

Findings

GeDTs and GeFs outperform KNN imputation in handling missing data

Models can detect outliers by monitoring marginal probabilities

Theoretical extension of consistency to missing at random scenarios

Abstract

Decision Trees (DTs) and Random Forests (RFs) are powerful discriminative learners and tools of central importance to the everyday machine learning practitioner and data scientist. Due to their discriminative nature, however, they lack principled methods to process inputs with missing features or to detect outliers, which requires pairing them with imputation techniques or a separate generative model. In this paper, we demonstrate that DTs and RFs can naturally be interpreted as generative models, by drawing a connection to Probabilistic Circuits, a prominent class of tractable probabilistic models. This reinterpretation equips them with a full joint distribution over the feature space and leads to Generative Decision Trees (GeDTs) and Generative Forests (GeFs), a family of novel hybrid generative-discriminative models. This family of models retains the overall characteristics of DTs and RFs while additionally being able to handle missing features by means of marginalisation. Under certain assumptions, frequently made for Bayes consistency results, we show that consistency in GeDTs and GeFs extend to any pattern of missing input features, if missing at random. Empirically, we show that our models often outperform common routines to treat missing data, such as K-nearest neighbour imputation, and moreover, that our models can naturally detect outliers by monitoring the marginal probability of input features.