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.

Knowledge graph embedding represents entities and relations in knowledge graph as low-dimensional, continuous vectors, and thus enables knowledge graph compatible with machine learning models. Though there have been a variety of models for knowledge graph embedding, most methods merely concentrate on the fact triples, while supplementary textual descriptions of entities and relations have not been fully employed. To this end, this paper proposes the semantic space projection (SSP) model which jointly learns from the symbolic triples and textual descriptions. Our model builds interaction between the two information sources, and employs textual descriptions to discover semantic relevance and offer precise semantic embedding. Extensive experiments show that our method achieves substantial improvements against baselines on the tasks of knowledge graph completion and entity classification.