The Value of Graph-based Encoding in NBA Salary Prediction

Accurate salary prediction is critical for bridging the information gap between employers and job seekers in modern labor markets. Existing approaches predominantly yield a single point estimate and treat job attributes such as location, occupation, and industry as independent categorical features, ignoring both the inherent uncertainty and multi-modality of real-world compensation data and the rich hierarchical and semantic-similarity relationships that govern pay norms. In this paper we propose GAT-MDN, a unified framework that addresses both limitations simultaneously. For each of the three attribute domains we construct a domain-specific graph whose edges encode (i) hierarchical parent-child containment and (ii) weighted similarity links derived from a pre-trained Sentence-Transformer. Parallel Graph Attention Networks (GATs) with edge-feature-aware attention learn rich, context-sensitive node representations from these multi-relational graphs. A priority-based hierarchical selection module then assembles a composite feature vector that gracefully handles missing or coarse attributes, and a Mixture Density Network (MDN) head maps this vector to the parameters of a Gaussian Mixture Model (GMM), yielding a full conditional salary distribution. Extensive experiments on a real-world Dutch job-posting dataset of over 1 million records demonstrate that GAT-MDN significantly outperforms a non-graph MLP-MDN baseline in both Negative Log-Likelihood (NLL) and Mean Squared Error (MSE).

In recent years, transductive knowledge graph embedding models have been applied to tasks such as link prediction and query answering. Although knowledge graphs often contain rich numerical attributes, most embedding models neglect them, limiting their ability to represent real-world knowledge graphs with diverse information. In this work, we propose a neural regression model (LitEm) that enables transductive knowledge graph embedding models to predict numerical attributes within knowledge graphs. Experimental results demonstrate that LitEm achieves the best or second-best results on most attributes across FB15K-237, YAGO15K, DB15K, and Mutagenesis. Furthermore, we propose a co-training framework that jointly trains state-of-the-art transductive knowledge graph embedding models with LitEm, which improves link prediction performance mainly for bilinear models and simultaneously enables them to predict numerical attributes. In addition, the literal-awareness evaluation demonstrates that co-training helps models to encode and exploit attribute information in a "literal-aware'' manner, suggesting that the observed gains are not merely due to additional parameters. We publicly release our implementation at https://github.com/dice-group/dice-embeddings.

We present a method for finding hierarchy-aware embeddings of knowledge graphs (KGs) using graph neural networks (GNNs) enriched with a semantic loss derived from underlying ontologies. This method yields embeddings that better reflect domain knowledge. To demonstrate their utility, we predict and interpret the effects of gene deletions in the yeast Saccharomyces cerevisiae and learn box embeddings for KGs in the absence of a prediction task. We further show how box embeddings can serve as the basis for evaluating KG revisions. Our yeast KG is constructed from community databases and ontology terms. Low-dimensional box embeddings combined with GNNs are used to predict cell growth for double gene knockouts. Over 10-fold cross validation, these predictions have a mean $R^2$scoreof~0.360, significantly higher than baseline comparisons, demonstrating that high-level qualitative knowledge is informative about experimental outcomes. Incorporating semantic loss terms in the training of the models improves their predictive performance ($R^2$=0.377) by aligning embeddings with ontology structure. This shows that class hierarchies from ontologies can be exploited for quantitative prediction. We also test the trained models on triple gene knockouts, showing they generalise to data beyond those seen in training. Additionally, by identifying co-occurring relations in the yeast KG important for the cell-growth predictions, we construct hypotheses about interacting traits in yeast. A biological experiment validates one such finding, revealing an association between inositol utilisation and osmotic stress resistance, highlighting the model's potential to guide biological discovery.