Relation-weighted Link Prediction for Disease Gene Identification

Identification of disease genes, which are a set of genes associated with a disease, plays an important role in understanding and curing diseases. In this paper, we present a biomedical knowledge graph designed specifically for this problem, propose a novel machine learning method that identifies disease genes on such graphs by leveraging recent advances in network biology and graph representation learning, study the effects of various relation types on prediction performance, and empirically demonstrate that our algorithms outperform its closest state-of-the-art competitor in disease gene identification by 24.1%. We also show that we achieve higher precision than Open Targets, the leading initiative for target identification, with respect to predicting drug targets in clinical trials for Parkinson's disease.

the effects of various relation types on prediction performance. Finally, we show that we achieve higher precision than Open Targets, the leading initiative for target identification, with respect to predicting drug targets in clinical trials for Parkinson's disease.

Relation-weighted link prediction
Our goal is to identify disease genes, which are a set of genes associated with a disease. We formulate this task as a link prediction problem [6,7], where we construct our biomedical knowledge graph and leverage the information in the graph to predict previously unknown links between genes and diseases.
A modern approach to solve link prediction is via graph representation learning (GRL) [8,9]. Historically, given a machine learning problem on a graph, the main challenge has been to decide on the most predictive way to encode information about the graph into a machine learning model. For example, in case of link prediction, researchers typically encoded the graph using pairwise attributes between the candidate node pairs, such as the number of their common friends. However, such hand-engineered features are time-consuming to design and are not necessarily optimal for the prediction task. In contrast, GRL studies algorithms that automatically learns how to encode the graph structure into low-dimensional vectors which are specifically tuned for the prediction task.
We introduce a simple but important modification to link prediction algorithms for knowledge graphs called relation-weighted link prediction. Existing link prediction algorithms for knowledge graphs, such as RotatE [10], CompGCN [11], and R-GCN [12], are able to model graphs with more than one relation type. However, they assign equal importance to all links regardless of their relation type and do not account for the imbalances in the number of links across different relation types. As a result, the model may be biased to predict well on relation types with more links and poorly on relation types with less links, even if the relation type of interest has only a small proportion of the total links. Relation-weighted link prediction is a modification of existing learning algorithms such that each relation type is assigned a weight parameter that is optimized to maximize the predictive accuracy on the relation type of interest, which in our case is gene-disease. In general, relation-weighted link prediction can be used to modify any heterogeneous link prediction algorithm.
We demonstrate relation-weighted link prediction on RotatE [10], a GRL method that has been shown to achieve state-of-the-art performance on benchmark tasks like link prediction, node classification, and graph classification. Given an edge of the form < h, r, t >, it learns low-dimensional vectors h, r, t ∈ C k for nodes and relation types such that an edge is assumed to be a rotation from the head node to the tail node in the complex vector space. Equation 1 shows the loss function of RotatE for a single edge < h, r, t >. It optimizes a distancebased model with a negative sampling loss where, d r is the relation-specific distance function, γ is the margin, σ is the sigmoid function, h, t ∈ C k are the low-dimensional vector representations of h, t ∈ V , and < h i , r, t i > is a negative edge which is corrupted from the original edge.
In equation 2, we modify the original loss by introducing a relation-specific weight w r that scales the contribution of the relation type r to the loss

Experiments
In this section, we present our experimental results. To prepare for training and evaluation, we split disease-gene links into train (80%), validation (10%), and test (10%) sets. During splitting, we ensure that all nodes in the disease-gene layer occur at least once in the train set. We then incrementally augment each of the remaining layers to the train set (e.g. protein-protein, protein-reaction, pathwaydisease, etc.) in order to estimate the contribution of each layer to predictive accuracy. More details  about the biomedical knowledge graph that we constructed and its data sources, node types, and relation types can be found in the Table S1 and S2.
Since our goal is to identify disease genes, when evaluating disease-gene links in the test set, we treat all possible genes as candidates for the disease. We use two well-known link prediction metrics, filtered hit@k and filtered mean rank (MR) [13], to measure predictive accuracy. We also introduce a new metric called filtered mean percentile (MP), which is mean rank normalized by the number of candidates, to enable a fair comparison between test sets where the number of gene candidates differ.
For hyperparameter optimization, we use a library called Optuna [14]. Optuna allows us to sample the hyperparameter space efficiently and prune unpromising runs early. We optimize on the validation set and report results of the best performing model on the test set.

Relation layers
Here, we demonstrate how augmenting the graph with new relation layers and modifying the objective function affects prediction performance. For these experiments, we let valid and test splits consist only of disease-gene edges, which we keep constant across experiments. The only thing we change between experiments is the new relation layers we augment to the train split. As the link prediction algorithm, we use the relation-weighted modification of RotatE.
Results are shown in Table 1. Due to lack of space, we abbreviate curated DoidGeNET as DG, uncurated DoidGeNET as DG_UC, Disease Ontology as DO, and Reactome as RT. We observe that each relation layer we add to the train split improves the prediction performance compared to the preceding one, and the fully augmented graph achieves the best performance. This shows the benefits of adding relevant biological information to the graph. Furthermore, in Table 2, we compare the prediction performance of the original and the relation-weighted RotatE on the fully augmented graph. We observe that the relation-weighted variant performs better than the original, thus showing the utility of weighting relation types in heterogeneous graphs. More details about the optimal relation weights learned by the model can be found in the Table S3.
In conclusion, when we augment our graph with all of the relation layers and apply our relationweighted objective, relative to the graph that only consists of the disease-gene layer, we achieve a relative reduction of 76.2% in MR, a relative increase of 98.4% in hit@30, and a relative increase of 28.2% in MP.

Comparison with state-of-the-art (SOTA)
We compare our best performing model against existing SOTA methods for disease gene prediction [15]. Specifically, we compare against direct neighborhood scoring [16], DIAMOnD [17], and random walks [18,19].
Direct neighborhood scoring [16] assigns each gene a score that is proportional to the percentage of its neighbors associated with the disease. To construct disease gene clusters, it initializes the clusters with a seed set of disease genes and recursively expands the cluster with the highest scoring genes. DIAMOnD [17] also initializes clusters with seed genes, but uses a statistic called connectivity significance to expand them. Random walks [18,19] use seed genes to initialize a random walker that randomly visits neighbor genes. Upon convergence, the frequency with which the nodes in the network are visited is used to rank the disease genes.
For a fair comparison, we initialize all these methods with the same seed genes that were used to train our own models. When appropriate, we optimize their hyperparameters using the validation set. Because of the way these methods are designed, we train them on a subgraph consisting of two layers: disease-gene (DoidGeNET) and protein-protein interaction (STRING).
In Table 3, we share the results we obtained on the test set 2 . In conclusion, relation-weighted RotatE outperforms all SOTA methods for disease gene prediction, including its closest competitor DIAMOnD. Specifically, compared to DIAMOnD, our model achieves a relative increase in hit@30 of 11.6% and a relative increase in hit@100 of 24.1%.

Comparison with Open Targets
To further assess the practical utility of our approach in identifying disease genes, we compared our predictions against those of Open Targets [20], the leading initiative for target identification, with respect to predicting drug targets in clinical trials for Parkinson's disease. To obtain the list of targets in clinical trials, we used Trialtrove [21], the most comprehensive database for clinical trials. To ensure a worst-case comparison, we removed all genes that appeared in the evaluation data from the training data of our models, but we were not able to do the same for the Open Targets model, which obtained an unfair advantage because of that.
In Figure 1, we show a comparison between the top 50 prediction from our best performing model (i.e. relation-weighted RotatE trained on the fully augmented graph) and Open Targets. We observe that, in the top 50 predictions, our model finds more candidates than those listed by Open Targets, while also consistently achieving higher precision than Open Targets.

Conclusion
In this paper, we presented a biomedical knowledge graph designed specifically for disease gene identification, proposed a novel machine learning method that identifies such genes by leveraging recent advances in network biology and graph representation learning, studied the effects of various relation types on prediction performance, and empirically demonstrated that our algorithms outperform its closest state-of-the-art competitor in disease gene identification by 24.1% . We also showed that we achieve higher precision than Open Targets, the leading initiative for target identification, with respect to predicting drug targets in clinical trials for Parkinson's disease.