Knowledge graph embedding research has overlooked the problem of probability calibration. We show popular embedding models are indeed uncalibrated. That means probability estimates associated to predicted triples are unreliable. We present a novel method to calibrate a model when ground truth negatives are not available, which is the usual case in knowledge graphs. We propose to use Platt scaling and isotonic regression alongside our method. Experiments on three datasets with ground truth negatives show our contribution leads to well calibrated models when compared to the gold standard of using negatives. We get significantly better results than the uncalibrated models from all calibration methods. We show isotonic regression offers the best the performance overall, not without trade-offs. We also show that calibrated models reach state-of-the-art accuracy without the need to define relation-specific decision thresholds. Knowledge graph embedding models are neural architectures that learn vector representations (i.e. embeddings) of nodes and edges of a knowledge graph. Such knowledge graph embeddings have applications in knowledge graph completion, knowledge discovery, entity resolution, and link-based clustering, just to cite a few (Nickel et al., 2016a) . Despite burgeoning research, the problem of calibrating such models has been overlooked, and existing knowledge graph embedding models do not offer any guarantee on the probability estimates they assign to predicted facts. Probability calibration is important whenever you need the predictions to make probabilistic sense, i.e., if the model predicts a fact is true with 80% confidence, it should to be correct 80% of the times. Prior art suggests to use a sigmoid layer to turn logits returned by models into probabilities (Nickel et al., 2016a ) (also called the expit transform), but we show that this provides poor calibration. Figure 1 shows reliability diagrams for off-the-shelf TransE and ComplEx. The identity function represents perfect calibration. Both models are miscalibrated: all TransE combinations in Figure 1a under-forecast the probabilities (i.e. probabilities are too small), whereas ComplEx under-forecasts or over-forecasts according to which loss is used (Figure1b). Calibration is crucial in high-stakes scenarios such as drug-target discovery from biological networks, where end-users need trustworthy and interpretable decisions. Moreover, since probabilities are not calibrated, when classifying triples (i.e. facts) as true or false, users must define relationspecific thresholds, which can be awkward for graphs with a great number of relation types. To the best of our knowledge, this is the first work to focus on calibration for knowledge embeddings. Our contribution is two-fold: First, we use Platt Scaling and isotonic regression to calibrate knowledge graph embedding models on datasets that include ground truth negatives. One peculiar feature of knowledge graphs is that they usually rely on the open world assumption (facts not present are not necessarily false, they are simply unknown). This makes calibration troublesome because of the lack of ground truth negatives. For this reason, our second and main contribution is a calibration heuristics that combines Platt-scaling or isotonic regression with synthetically generated negatives. Experimental results show that we obtain better-calibrated models and that it is possible to calibrate knowledge graph embedding models even when ground truth negatives are not present. We also experiment with triple classification, and we show that calibrated models reach state-of-the-art accuracy without the need to define relation-specific decision thresholds. We propose a method to calibrate knowledge graph embedding models. We target datasets with and without ground truth negatives. We experiment on triple classification datasets and apply Platt scaling and isotonic regression with and without synthetic negatives controlled by our heuristics. All calibration methods perform significantly better than uncalibrated scores. We show that isotonic regression brings better calibration performance, but it is computationally more expensive. Additional experiments on triple classification shows that calibration allows to use a single decision threshold, reaching state-of-the-art results without the need to learn per-relation thresholds. Future work will evaluate additional calibration algorithms, such as beta calibration (Kull et al., 2017) or Bayesian binning (Naeini et al., 2015) . We will also experiment on ensembling of knowledge graph embedding models, inspired by (Krompaß & Tresp, 2015) . The rationale is that different models operate on different scales, but calibrating brings them all to the same probability scale, so their output can be easily combined.
We propose a novel method to calibrate knowledge graph embedding models without the need of negative examples.
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