Performance¶
Predictive Performance¶
We report the filtered MR, MRR, Hits@1,3,10 for the most common datasets used in literature.
FB15K-237¶
| Model | MR | MRR | Hits@1 | Hits@3 | Hits@10 | Hyperparameters |
|---|---|---|---|---|---|---|
| TransE | 208 | 0.31 | 0.22 | 0.35 | 0.50 | k: 400; epochs: 4000; eta: 30; loss: multiclass_nll; regularizer: LP; regularizer_params: lambda: 0.0001; p: 2; optimizer: adam; optimizer_params: lr: 0.0001; embedding_model_params: norm: 1; normalize_ent_emb: false; seed: 0; batches_count: 64; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| DistMult | 201 | 0.31 | 0.22 | 0.34 | 0.49 | k: 300; epochs: 4000; eta: 50; loss: multiclass_nll; regularizer: LP; regularizer_params: lambda: 0.0001; p: 3; optimizer: adam; optimizer_params: lr: 0.00005; seed: 0; batches_count: 50; normalize_ent_emb: false; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| ComplEx | 186 | 0.32 | 0.22 | 0.35 | 0.50 | k: 350; epochs: 4000; eta: 30; loss: multiclass_nll; optimizer: adam; optimizer_params: lr: 0.00005; seed: 0; regularizer: LP; regularizer_params: lambda: 0.0001; p: 3; batches_count: 64; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| HolE | 182 | 0.31 | 0.21 | 0.34 | 0.48 | k: 350; epochs: 4000; eta: 50; loss: multiclass_nll; regularizer: LP; regularizer_params: lambda: 0.0001; p: 2; optimizer: adam; optimizer_params: lr: 0.0001; seed: 0; batches_count: 64; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
Note
FB15K-237 validation and test sets include triples with entities that do not occur in the training set. We found 8 unseen entities in the validation set and 29 in the test set. In the experiments we excluded the triples where such entities appear (9 triples in from the validation set and 28 from the test set).
WN18RR¶
| Model | MR | MRR | Hits@1 | Hits@3 | Hits@10 | Hyperparameters |
|---|---|---|---|---|---|---|
| TransE | 2929 | 0.22 | 0.03 | 0.39 | 0.54 | k: 350; epochs: 4000; eta: 30; loss: multiclass_nll; optimizer: adam; optimizer_params: lr: 0.0001; regularizer: LP; regularizer_params: lambda: 0.0001; p: 2; seed: 0; normalize_ent_emb: false; embedding_model_params: norm: 1; batches_count: 150; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| DistMult | 5186 | 0.45 | 0.45 | 0.49 | 0.54 | k: 350; epochs: 4000; eta: 30; loss: multiclass_nll; optimizer: adam; optimizer_params: lr: 0.0001; regularizer: LP; regularizer_params: lambda: 0.0001; p: 2; seed: 0; normalize_ent_emb: false; batches_count: 100; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| ComplEx | 4550 | 0.50 | 0.47 | 0.52 | 0.57 | k: 200; epochs: 4000; eta: 20; loss: multiclass_nll; loss_params: margin: 1; optimizer: adam; optimizer_params: lr: 0.0005; seed: 0; regularizer: LP; regularizer_params: lambda: 0.05; p: 3; batches_count: 10; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| HolE | 7236 | 0.47 | 0.43 | 0.48 | 0.53 | k: 200; epochs: 4000; eta: 20; loss: self_adversarial; loss_params: margin: 1; optimizer: adam; optimizer_params: lr: 0.0005; seed: 0; batches_count: 50; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
Note
WN18RR validation and test sets include triples with entities that do not occur in the training set. We found 198 unseen entities in the validation set and 209 in the test set. In the experiments we excluded the triples where such entities appear (210 triples in from the validation set and 210 from the test set).
YAGO3-10¶
| Model | MR | MRR | Hits@1 | Hits@3 | Hits@10 | Hyperparameters |
|---|---|---|---|---|---|---|
| TransE | 1124 | 0.49 | 0.39 | 0.56 | 0.67 | k: 350; epochs: 4000; eta: 30; loss: multiclass_nll; optimizer: adam; optimizer_params: lr: 0.0001; regularizer: LP; regularizer_params: lambda: 0.0001; p: 2; embedding_model_params: norm: 1; normalize_ent_emb: false; seed: 0; batches_count: 100; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| DistMult | 1063 | 0.49 | 0.40 | 0.55 | 0.56 | k: 350; epochs: 4000; eta: 50; loss: multiclass_nll; optimizer: adam; optimizer_params: lr: 5e-05; regularizer: LP; regularizer_params: lambda: 0.0001; p: 3; seed: 0; normalize_ent_emb: false; batches_count: 100; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| ComplEx | 1508 | 0.50 | 0.41 | 0.55 | 0.66 | k: 350; epochs: 4000; eta: 30; loss: multiclass_nll; optimizer: adam; optimizer_params: lr: 5e-05; regularizer: LP; regularizer_params: lambda: 0.0001; p: 3; seed: 0; batches_count: 100 early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| HolE | 6365 | 0.50 | 0.42 | 0.55 | 0.65 | k: 350; epochs: 4000; eta: 30; loss: self_adversarial; loss_params: alpha: 1; margin: 0.5; optimizer: adam; optimizer_params: lr: 0.0001; seed: 0; batches_count: 100 early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
Note
YAGO3-10 validation and test sets include triples with entities that do not occur in the training set. We found 22 unseen entities in the validation set and 18 in the test set. In the experiments we excluded the triples where such entities appear (22 triples in from the validation set and 18 from the test set).
FB15K¶
Warning
The dataset includes a large number of inverse relations, and its use in experiments has been deprecated. Use FB15k-237 instead.
| Model | MR | MRR | Hits@1 | Hits@3 | Hits@10 | Hyperparameters |
|---|---|---|---|---|---|---|
| TransE | 44 | 0.63 | 0.50 | 0.73 | 0.85 | k: 150; epochs: 4000; eta: 10; loss: multiclass_nll; optimizer: adam; optimizer_params: lr: 5e-5; regularizer: LP; regularizer_params: lambda: 0.0001; p: 3; embedding_model_params: norm: 1; normalize_ent_emb: false; seed: 0; batches_count: 100; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| DistMult | 179 | 0.78 | 0.74 | 0.82 | 0.86 | k: 200; epochs: 4000; eta: 20; loss: self_adversarial; loss_params: margin: 1; optimizer: adam; optimizer_params: lr: 0.0005; seed: 0; normalize_ent_emb: false; batches_count: 50; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| ComplEx | 183 | 0.80 | 0.75 | 0.82 | 0.87 | k: 200; epochs: 4000; eta: 20; loss: self_adversarial; loss_params: margin: 1; optimizer: adam; optimizer_params: lr: 0.0005; seed: 0; batches_count: 100; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| HolE | 215 | 0.80 | 0.76 | 0.83 | 0.87 | k: 200; epochs: 4000; eta: 20; loss: self_adversarial; loss_params: margin: 1; optimizer: adam; optimizer_params: lr: 0.0005; seed: 0; batches_count: 50; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
WN18¶
Warning
The dataset includes a large number of inverse relations, and its use in experiments has been deprecated. Use WN18RR instead.
| Model | MR | MRR | Hits@1 | Hits@3 | Hits@10 | Hyperparameters |
|---|---|---|---|---|---|---|
| TransE | 262 | 0.65 | 0.41 | 0.88 | 0.95 | k: 150; epochs: 4000; eta: 10; loss: multiclass_nll; optimizer: adam; optimizer_params: lr: 5e-5; regularizer: LP; regularizer_params: lambda: 0.0001; p: 3; embedding_model_params: norm: 1; normalize_ent_emb: false; seed: 0; batches_count: 100; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| DistMult | 755 | 0.82 | 0.72 | 0.92 | 0.94 | k: 200; epochs: 4000; eta: 20; loss: nll; loss_params: margin: 1; optimizer: adam; optimizer_params: lr: 0.0005; seed: 0; normalize_ent_emb: false; batches_count: 50; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| ComplEx | 749 | 0.94 | 0.94 | 0.95 | 0.95 | k: 200; epochs: 4000; eta: 20; loss: nll; loss_params: margin: 1; optimizer: adam; optimizer_params: lr: 0.0005; seed: 0; batches_count: 50; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
| HolE | 641 | 0.93 | 0.93 | 0.94 | 0.95 | k: 200; epochs: 4000; eta: 20; loss: self_adversarial; loss_params: margin: 1; optimizer: adam; optimizer_params: lr: 0.0005; seed: 0; batches_count: 50; early_stopping:{ x_valid: validation[::10], criteria: mrr, x_filter: train + validation + test, stop_interval: 2, burn_in: 0, check_interval: 100 }; |
To reproduce the above results:
$ cd experiments
$ python predictive_performance.py
Note
Running predictive_performance.py on all datasets, for all models takes ~53 hours on
an Intel Xeon Gold 6142, 64 GB Ubuntu 16.04 box equipped with a Tesla V100 16GB.
Experiments can be limited to specific models-dataset combinations as follows:
$ python predictive_performance.py -h
usage: predictive_performance.py [-h] [-d {fb15k,fb15k-237,wn18,wn18rr,yago310}]
[-m {complex,transe,distmult,hole}]
optional arguments:
-h, --help show this help message and exit
-d {fb15k,fb15k-237,wn18,wn18rr,yago310}, --dataset {fb15k,fb15k-237,wn18,wn18rr,yago310}
-m {complex,transe,distmult,hole}, --model {complex,transe,distmult,hole}
Runtime Performance¶
Training the models on FB15K-237 (k=350, eta=30, batches_count=100, loss=multiclass_nll), on an Intel Xeon Gold 6142, 64 GB
Ubuntu 16.04 box equipped with a Tesla V100 16GB gives the following runtime report:
| model | seconds/epoch |
|---|---|
| ComplEx | 3.40 |
| TransE | 2.39 |
| DistMult | 2.40 |
| HolE | 3.30 |