Note
Click here to download the full example code
EL Embeddings
This example corresponds to the paper EL Embeddings: Geometric Construction of Models for the Description Logic EL++.
The idea of this paper is to embed EL by modeling ontology classes as \(n\)-dimensional balls (\(n\)-balls) and ontology object properties as transformations of those \(n\)-balls. For each of the normal forms, there is a distance function defined that will work as loss functions in the optimization framework.
Let’s just define the imports that will be needed along the example:
import mowl
mowl.init_jvm("10g")
import torch as th
The EL-Embeddings model, maps ontology classes, object properties and operators into a geometric model. The \(\mathcal{EL}\) description logic is expressed using the following General Concept Inclusions (GCIs):
\[\begin{split}\begin{align}
C &\sqsubseteq D & (\text{GCI 0}) \\
C_1 \sqcap C_2 &\sqsubseteq D & (\text{GCI 1}) \\
C &\sqsubseteq \exists R. D & (\text{GCI 2})\\
\exists R. C &\sqsubseteq D & (\text{GCI 3})\\
C &\sqsubseteq \bot & (\text{GCI BOT 0}) \\
C_1 \sqcap C_2 &\sqsubseteq \bot & (\text{GCI BOT 1}) \\
\exists R. C &\sqsubseteq \bot & (\text{GCI BOT 3})
\end{align}\end{split}\]
where \(C,C_1, C_2,D\) are ontology classes and \(R\) is an ontology object property
EL-Embeddings (PyTorch) module.
EL-Embeddings defines a geometric modelling for all the GCIs in the EL language.
The implementation of ELEmbeddings module can be found at mowl.nn.el.elem.module.ELEmModule.
EL-Embeddings model
The module mowl.nn.el.elem.module.ELEmModule is used in the mowl.models.elembeddings.model.ELEmbeddings.
In the use case of this example, we will test over a biological problem, which is
protein-protein interactions. Given two proteins \(p_1,p_2\), the phenomenon
“\(p_1\) interacts with \(p_2\)” is encoded using GCI 2 as:
\[p_1 \sqsubseteq interacts\_with. p_2\]
For that, we can use the class mowl.models.elembeddings.examples.model_ppi.ELEmPPI mode, which uses the mowl.datasets.builtin.PPIYeastSlimDataset dataset.
Training the model
from mowl.datasets.builtin import PPIYeastSlimDataset
from mowl.models.elembeddings.examples.model_ppi import ELEmPPI
dataset = PPIYeastSlimDataset()
model = ELEmPPI(dataset,
embed_dim=30,
margin=0.1,
reg_norm=1,
learning_rate=0.001,
epochs=20,
batch_size=4096,
model_filepath=None,
device='cpu')
model.train()
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1
Evaluating the model
Now, it is time to evaluate embeddings. For this, we use the
ModelRankBasedEvaluator class.
from mowl.evaluation.rank_based import ModelRankBasedEvaluator
with th.no_grad():
model.load_best_model()
evaluator = ModelRankBasedEvaluator(
model,
device = "cpu",
eval_method = model.eval_method
)
evaluator.evaluate(show=True)
['http://4932.Q0010', 'http://4932.Q0017', 'http://4932.Q0032', 'http://4932.Q0045', 'http://4932.Q0050', 'http://4932.Q0055', 'http://4932.Q0060', 'http://4932.Q0065', 'http://4932.Q0070', 'http://4932.Q0075', 'http://4932.Q0080', 'http://4932.Q0085', 'http://4932.Q0092', 'http://4932.Q0105', 'http://4932.Q0110', 'http://4932.Q0115', 'http://4932.Q0120', 'http://4932.Q0130', 'http://4932.Q0140', 'http://4932.Q0142', 'http://4932.Q0143', 'http://4932.Q0160', 'http://4932.Q0182', 'http://4932.Q0250', 'http://4932.Q0255', 'http://4932.Q0275', 'http://4932.Q0297', 'http://4932.YAL001C', 'http://4932.YAL002W', 'http://4932.YAL003W', 'http://4932.YAL004W', 'http://4932.YAL005C', 'http://4932.YAL007C', 'http://4932.YAL008W', 'http://4932.YAL009W', 'http://4932.YAL010C', 'http://4932.YAL011W', 'http://4932.YAL012W', 'http://4932.YAL013W', 'http://4932.YAL014C', 'http://4932.YAL015C', 'http://4932.YAL016C-B', 'http://4932.YAL016W', 'http://4932.YAL017W', 'http://4932.YAL018C', 'http://4932.YAL019W', 'http://4932.YAL020C', 'http://4932.YAL021C', 'http://4932.YAL022C', 'http://4932.YAL023C', 'http://4932.YAL024C', 'http://4932.YAL025C', 'http://4932.YAL026C', 'http://4932.YAL027W', 'http://4932.YAL028W', 'http://4932.YAL029C', 'http://4932.YAL030W', 'http://4932.YAL031C', 'http://4932.YAL032C', 'http://4932.YAL033W', 'http://4932.YAL034C', 'http://4932.YAL034W-A', 'http://4932.YAL035W', 'http://4932.YAL036C', 'http://4932.YAL038W', 'http://4932.YAL039C', 'http://4932.YAL040C', 'http://4932.YAL041W', 'http://4932.YAL042W', 'http://4932.YAL043C', 'http://4932.YAL044C', 'http://4932.YAL044W-A', 'http://4932.YAL046C', 'http://4932.YAL047C', 'http://4932.YAL048C', 'http://4932.YAL049C', 'http://4932.YAL051W', 'http://4932.YAL053W', 'http://4932.YAL054C', 'http://4932.YAL055W', 'http://4932.YAL056C-A', 'http://4932.YAL056W', 'http://4932.YAL058W', 'http://4932.YAL059C-A', 'http://4932.YAL059W', 'http://4932.YAL060W', 'http://4932.YAL061W', 'http://4932.YAL062W', 'http://4932.YAL063C', 'http://4932.YAL064W-B', 'http://4932.YAL065C', 'http://4932.YAL067C', 'http://4932.YAL068C', 'http://4932.YAL068W-A', 'http://4932.YAL069W', 'http://4932.YAR002C-A', 'http://4932.YAR002W', 'http://4932.YAR003W', 'http://4932.YAR007C', 'http://4932.YAR008W', 'http://4932.YAR009C', 'http://4932.YAR010C', 'http://4932.YAR014C', 'http://4932.YAR015W', 'http://4932.YAR018C', 'http://4932.YAR019C', 'http://4932.YAR020C', 'http://4932.YAR023C', 'http://4932.YAR027W', 'http://4932.YAR028W', 'http://4932.YAR029W', 'http://4932.YAR031W', 'http://4932.YAR033W', 'http://4932.YAR035C-A', 'http://4932.YAR035W', 'http://4932.YAR042W', 'http://4932.YAR047C', 'http://4932.YAR050W', 'http://4932.YAR064W', 'http://4932.YAR068W', 'http://4932.YAR070C', 'http://4932.YAR071W', 'http://4932.YAR073W', 'http://4932.YAR075W', 'http://4932.YBL001C', 'http://4932.YBL002W', 'http://4932.YBL003C', 'http://4932.YBL004W', 'http://4932.YBL005W', 'http://4932.YBL005W-A', 'http://4932.YBL005W-B', 'http://4932.YBL006C', 'http://4932.YBL007C', 'http://4932.YBL008W', 'http://4932.YBL009W', 'http://4932.YBL010C', 'http://4932.YBL011W', 'http://4932.YBL012C', 'http://4932.YBL013W', 'http://4932.YBL014C', 'http://4932.YBL015W', 'http://4932.YBL016W', 'http://4932.YBL017C', 'http://4932.YBL018C', 'http://4932.YBL019W', 'http://4932.YBL020W', 'http://4932.YBL021C', 'http://4932.YBL022C', 'http://4932.YBL023C', 'http://4932.YBL024W', 'http://4932.YBL025W', 'http://4932.YBL026W', 'http://4932.YBL027W', 'http://4932.YBL028C', 'http://4932.YBL029C-A', 'http://4932.YBL029W', 'http://4932.YBL030C', 'http://4932.YBL031W', 'http://4932.YBL032W', 'http://4932.YBL033C', 'http://4932.YBL034C', 'http://4932.YBL035C', 'http://4932.YBL036C', 'http://4932.YBL037W', 'http://4932.YBL038W', 'http://4932.YBL039C', 'http://4932.YBL039W-B', 'http://4932.YBL040C', 'http://4932.YBL041W', 'http://4932.YBL042C', 'http://4932.YBL043W', 'http://4932.YBL044W', 'http://4932.YBL045C', 'http://4932.YBL046W', 'http://4932.YBL047C', 'http://4932.YBL048W', 'http://4932.YBL049W', 'http://4932.YBL050W', 'http://4932.YBL051C', 'http://4932.YBL052C', 'http://4932.YBL054W', 'http://4932.YBL055C', 'http://4932.YBL056W', 'http://4932.YBL057C', 'http://4932.YBL058W', 'http://4932.YBL059C-A', 'http://4932.YBL059W', 'http://4932.YBL060W', 'http://4932.YBL061C', 'http://4932.YBL062W', 'http://4932.YBL063W', 'http://4932.YBL064C', 'http://4932.YBL065W', 'http://4932.YBL066C', 'http://4932.YBL067C', 'http://4932.YBL068W', 'http://4932.YBL068W-A', 'http://4932.YBL069W', 'http://4932.YBL070C', 'http://4932.YBL071C', 'http://4932.YBL071W-A', 'http://4932.YBL072C', 'http://4932.YBL074C', 'http://4932.YBL075C', 'http://4932.YBL076C', 'http://4932.YBL077W', 'http://4932.YBL078C', 'http://4932.YBL079W', 'http://4932.YBL080C', 'http://4932.YBL081W', 'http://4932.YBL082C', 'http://4932.YBL083C', 'http://4932.YBL084C', 'http://4932.YBL085W', 'http://4932.YBL086C', 'http://4932.YBL087C', 'http://4932.YBL088C', 'http://4932.YBL089W', 'http://4932.YBL090W', 'http://4932.YBL091C', 'http://4932.YBL091C-A', 'http://4932.YBL092W', 'http://4932.YBL093C', 'http://4932.YBL094C', 'http://4932.YBL095W', 'http://4932.YBL096C', 'http://4932.YBL097W', 'http://4932.YBL098W', 'http://4932.YBL099W', 'http://4932.YBL101C', 'http://4932.YBL102W', 'http://4932.YBL103C', 'http://4932.YBL104C', 'http://4932.YBL105C', 'http://4932.YBL106C', 'http://4932.YBL107C', 'http://4932.YBL108W', 'http://4932.YBL109W', 'http://4932.YBL111C', 'http://4932.YBL113C', 'http://4932.YBL113W-A', 'http://4932.YBR001C', 'http://4932.YBR002C', 'http://4932.YBR003W', 'http://4932.YBR004C', 'http://4932.YBR005W', 'http://4932.YBR006W', 'http://4932.YBR007C', 'http://4932.YBR008C', 'http://4932.YBR009C', 'http://4932.YBR010W', 'http://4932.YBR011C', 'http://4932.YBR012W-B', 'http://4932.YBR013C', 'http://4932.YBR014C', 'http://4932.YBR015C', 'http://4932.YBR016W', 'http://4932.YBR017C', 'http://4932.YBR018C', 'http://4932.YBR019C', 'http://4932.YBR020W', 'http://4932.YBR021W', 'http://4932.YBR022W', 'http://4932.YBR023C', 'http://4932.YBR024W', 'http://4932.YBR025C', 'http://4932.YBR026C', 'http://4932.YBR028C', 'http://4932.YBR029C', 'http://4932.YBR030W', 'http://4932.YBR031W', 'http://4932.YBR032W', 'http://4932.YBR033W', 'http://4932.YBR034C', 'http://4932.YBR035C', 'http://4932.YBR036C', 'http://4932.YBR037C', 'http://4932.YBR038W', 'http://4932.YBR039W', 'http://4932.YBR040W', 'http://4932.YBR041W', 'http://4932.YBR042C', 'http://4932.YBR043C', 'http://4932.YBR044C', 'http://4932.YBR045C', 'http://4932.YBR046C', 'http://4932.YBR047W', 'http://4932.YBR048W', 'http://4932.YBR049C', 'http://4932.YBR050C', 'http://4932.YBR052C', 'http://4932.YBR053C', 'http://4932.YBR054W', 'http://4932.YBR055C', 'http://4932.YBR056W', 'http://4932.YBR056W-A', 'http://4932.YBR057C', 'http://4932.YBR058C', 'http://4932.YBR058C-A', 'http://4932.YBR059C', 'http://4932.YBR060C', 'http://4932.YBR061C', 'http://4932.YBR062C', 'http://4932.YBR065C', 'http://4932.YBR066C', 'http://4932.YBR067C', 'http://4932.YBR068C', 'http://4932.YBR069C', 'http://4932.YBR070C', 'http://4932.YBR071W', 'http://4932.YBR072C-A', 'http://4932.YBR072W', 'http://4932.YBR073W', 'http://4932.YBR074W', 'http://4932.YBR076W', 'http://4932.YBR077C', 'http://4932.YBR078W', 'http://4932.YBR079C', 'http://4932.YBR080C', 'http://4932.YBR081C', 'http://4932.YBR082C', 'http://4932.YBR083W', 'http://4932.YBR084C-A', 'http://4932.YBR084W', 'http://4932.YBR085C-A', 'http://4932.YBR085W', 'http://4932.YBR086C', 'http://4932.YBR087W', 'http://4932.YBR088C', 'http://4932.YBR089C-A', 'http://4932.YBR091C', 'http://4932.YBR092C', 'http://4932.YBR093C', 'http://4932.YBR094W', 'http://4932.YBR095C', 'http://4932.YBR096W', 'http://4932.YBR097W', 'http://4932.YBR098W', 'http://4932.YBR099C', 'http://4932.YBR101C', 'http://4932.YBR102C', 'http://4932.YBR103W', 'http://4932.YBR104W', 'http://4932.YBR105C', 'http://4932.YBR106W', 'http://4932.YBR107C', 'http://4932.YBR108W', 'http://4932.YBR109C', 'http://4932.YBR110W', 'http://4932.YBR111C', 'http://4932.YBR111W-A', 'http://4932.YBR112C', 'http://4932.YBR113W', 'http://4932.YBR114W', 'http://4932.YBR115C', 'http://4932.YBR116C', 'http://4932.YBR117C', 'http://4932.YBR118W', 'http://4932.YBR119W', 'http://4932.YBR120C', 'http://4932.YBR121C', 'http://4932.YBR122C', 'http://4932.YBR123C', 'http://4932.YBR124W', 'http://4932.YBR125C', 'http://4932.YBR126C', 'http://4932.YBR126W-A', 'http://4932.YBR126W-B', 'http://4932.YBR127C', 'http://4932.YBR128C', 'http://4932.YBR129C', 'http://4932.YBR130C', 'http://4932.YBR131C-A', 'http://4932.YBR131W', 'http://4932.YBR132C', 'http://4932.YBR133C', 'http://4932.YBR135W', 'http://4932.YBR136W', 'http://4932.YBR137W', 'http://4932.YBR138C', 'http://4932.YBR139W', 'http://4932.YBR140C', 'http://4932.YBR141C', 'http://4932.YBR142W', 'http://4932.YBR143C', 'http://4932.YBR144C', 'http://4932.YBR145W', 'http://4932.YBR146W', 'http://4932.YBR147W', 'http://4932.YBR148W', 'http://4932.YBR149W', 'http://4932.YBR150C', 'http://4932.YBR151W', 'http://4932.YBR152W', 'http://4932.YBR153W', 'http://4932.YBR154C', 'http://4932.YBR155W', 'http://4932.YBR156C', 'http://4932.YBR157C', 'http://4932.YBR158W', 'http://4932.YBR159W', 'http://4932.YBR160W', 'http://4932.YBR161W', 'http://4932.YBR162C', 'http://4932.YBR162W-A', 'http://4932.YBR163W', 'http://4932.YBR164C', 'http://4932.YBR165W', 'http://4932.YBR166C', 'http://4932.YBR167C', 'http://4932.YBR168W', 'http://4932.YBR169C', 'http://4932.YBR170C', 'http://4932.YBR171W', 'http://4932.YBR172C', 'http://4932.YBR173C', 'http://4932.YBR175W', 'http://4932.YBR176W', 'http://4932.YBR177C', 'http://4932.YBR179C', 'http://4932.YBR180W', 'http://4932.YBR181C', 'http://4932.YBR182C', 'http://4932.YBR182C-A', 'http://4932.YBR183W', 'http://4932.YBR184W', 'http://4932.YBR185C', 'http://4932.YBR186W', 'http://4932.YBR187W', 'http://4932.YBR188C', 'http://4932.YBR189W', 'http://4932.YBR190W', 'http://4932.YBR191W', 'http://4932.YBR191W-A', 'http://4932.YBR192W', 'http://4932.YBR193C', 'http://4932.YBR194W', 'http://4932.YBR195C', 'http://4932.YBR196C', 'http://4932.YBR196C-A', 'http://4932.YBR197C', 'http://4932.YBR198C', 'http://4932.YBR199W', 'http://4932.YBR200W', 'http://4932.YBR200W-A', 'http://4932.YBR201W', 'http://4932.YBR202W', 'http://4932.YBR203W', 'http://4932.YBR204C', 'http://4932.YBR205W', 'http://4932.YBR207W', 'http://4932.YBR208C', 'http://4932.YBR209W', 'http://4932.YBR210W', 'http://4932.YBR211C', 'http://4932.YBR212W', 'http://4932.YBR213W', 'http://4932.YBR214W', 'http://4932.YBR215W', 'http://4932.YBR216C', 'http://4932.YBR217W', 'http://4932.YBR218C', 'http://4932.YBR219C', 'http://4932.YBR220C', 'http://4932.YBR221C', 'http://4932.YBR222C', 'http://4932.YBR223C', 'http://4932.YBR225W', 'http://4932.YBR227C', 'http://4932.YBR228W', 'http://4932.YBR229C', 'http://4932.YBR230C', 'http://4932.YBR230W-A', 'http://4932.YBR231C', 'http://4932.YBR233W', 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10%|# | 1205/12040 [00:07<01:16, 142.02it/s]
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11%|#1 | 1332/12040 [00:08<01:21, 131.93it/s]
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15%|#5 | 1844/12040 [00:11<01:00, 167.56it/s]
15%|#5 | 1865/12040 [00:12<01:16, 133.04it/s]
16%|#5 | 1887/12040 [00:12<01:07, 151.31it/s]
16%|#5 | 1910/12040 [00:12<01:00, 168.32it/s]
16%|#6 | 1929/12040 [00:12<01:16, 132.89it/s]
16%|#6 | 1951/12040 [00:12<01:06, 151.02it/s]
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17%|#6 | 1992/12040 [00:13<01:16, 131.62it/s]
17%|#6 | 2015/12040 [00:13<01:06, 151.39it/s]
17%|#6 | 2037/12040 [00:13<01:00, 165.67it/s]
17%|#7 | 2059/12040 [00:13<00:55, 178.43it/s]
17%|#7 | 2081/12040 [00:13<00:52, 188.81it/s]
17%|#7 | 2102/12040 [00:13<01:09, 142.93it/s]
18%|#7 | 2124/12040 [00:13<01:02, 159.79it/s]
18%|#7 | 2146/12040 [00:13<00:56, 174.12it/s]
18%|#7 | 2166/12040 [00:14<01:12, 135.57it/s]
18%|#8 | 2187/12040 [00:14<01:05, 151.15it/s]
18%|#8 | 2209/12040 [00:14<00:58, 166.83it/s]
19%|#8 | 2228/12040 [00:14<01:14, 131.38it/s]
19%|#8 | 2250/12040 [00:14<01:05, 149.82it/s]
19%|#8 | 2272/12040 [00:14<00:58, 165.77it/s]
19%|#9 | 2291/12040 [00:14<01:14, 131.09it/s]
19%|#9 | 2314/12040 [00:15<01:04, 150.85it/s]
19%|#9 | 2337/12040 [00:15<00:57, 167.71it/s]
20%|#9 | 2356/12040 [00:15<00:56, 172.72it/s]
20%|#9 | 2379/12040 [00:15<00:52, 185.54it/s]
20%|#9 | 2399/12040 [00:15<01:08, 140.53it/s]
20%|## | 2418/12040 [00:15<01:03, 150.68it/s]
20%|## | 2440/12040 [00:15<00:57, 166.67it/s]
20%|## | 2462/12040 [00:15<00:53, 179.83it/s]
21%|## | 2482/12040 [00:16<01:11, 134.45it/s]
21%|## | 2502/12040 [00:16<01:04, 147.95it/s]
21%|## | 2523/12040 [00:16<00:58, 162.33it/s]
21%|##1 | 2542/12040 [00:16<01:14, 127.17it/s]
21%|##1 | 2561/12040 [00:16<01:08, 139.20it/s]
21%|##1 | 2579/12040 [00:16<01:22, 115.05it/s]
22%|##1 | 2601/12040 [00:16<01:09, 136.22it/s]
22%|##1 | 2622/12040 [00:17<01:02, 151.59it/s]
22%|##1 | 2640/12040 [00:17<01:00, 156.24it/s]
22%|##2 | 2661/12040 [00:17<00:55, 168.66it/s]
22%|##2 | 2682/12040 [00:17<01:11, 130.47it/s]
22%|##2 | 2704/12040 [00:17<01:02, 149.19it/s]
23%|##2 | 2724/12040 [00:17<00:58, 160.32it/s]
23%|##2 | 2745/12040 [00:17<00:54, 170.93it/s]
23%|##2 | 2764/12040 [00:18<01:13, 127.04it/s]
23%|##3 | 2785/12040 [00:18<01:04, 143.68it/s]
23%|##3 | 2806/12040 [00:18<00:58, 158.98it/s]
23%|##3 | 2825/12040 [00:18<01:12, 127.24it/s]
24%|##3 | 2846/12040 [00:18<01:03, 144.71it/s]
24%|##3 | 2868/12040 [00:18<00:56, 161.83it/s]
24%|##3 | 2887/12040 [00:18<01:11, 128.74it/s]
24%|##4 | 2909/12040 [00:19<01:01, 148.20it/s]
24%|##4 | 2931/12040 [00:19<00:55, 164.75it/s]
25%|##4 | 2953/12040 [00:19<00:51, 177.25it/s]
25%|##4 | 2975/12040 [00:19<00:48, 188.17it/s]
25%|##4 | 2996/12040 [00:19<01:04, 139.95it/s]
25%|##5 | 3015/12040 [00:19<01:00, 150.07it/s]
25%|##5 | 3037/12040 [00:19<00:54, 165.70it/s]
25%|##5 | 3059/12040 [00:19<00:50, 178.82it/s]
26%|##5 | 3079/12040 [00:20<01:05, 136.65it/s]
26%|##5 | 3101/12040 [00:20<00:57, 154.43it/s]
26%|##5 | 3121/12040 [00:20<00:54, 165.02it/s]
26%|##6 | 3140/12040 [00:20<01:08, 129.37it/s]
26%|##6 | 3163/12040 [00:20<00:59, 149.50it/s]
26%|##6 | 3181/12040 [00:20<01:12, 122.47it/s]
27%|##6 | 3204/12040 [00:20<01:01, 143.39it/s]
27%|##6 | 3226/12040 [00:21<00:54, 160.31it/s]
27%|##6 | 3248/12040 [00:21<00:50, 174.18it/s]
27%|##7 | 3271/12040 [00:21<00:46, 187.36it/s]
27%|##7 | 3292/12040 [00:21<01:01, 142.44it/s]
28%|##7 | 3315/12040 [00:21<00:54, 160.67it/s]
28%|##7 | 3338/12040 [00:21<00:49, 174.17it/s]
28%|##7 | 3358/12040 [00:21<00:48, 180.49it/s]
28%|##8 | 3378/12040 [00:22<01:02, 138.84it/s]
28%|##8 | 3401/12040 [00:22<00:54, 157.56it/s]
28%|##8 | 3423/12040 [00:22<01:06, 130.17it/s]
29%|##8 | 3445/12040 [00:22<00:58, 147.69it/s]
29%|##8 | 3468/12040 [00:22<00:52, 164.83it/s]
29%|##8 | 3487/12040 [00:22<01:05, 131.11it/s]
29%|##9 | 3510/12040 [00:22<00:56, 150.43it/s]
29%|##9 | 3533/12040 [00:23<00:50, 167.66it/s]
30%|##9 | 3556/12040 [00:23<00:46, 181.22it/s]
30%|##9 | 3578/12040 [00:23<00:44, 191.09it/s]
30%|##9 | 3599/12040 [00:23<00:58, 144.41it/s]
30%|### | 3622/12040 [00:23<00:51, 162.06it/s]
30%|### | 3645/12040 [00:23<00:47, 176.67it/s]
30%|### | 3665/12040 [00:23<01:00, 137.67it/s]
31%|### | 3688/12040 [00:24<00:53, 156.36it/s]
31%|### | 3711/12040 [00:24<00:48, 172.32it/s]
31%|### | 3731/12040 [00:24<01:01, 135.97it/s]
31%|###1 | 3754/12040 [00:24<00:53, 154.74it/s]
31%|###1 | 3775/12040 [00:24<01:04, 127.90it/s]
32%|###1 | 3796/12040 [00:24<00:57, 143.55it/s]
32%|###1 | 3817/12040 [00:24<00:52, 156.68it/s]
32%|###1 | 3837/12040 [00:25<00:49, 166.38it/s]
32%|###2 | 3856/12040 [00:25<00:48, 169.88it/s]
32%|###2 | 3875/12040 [00:25<00:49, 164.54it/s]
32%|###2 | 3893/12040 [00:25<01:04, 126.46it/s]
33%|###2 | 3914/12040 [00:25<00:56, 143.61it/s]
33%|###2 | 3936/12040 [00:25<00:50, 161.02it/s]
33%|###2 | 3958/12040 [00:25<01:01, 130.81it/s]
33%|###3 | 3980/12040 [00:26<00:53, 149.60it/s]
33%|###3 | 4001/12040 [00:26<00:49, 162.81it/s]
33%|###3 | 4021/12040 [00:26<01:01, 129.76it/s]
34%|###3 | 4042/12040 [00:26<00:54, 146.29it/s]
34%|###3 | 4064/12040 [00:26<00:49, 161.83it/s]
34%|###3 | 4083/12040 [00:26<01:03, 124.95it/s]
34%|###4 | 4106/12040 [00:26<00:54, 145.92it/s]
34%|###4 | 4129/12040 [00:26<00:48, 163.97it/s]
34%|###4 | 4152/12040 [00:27<00:44, 178.94it/s]
35%|###4 | 4174/12040 [00:27<00:41, 189.17it/s]
35%|###4 | 4195/12040 [00:27<00:54, 143.15it/s]
35%|###5 | 4218/12040 [00:27<00:48, 161.09it/s]
35%|###5 | 4240/12040 [00:27<00:44, 175.06it/s]
35%|###5 | 4260/12040 [00:27<00:56, 136.77it/s]
36%|###5 | 4282/12040 [00:27<00:50, 154.61it/s]
36%|###5 | 4305/12040 [00:28<00:45, 170.68it/s]
36%|###5 | 4325/12040 [00:28<00:57, 134.89it/s]
36%|###6 | 4347/12040 [00:28<00:50, 152.93it/s]
36%|###6 | 4370/12040 [00:28<00:45, 169.28it/s]
36%|###6 | 4390/12040 [00:28<00:56, 134.24it/s]
37%|###6 | 4413/12040 [00:28<00:49, 153.61it/s]
37%|###6 | 4436/12040 [00:28<00:44, 170.38it/s]
37%|###7 | 4459/12040 [00:29<00:41, 184.21it/s]
37%|###7 | 4480/12040 [00:29<00:53, 142.01it/s]
37%|###7 | 4503/12040 [00:29<00:47, 160.02it/s]
38%|###7 | 4526/12040 [00:29<00:42, 175.30it/s]
38%|###7 | 4548/12040 [00:29<00:40, 185.02it/s]
38%|###7 | 4569/12040 [00:29<00:52, 142.02it/s]
38%|###8 | 4592/12040 [00:29<00:46, 159.95it/s]
38%|###8 | 4615/12040 [00:30<00:42, 175.01it/s]
38%|###8 | 4635/12040 [00:30<00:54, 137.01it/s]
39%|###8 | 4658/12040 [00:30<00:47, 155.50it/s]
39%|###8 | 4677/12040 [00:30<00:57, 127.17it/s]
39%|###9 | 4700/12040 [00:30<00:49, 147.34it/s]
39%|###9 | 4723/12040 [00:30<00:44, 164.92it/s]
39%|###9 | 4746/12040 [00:30<00:40, 179.51it/s]
40%|###9 | 4769/12040 [00:30<00:38, 191.00it/s]
40%|###9 | 4790/12040 [00:31<00:50, 144.61it/s]
40%|###9 | 4813/12040 [00:31<00:44, 161.94it/s]
40%|#### | 4836/12040 [00:31<00:40, 176.37it/s]
40%|#### | 4856/12040 [00:31<00:52, 137.03it/s]
40%|#### | 4876/12040 [00:31<00:48, 147.46it/s]
41%|#### | 4898/12040 [00:31<00:43, 163.94it/s]
41%|#### | 4918/12040 [00:32<00:54, 131.33it/s]
41%|####1 | 4940/12040 [00:32<00:47, 149.57it/s]
41%|####1 | 4963/12040 [00:32<00:42, 166.51it/s]
41%|####1 | 4982/12040 [00:32<00:53, 131.90it/s]
42%|####1 | 5005/12040 [00:32<00:46, 151.46it/s]
42%|####1 | 5028/12040 [00:32<00:41, 168.28it/s]
42%|####1 | 5051/12040 [00:32<00:38, 180.79it/s]
42%|####2 | 5073/12040 [00:32<00:36, 190.40it/s]
42%|####2 | 5094/12040 [00:33<00:48, 142.60it/s]
42%|####2 | 5117/12040 [00:33<00:43, 160.47it/s]
43%|####2 | 5140/12040 [00:33<00:39, 175.16it/s]
43%|####2 | 5160/12040 [00:33<00:50, 136.96it/s]
43%|####3 | 5183/12040 [00:33<00:44, 155.35it/s]
43%|####3 | 5206/12040 [00:33<00:40, 170.83it/s]
43%|####3 | 5226/12040 [00:34<00:50, 135.02it/s]
44%|####3 | 5249/12040 [00:34<00:44, 153.62it/s]
44%|####3 | 5270/12040 [00:34<00:53, 126.85it/s]
44%|####3 | 5293/12040 [00:34<00:46, 146.28it/s]
44%|####4 | 5316/12040 [00:34<00:41, 163.58it/s]
44%|####4 | 5339/12040 [00:34<00:37, 178.08it/s]
45%|####4 | 5362/12040 [00:34<00:35, 189.64it/s]
45%|####4 | 5383/12040 [00:35<00:46, 144.28it/s]
45%|####4 | 5406/12040 [00:35<00:41, 161.65it/s]
45%|####5 | 5427/12040 [00:35<00:38, 172.92it/s]
45%|####5 | 5450/12040 [00:35<00:35, 185.62it/s]
45%|####5 | 5471/12040 [00:35<00:46, 141.54it/s]
46%|####5 | 5494/12040 [00:35<00:41, 159.25it/s]
46%|####5 | 5516/12040 [00:35<00:49, 131.09it/s]
46%|####5 | 5538/12040 [00:36<00:43, 148.54it/s]
46%|####6 | 5561/12040 [00:36<00:39, 165.26it/s]
46%|####6 | 5580/12040 [00:36<00:48, 132.05it/s]
47%|####6 | 5603/12040 [00:36<00:42, 151.43it/s]
47%|####6 | 5626/12040 [00:36<00:38, 168.34it/s]
47%|####6 | 5649/12040 [00:36<00:35, 181.92it/s]
47%|####7 | 5672/12040 [00:36<00:44, 142.76it/s]
47%|####7 | 5694/12040 [00:37<00:39, 159.03it/s]
47%|####7 | 5717/12040 [00:37<00:36, 174.12it/s]
48%|####7 | 5739/12040 [00:37<00:34, 183.92it/s]
48%|####7 | 5760/12040 [00:37<00:44, 141.64it/s]
48%|####8 | 5783/12040 [00:37<00:39, 159.37it/s]
48%|####8 | 5806/12040 [00:37<00:35, 174.25it/s]
48%|####8 | 5826/12040 [00:37<00:45, 136.54it/s]
49%|####8 | 5846/12040 [00:37<00:41, 148.65it/s]
49%|####8 | 5868/12040 [00:38<00:49, 125.36it/s]
49%|####8 | 5891/12040 [00:38<00:42, 145.16it/s]
49%|####9 | 5914/12040 [00:38<00:37, 162.61it/s]
49%|####9 | 5937/12040 [00:38<00:34, 177.47it/s]
50%|####9 | 5960/12040 [00:38<00:32, 189.31it/s]
50%|####9 | 5981/12040 [00:38<00:42, 144.21it/s]
50%|####9 | 6004/12040 [00:38<00:37, 161.62it/s]
50%|##### | 6027/12040 [00:39<00:34, 176.21it/s]
50%|##### | 6050/12040 [00:39<00:31, 187.92it/s]
50%|##### | 6071/12040 [00:39<00:41, 143.54it/s]
51%|##### | 6094/12040 [00:39<00:36, 160.74it/s]
51%|##### | 6114/12040 [00:39<00:45, 130.27it/s]
51%|##### | 6136/12040 [00:39<00:39, 148.18it/s]
51%|#####1 | 6159/12040 [00:39<00:35, 165.06it/s]
51%|#####1 | 6178/12040 [00:40<00:44, 131.64it/s]
52%|#####1 | 6201/12040 [00:40<00:38, 151.06it/s]
52%|#####1 | 6224/12040 [00:40<00:34, 167.92it/s]
52%|#####1 | 6247/12040 [00:40<00:31, 181.96it/s]
52%|#####2 | 6270/12040 [00:40<00:40, 142.67it/s]
52%|#####2 | 6292/12040 [00:40<00:36, 158.85it/s]
52%|#####2 | 6315/12040 [00:40<00:32, 174.02it/s]
53%|#####2 | 6337/12040 [00:41<00:30, 185.43it/s]
53%|#####2 | 6358/12040 [00:41<00:39, 142.28it/s]
53%|#####2 | 6381/12040 [00:41<00:35, 159.80it/s]
53%|#####3 | 6403/12040 [00:41<00:32, 172.85it/s]
53%|#####3 | 6423/12040 [00:41<00:41, 135.81it/s]
53%|#####3 | 6441/12040 [00:41<00:38, 145.11it/s]
54%|#####3 | 6464/12040 [00:41<00:34, 163.26it/s]
54%|#####3 | 6483/12040 [00:42<00:42, 129.63it/s]
54%|#####4 | 6506/12040 [00:42<00:36, 149.96it/s]
54%|#####4 | 6529/12040 [00:42<00:33, 166.93it/s]
54%|#####4 | 6552/12040 [00:42<00:30, 180.98it/s]
55%|#####4 | 6572/12040 [00:42<00:39, 139.50it/s]
55%|#####4 | 6595/12040 [00:42<00:34, 157.87it/s]
55%|#####4 | 6618/12040 [00:42<00:31, 173.24it/s]
55%|#####5 | 6641/12040 [00:42<00:29, 185.50it/s]
55%|#####5 | 6662/12040 [00:43<00:37, 142.33it/s]
56%|#####5 | 6685/12040 [00:43<00:33, 159.97it/s]
56%|#####5 | 6707/12040 [00:43<00:30, 174.01it/s]
56%|#####5 | 6727/12040 [00:43<00:39, 136.04it/s]
56%|#####6 | 6749/12040 [00:43<00:34, 153.87it/s]
56%|#####6 | 6767/12040 [00:43<00:42, 125.10it/s]
56%|#####6 | 6790/12040 [00:44<00:36, 145.81it/s]
57%|#####6 | 6813/12040 [00:44<00:32, 163.25it/s]
57%|#####6 | 6836/12040 [00:44<00:29, 177.65it/s]
57%|#####6 | 6859/12040 [00:44<00:27, 189.09it/s]
57%|#####7 | 6880/12040 [00:44<00:35, 143.92it/s]
57%|#####7 | 6903/12040 [00:44<00:31, 161.41it/s]
58%|#####7 | 6926/12040 [00:44<00:29, 175.94it/s]
58%|#####7 | 6948/12040 [00:45<00:36, 139.37it/s]
58%|#####7 | 6969/12040 [00:45<00:33, 153.64it/s]
58%|#####8 | 6991/12040 [00:45<00:29, 168.57it/s]
58%|#####8 | 7011/12040 [00:45<00:37, 133.68it/s]
58%|#####8 | 7033/12040 [00:45<00:33, 151.53it/s]
59%|#####8 | 7054/12040 [00:45<00:30, 164.91it/s]
59%|#####8 | 7073/12040 [00:45<00:37, 130.90it/s]
59%|#####8 | 7095/12040 [00:46<00:33, 149.42it/s]
59%|#####9 | 7117/12040 [00:46<00:29, 164.42it/s]
59%|#####9 | 7140/12040 [00:46<00:27, 178.90it/s]
59%|#####9 | 7163/12040 [00:46<00:25, 190.55it/s]
60%|#####9 | 7184/12040 [00:46<00:33, 144.21it/s]
60%|#####9 | 7207/12040 [00:46<00:29, 161.82it/s]
60%|###### | 7230/12040 [00:46<00:27, 176.42it/s]
60%|###### | 7250/12040 [00:47<00:34, 138.02it/s]
60%|###### | 7273/12040 [00:47<00:30, 156.34it/s]
61%|###### | 7295/12040 [00:47<00:27, 171.10it/s]
61%|###### | 7315/12040 [00:47<00:35, 134.76it/s]
61%|###### | 7338/12040 [00:47<00:30, 153.47it/s]
61%|######1 | 7360/12040 [00:47<00:27, 168.64it/s]
61%|######1 | 7380/12040 [00:47<00:34, 133.99it/s]
61%|######1 | 7403/12040 [00:47<00:30, 153.18it/s]
62%|######1 | 7426/12040 [00:48<00:27, 169.61it/s]
62%|######1 | 7449/12040 [00:48<00:25, 182.96it/s]
62%|######2 | 7470/12040 [00:48<00:32, 139.86it/s]
62%|######2 | 7493/12040 [00:48<00:28, 157.83it/s]
62%|######2 | 7516/12040 [00:48<00:26, 172.98it/s]
63%|######2 | 7539/12040 [00:48<00:24, 185.32it/s]
63%|######2 | 7560/12040 [00:48<00:31, 142.51it/s]
63%|######2 | 7583/12040 [00:49<00:27, 159.87it/s]
63%|######3 | 7605/12040 [00:49<00:25, 173.82it/s]
63%|######3 | 7625/12040 [00:49<00:32, 135.90it/s]
64%|######3 | 7648/12040 [00:49<00:28, 154.46it/s]
64%|######3 | 7666/12040 [00:49<00:34, 125.45it/s]
64%|######3 | 7689/12040 [00:49<00:29, 145.81it/s]
64%|######4 | 7712/12040 [00:49<00:26, 163.43it/s]
64%|######4 | 7735/12040 [00:50<00:24, 178.05it/s]
64%|######4 | 7758/12040 [00:50<00:22, 189.27it/s]
65%|######4 | 7779/12040 [00:50<00:29, 143.97it/s]
65%|######4 | 7802/12040 [00:50<00:26, 161.38it/s]
65%|######4 | 7825/12040 [00:50<00:23, 175.83it/s]
65%|######5 | 7845/12040 [00:50<00:30, 137.95it/s]
65%|######5 | 7867/12040 [00:50<00:26, 155.03it/s]
66%|######5 | 7890/12040 [00:51<00:24, 170.87it/s]
66%|######5 | 7910/12040 [00:51<00:30, 134.89it/s]
66%|######5 | 7932/12040 [00:51<00:26, 152.81it/s]
66%|######6 | 7954/12040 [00:51<00:24, 168.03it/s]
66%|######6 | 7974/12040 [00:51<00:30, 133.41it/s]
66%|######6 | 7992/12040 [00:51<00:28, 143.11it/s]
67%|######6 | 8014/12040 [00:51<00:25, 160.52it/s]
67%|######6 | 8034/12040 [00:51<00:23, 168.97it/s]
67%|######6 | 8053/12040 [00:52<00:22, 173.74it/s]
67%|######7 | 8072/12040 [00:52<00:29, 132.85it/s]
67%|######7 | 8095/12040 [00:52<00:25, 153.11it/s]
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100%|##########| 12040/12040 [01:17<00:00, 154.47it/s]
Hits@1: 0.00 Filtered: 0.00
Hits@10: 0.00 Filtered: 0.00
Hits@100: 0.02 Filtered: 0.02
MR: 2820.77 Filtered: 2766.16
AUC: 0.53 Filtered: 0.54
Evaluation finished. Access the results using the "metrics" attribute.
Total running time of the script: ( 3 minutes 31.689 seconds)
Estimated memory usage: 3429 MB