ComplEx¶

class
ampligraph.latent_features.
ComplEx
(k=100, eta=2, epochs=100, batches_count=100, seed=0, embedding_model_params={'corrupt_sides': ['s+o'], 'negative_corruption_entities': 'all'}, optimizer='adam', optimizer_params={'lr': 0.0005}, loss='nll', loss_params={}, regularizer=None, regularizer_params={}, initializer='xavier', initializer_params={'uniform': False}, verbose=False)¶ Complex embeddings (ComplEx)
The ComplEx model [TWR+16] is an extension of the
ampligraph.latent_features.DistMult
bilinear diagonal model . ComplEx scoring function is based on the trilinear Hermitian dot product in \(\mathcal{C}\):\[f_{ComplEx}=Re(\langle \mathbf{r}_p, \mathbf{e}_s, \overline{\mathbf{e}_o} \rangle)\]ComplEx can be improved if used alongside the nuclear 3norm (the ComplExN3 model [LUO18]), which can be easily added to the loss function via the
regularizer
hyperparameter withp=3
and a chosen regularisation weight (represented bylambda
), as shown in the example below. See alsoampligraph.latent_features.LPRegularizer()
.Note
Since ComplEx embeddings belong to \(\mathcal{C}\), this model uses twice as many parameters as
ampligraph.latent_features.DistMult
.Examples
>>> import numpy as np >>> from ampligraph.latent_features import ComplEx >>> >>> model = ComplEx(batches_count=2, seed=555, epochs=100, k=20, eta=5, >>> loss='pairwise', loss_params={'margin':1}, >>> regularizer='LP', regularizer_params={'p': 2, 'lambda':0.1}) >>> X = np.array([['a', 'y', 'b'], >>> ['b', 'y', 'a'], >>> ['a', 'y', 'c'], >>> ['c', 'y', 'a'], >>> ['a', 'y', 'd'], >>> ['c', 'y', 'd'], >>> ['b', 'y', 'c'], >>> ['f', 'y', 'e']]) >>> model.fit(X) >>> model.predict(np.array([['f', 'y', 'e'], ['b', 'y', 'd']])) [[0.019520484], [0.14998421]] >>> model.get_embeddings(['f','e'], embedding_type='entity') array([[0.33021057, 0.26524785, 0.0446662 , 0.07932718, 0.15453218, 0.22342539, 0.03382565, 0.17444217, 0.03009969, 0.33569157, 0.3200497 , 0.03803705, 0.05536304, 0.00929996, 0.24446663, 0.34408194, 0.16192885, 0.15033236, 0.19703785, 0.00783876, 0.1495124 , 0.3578853 , 0.04975723, 0.03930473, 0.1663541 , 0.24731971, 0.141296 , 0.03150219, 0.15328223, 0.18549544, 0.39240393, 0.10824018, 0.03394471, 0.11075485, 0.1367736 , 0.10059565, 0.32808647, 0.00472086, 0.14231135, 0.13876757], [0.09483694, 0.3531292 , 0.04992269, 0.07774793, 0.1635035 , 0.30610007, 0.3666711 , 0.13785957, 0.3143734 , 0.36909637, 0.13792469, 0.07069954, 0.0368113 , 0.16743314, 0.4090072 , 0.03407392, 0.3113114 , 0.08418448, 0.21435146, 0.12006859, 0.08447982, 0.02025972, 0.38752195, 0.11451488, 0.0258422 , 0.10990044, 0.22661531, 0.00478273, 0.0238297 , 0.14207476, 0.11064807, 0.20135397, 0.22501846, 0.1731076 , 0.2770435 , 0.30784574, 0.15043163, 0.11599299, 0.05718031, 0.1300622 ]], dtype=float32)
Methods
__init__
([k, eta, epochs, batches_count, …])Initialize an EmbeddingModel
fit
(X[, early_stopping, early_stopping_params])Train a ComplEx model.
get_embeddings
(entities[, embedding_type])Get the embeddings of entities or relations.
Returns hyperparameters of the model.
predict
(X[, from_idx])Predict the scores of triples using a trained embedding model.
calibrate
(X_pos[, X_neg, …])Calibrates the predictions using Platt scaling [P+99].
Predicts probabilities using the Platt scaling model (after calibration).

__init__
(k=100, eta=2, epochs=100, batches_count=100, seed=0, embedding_model_params={'corrupt_sides': ['s+o'], 'negative_corruption_entities': 'all'}, optimizer='adam', optimizer_params={'lr': 0.0005}, loss='nll', loss_params={}, regularizer=None, regularizer_params={}, initializer='xavier', initializer_params={'uniform': False}, verbose=False)¶ Initialize an EmbeddingModel
Also creates a new Tensorflow session for training.
 Parameters
k (int) – Embedding space dimensionality
eta (int) – The number of negatives that must be generated at runtime during training for each positive.
epochs (int) – The iterations of the training loop.
batches_count (int) – The number of batches in which the training set must be split during the training loop.
seed (int) – The seed used by the internal random numbers generator.
embedding_model_params (dict) –
ComplExspecific hyperparams:
’negative_corruption_entities’  Entities to be used for generation of corruptions while training. It can take the following values :
all
(default: all entities),batch
(entities present in each batch), list of entities or an int (which indicates how many entities that should be used for corruption generation).corrupt_sides : Specifies how to generate corruptions for training. Takes values s, o, s+o or any combination passed as a list
optimizer (string) – The optimizer used to minimize the loss function. Choose between ‘sgd’, ‘adagrad’, ‘adam’, ‘momentum’.
optimizer_params (dict) –
Arguments specific to the optimizer, passed as a dictionary.
Supported keys:
’lr’ (float): learning rate (used by all the optimizers). Default: 0.1.
’momentum’ (float): learning momentum (only used when
optimizer=momentum
). Default: 0.9.
Example:
optimizer_params={'lr': 0.01}
loss (string) –
The type of loss function to use during training.
pairwise
the model will use pairwise marginbased loss function.nll
the model will use negative loss likelihood.absolute_margin
the model will use absolute margin likelihood.self_adversarial
the model will use adversarial sampling loss function.multiclass_nll
the model will use multiclass nll loss. Switch to multiclass loss defined in [aC15] by passing ‘corrupt_sides’ as [‘s’,’o’] to embedding_model_params. To use loss defined in [KBK17] pass ‘corrupt_sides’ as ‘o’ to embedding_model_params.
loss_params (dict) –
Dictionary of lossspecific hyperparameters. See loss functions documentation for additional details.
Example:
optimizer_params={'lr': 0.01}
ifloss='pairwise'
.regularizer (string) –
The regularization strategy to use with the loss function.
None
: the model will not use any regularizer (default)’LP’: the model will use L1, L2 or L3 based on the value of
regularizer_params['p']
(see below).
regularizer_params (dict) –
Dictionary of regularizerspecific hyperparameters. See the regularizers documentation for additional details.
Example:
regularizer_params={'lambda': 1e5, 'p': 2}
ifregularizer='LP'
.initializer (string) –
The type of initializer to use.
normal
: The embeddings will be initialized from a normal distributionuniform
: The embeddings will be initialized from a uniform distributionxavier
: The embeddings will be initialized using xavier strategy (default)
initializer_params (dict) –
Dictionary of initializerspecific hyperparameters. See the initializer documentation for additional details.
Example:
initializer_params={'mean': 0, 'std': 0.001}
ifinitializer='normal'
.verbose (bool) – Verbose mode.

fit
(X, early_stopping=False, early_stopping_params={})¶ Train a ComplEx model.
The model is trained on a training set X using the training protocol described in [TWR+16].
 Parameters
X (ndarray, shape [n, 3]) – The training triples
early_stopping (bool) –
Flag to enable early stopping (default:False).
If set to
True
, the training loop adopts the following early stopping heuristic:The model will be trained regardless of early stopping for
burn_in
epochs.Every
check_interval
epochs the method will compute the metric specified incriteria
.
If such metric decreases for
stop_interval
checks, we stop training early.Note the metric is computed on
x_valid
. This is usually a validation set that you held out.Also, because
criteria
is a ranking metric, it requires generating negatives. Entities used to generate corruptions can be specified, as long as the side(s) of a triple to corrupt. The method supports filtered metrics, by passing an array of positives tox_filter
. This will be used to filter the negatives generated on the fly (i.e. the corruptions).Note
Keep in mind the early stopping criteria may introduce a certain overhead (caused by the metric computation). The goal is to strike a good tradeoff between such overhead and saving training epochs.
A common approach is to use MRR unfiltered:
early_stopping_params={x_valid=X['valid'], 'criteria': 'mrr'}
Note the size of validation set also contributes to such overhead. In most cases a smaller validation set would be enough.
early_stopping_params (dictionary) –
Dictionary of hyperparameters for the early stopping heuristics.
The following string keys are supported:
’x_valid’: ndarray, shape [n, 3] : Validation set to be used for early stopping.
’criteria’: string : criteria for early stopping ‘hits10’, ‘hits3’, ‘hits1’ or ‘mrr’(default).
’x_filter’: ndarray, shape [n, 3] : Positive triples to use as filter if a ‘filtered’ early stopping criteria is desired (i.e. filteredMRR if ‘criteria’:’mrr’). Note this will affect training time (no filter by default).
’burn_in’: int : Number of epochs to pass before kicking in early stopping (default: 100).
check_interval’: int : Early stopping interval after burnin (default:10).
’stop_interval’: int : Stop if criteria is performing worse over n consecutive checks (default: 3)
’corruption_entities’: List of entities to be used for corruptions. If ‘all’, it uses all entities (default: ‘all’)
’corrupt_side’: Specifies which side to corrupt. ‘s’, ‘o’, ‘s+o’ (default)
Example:
early_stopping_params={x_valid=X['valid'], 'criteria': 'mrr'}

get_embeddings
(entities, embedding_type='entity')¶ Get the embeddings of entities or relations.
Note
Use
ampligraph.utils.create_tensorboard_visualizations()
to visualize the embeddings with TensorBoard. Parameters
entities (arraylike, dtype=int, shape=[n]) – The entities (or relations) of interest. Element of the vector must be the original string literals, and not internal IDs.
embedding_type (string) – If ‘entity’,
entities
argument will be considered as a list of knowledge graph entities (i.e. nodes). If set to ‘relation’, they will be treated as relation types instead (i.e. predicates).
 Returns
embeddings – An array of kdimensional embeddings.
 Return type
ndarray, shape [n, k]

get_hyperparameter_dict
()¶ Returns hyperparameters of the model.
 Returns
hyperparam_dict – Dictionary of hyperparameters that were used for training.
 Return type
dict

predict
(X, from_idx=False)¶ Predict the scores of triples using a trained embedding model. The function returns raw scores generated by the model.
Note
To obtain probability estimates, calibrate the model with
calibrate()
, then callpredict_proba()
. Parameters
X (ndarray, shape [n, 3]) – The triples to score.
from_idx (bool) – If True, will skip conversion to internal IDs. (default: False).
 Returns
scores_predict – The predicted scores for input triples X.
 Return type
ndarray, shape [n]

calibrate
(X_pos, X_neg=None, positive_base_rate=None, batches_count=100, epochs=50)¶ Calibrates the predictions using Platt scaling [P+99].
The calibrated predictions can be obtained with
predict_proba
after the calibration is done.Ideally, calibration should be performed on a validation set that was not used to train the embeddings.
There are two modes of operation, depending on the availability of negative triples:
Both positive and negative triples are provided via
X_pos
andX_neg
respectively. The optimization is done using a secondorder method (limitedmemory BFGS), therefore no hyperparameter needs to be specified.Only positive triples are provided, and the negative triples are generated by corruptions just like it is done in training or evaluation. The optimization is done using a firstorder method (ADAM), therefore
batches_count
andepochs
must be specified.
Calibration is highly dependent on the base rate of positive triples. Therefore, for mode (2) of operation, the user is required to provide the
positive_base_rate
argument. For mode (1), that can be inferred automatically by the relative sizes of the positive and negative sets, but the user can override that by providing a value topositive_base_rate
.Defining the positive base rate is the biggest challenge when calibrating without negatives. That depends on the user choice of which triples will be evaluated during test time. Let’s take WN11 as an example: it has around 50% positives triples on both the validation set and test set, so naturally the positive base rate is 50%. However, should the user resample it to have 75% positives and 25% negatives, its previous calibration will be degraded. The user must recalibrate the model now with a 75% positive base rate. Therefore, this parameter depends on how the user handles the dataset and cannot be determined automatically or a priori.
Note
Incompatible with large graph mode of operation (i.e.,
self.dealing_with_large_graphs
is True). Parameters
X_pos (ndarray (shape [n, 3])) – Numpy array of positive triples.
X_neg (ndarray (shape [n, 3])) –
Numpy array of negative triples.
If None, the negative triples are generated via corruptions and the user must provide a positive base rate instead.
positive_base_rate (float) –
Base rate of positive statements.
For example, if we assume there is a fiftyfifty chance of any query to be true, the base rate would be 50%.
If
X_neg
is provided and this is None, the relative sizes ofX_pos
andX_neg
will be used to determine the base rate. For example, if we have 50 positive triples and 200 negative triples, the positive base rate will be assumed to be 50/(50+200) = 1/5 = 0.2.This must be a value between 0 and 1.
batches_count (int) – Number of batches to complete one epoch of the Platt scaling training. Only applies when
X_neg
is None.epochs (int) – Number of epochs used to train the Platt scaling model. Only applies when
X_neg
is None.
Examples
>>> import numpy as np >>> from sklearn.metrics import brier_score_loss, log_loss >>> from scipy.special import expit >>> >>> from ampligraph.datasets import load_wn11 >>> from ampligraph.latent_features.models import TransE >>> >>> X = load_wn11() >>> X_valid_pos = X['valid'][X['valid_labels']] >>> X_valid_neg = X['valid'][~X['valid_labels']] >>> >>> model = TransE(batches_count=64, seed=0, epochs=500, k=100, eta=20, >>> optimizer='adam', optimizer_params={'lr':0.0001}, >>> loss='pairwise', verbose=True) >>> >>> model.fit(X['train']) >>> >>> # Raw scores >>> scores = model.predict(X['test']) >>> >>> # Calibrate with positives and negatives >>> model.calibrate(X_valid_pos, X_valid_neg, positive_base_rate=None) >>> probas_pos_neg = model.predict_proba(X['test']) >>> >>> # Calibrate with just positives and base rate of 50% >>> model.calibrate(X_valid_pos, positive_base_rate=0.5) >>> probas_pos = model.predict_proba(X['test']) >>> >>> # Calibration evaluation with the Brier score loss (the smaller, the better) >>> print("Brier scores") >>> print("Raw scores:", brier_score_loss(X['test_labels'], expit(scores))) >>> print("Positive and negative calibration:", brier_score_loss(X['test_labels'], probas_pos_neg)) >>> print("Positive only calibration:", brier_score_loss(X['test_labels'], probas_pos)) Brier scores Raw scores: 0.4925058891371126 Positive and negative calibration: 0.20434617882733366 Positive only calibration: 0.22597599585144656

predict_proba
(X)¶ Predicts probabilities using the Platt scaling model (after calibration).
Model must be calibrated beforehand with the
calibrate
method. Parameters
X (ndarray (shape [n, 3])) – Numpy array of triples to be evaluated.
 Returns
probas – Probability of each triple to be true according to the Platt scaling calibration.
 Return type
ndarray (shape [n])
