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 3-norm (the ComplEx-N3 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. predict
(X[, from_idx])Predict the scores of triples using a trained embedding model. -
__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) –
ComplEx-specific 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
- ’negative_corruption_entities’ - Entities to be used for generation of corruptions while training.
It can take the following values :
- 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 margin-based 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 loss-specific 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 regularizer-specific hyperparameters. See the regularizers documentation for additional details.
Example:
regularizer_params={'lambda': 1e-5, '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 initializer-specific hyperparameters. See the initializer documentation for additional details.
Example:
initializer_params={'mean': 0, 'std': 0.001}
ifinitializer='normal'
. - verbose (bool) – Verbose mode.
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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 trade-off 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.
- The model will be trained regardless of early stopping for
- 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. filtered-MRR 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 burn-in (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'}
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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 (array-like, 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 k-dimensional embeddings.
Return type: ndarray, shape [n, k]
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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, use a logistic sigmoid:
>>> model.fit(X) >>> y_pred = model.predict(np.array([['f', 'y', 'e'], ['b', 'y', 'd']])) >>> print(y_pred) [-0.31336197, 0.07829369] >>> from scipy.special import expit >>> expit(y_pred) array([0.42229432, 0.51956344], dtype=float32)
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]
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