class ampligraph.latent_features.HolE(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)

Holographic Embeddings

The HolE model [NRP+16] as re-defined by Hayashi et al. [HS17]:

\[f_{HolE}= \frac{2}{n} \, f_{ComplEx}\]


>>> import numpy as np
>>> from ampligraph.latent_features import HolE
>>> model = HolE(batches_count=1, seed=555, epochs=100, k=10, eta=5,
>>>             loss='pairwise', loss_params={'margin':1},
>>>             regularizer='LP', regularizer_params={'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']]))
[[0.009254738], [0.00023370088]]
array([[ 0.2503009 , -0.2598746 , -0.27378836,  0.15603328,  0.28826827,
    -0.19956978,  0.3039347 , -0.2473412 ,  0.08970609, -0.186578  ,
     0.13491984,  0.267222  ,  0.3285695 , -0.26081076, -0.2255996 ,
    -0.42164195,  0.02948518, -0.5940778 , -0.36562866,  0.14355545],
   [-0.18769145,  0.23636112, -0.43104184, -0.32185245,  0.07910233,
     0.20204252,  0.3211268 ,  0.10365302,  0.3958077 , -0.19850788,
    -0.06766941, -0.1205449 ,  0.09295252, -0.45956728, -0.03207169,
    -0.39183694,  0.04791561, -0.11758145, -0.3373933 ,  0.01187571]],


__init__([k, eta, epochs, batches_count, …]) Initialize an EmbeddingModel
fit(X[, early_stopping, early_stopping_params]) Train a HolE 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.

  • 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) –

    HolE-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.
  • 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} if loss='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} if regularizer='LP'.

  • initializer (string) –

    The type of initializer to use.

    • normal: The embeddings will be initialized from a normal distribution
    • uniform: The embeddings will be initialized from a uniform distribution
    • xavier: 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} if initializer='normal'.

  • verbose (bool) – Verbose mode.
fit(X, early_stopping=False, early_stopping_params={})

Train a HolE model.

The model is trained on a training set X using the training protocol described in [NRP+16].

  • 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 in criteria.

    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 to x_filter. This will be used to filter the negatives generated on the fly (i.e. the corruptions).


    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':

    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. 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'}

get_embeddings(entities, embedding_type='entity')

Get the embeddings of entities or relations.


Use ampligraph.utils.create_tensorboard_visualizations() to visualize the embeddings with TensorBoard.

  • 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).

embeddings – An array of k-dimensional embeddings.

Return type:

ndarray, shape [n, k]

predict(X, from_idx=False)

Predict the scores of triples using a trained embedding model.

The function returns raw scores generated by the model.


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)
[-0.06213863, 0.01563319]
>>> from scipy.special import expit
>>> expit(y_pred)
array([0.48447034, 0.5039082 ], dtype=float32)
  • X (ndarray, shape [n, 3]) – The triples to score.
  • from_idx (bool) – If True, will skip conversion to internal IDs. (default: False).

scores_predict – The predicted scores for input triples X.

Return type:

ndarray, shape [n]