FwFMClassifier

Field-weighted Factorization Machine for binary classification.

The model equation is defined as:

\[\hat{y}(x) = w_{0} + \sum_{j=1}^{p} w_{j} x_{j} + \sum_{j=1}^{p} \sum_{j'=j+1}^{p} r_{f_j, f_{j'}} \langle \mathbf{v}_j, \mathbf{v}_{j'} \rangle x_{j} x_{j'}\]

Where \(f_j\) and \(f_{j'}\) are \(j\) and \(j'\) fields, respectively, and \(\mathbf{v}_j\) and \(\mathbf{v}_{j'}\) are \(j\) and \(j'\) latent vectors, respectively.

For more efficiency, this model automatically one-hot encodes strings features considering them as categorical variables. Field names are inferred from feature names by taking everything before the first underscore: feature_name.split('_')[0].

Parameters

• n_factors – defaults to 10

  Dimensionality of the factorization or number of latent factors.

• weight_optimizer (optim.base.Optimizer) – defaults to None

  The sequential optimizer used for updating the feature weights. Note that the intercept is handled separately.

• latent_optimizer (optim.base.Optimizer) – defaults to None

  The sequential optimizer used for updating the latent factors.

• int_weight_optimizer (optim.base.Optimizer) – defaults to None

  The sequential optimizer used for updating the field pairs interaction weights.

• loss (optim.losses.BinaryLoss) – defaults to None

  The loss function to optimize for.

• sample_normalization – defaults to False

  Whether to divide each element of x by x's L2-norm.

• l1_weight – defaults to 0.0

  Amount of L1 regularization used to push weights towards 0.

• l2_weight – defaults to 0.0

  Amount of L2 regularization used to push weights towards 0.

• l1_latent – defaults to 0.0

  Amount of L1 regularization used to push latent weights towards 0.

• l2_latent – defaults to 0.0

  Amount of L2 regularization used to push latent weights towards 0.

• intercept – defaults to 0.0

  Initial intercept value.

• intercept_lr (Union[optim.base.Scheduler, float]) – defaults to 0.01

  Learning rate scheduler used for updating the intercept. An instance of optim.schedulers.Constant is used if a float is passed. No intercept will be used if this is set to 0.

• weight_initializer (optim.base.Initializer) – defaults to None

  Weights initialization scheme. Defaults to optim.initializers.Zeros().

• latent_initializer (optim.base.Initializer) – defaults to None

  Latent factors initialization scheme. Defaults to optim.initializers.Normal(mu=.0, sigma=.1, random_state=self.random_state).

• clip_gradient – defaults to 1000000000000.0

  Clips the absolute value of each gradient value.

• seed (int) – defaults to None

  Randomization seed used for reproducibility.

Attributes

• weights

  The current weights assigned to the features.

• latents

  The current latent weights assigned to the features.

• interaction_weights

  The current interaction strengths of field pairs.

Examples

>>> from river import facto

>>> dataset = (
...     ({'user': 'Alice', 'item': 'Superman'}, True),
...     ({'user': 'Alice', 'item': 'Terminator'}, True),
...     ({'user': 'Alice', 'item': 'Star Wars'}, True),
...     ({'user': 'Alice', 'item': 'Notting Hill'}, False),
...     ({'user': 'Alice', 'item': 'Harry Potter '}, True),
...     ({'user': 'Bob', 'item': 'Superman'}, True),
...     ({'user': 'Bob', 'item': 'Terminator'}, True),
...     ({'user': 'Bob', 'item': 'Star Wars'}, True),
...     ({'user': 'Bob', 'item': 'Notting Hill'}, False)
... )

>>> model = facto.FwFMClassifier(
...     n_factors=10,
...     seed=42,
... )

>>> for x, y in dataset:
...     model = model.learn_one(x, y)

>>> model.predict_one({'Bob': 1, 'Harry Potter': 1})
True

Methods

debug_one

Debugs the output of the FM regressor.

Parameters

• x (dict)
• decimals (int) – defaults to 5

Returns

str: A table which explains the output.

learn_one

Update the model with a set of features x and a label y.

Parameters

• x (dict)
• y (Union[bool, str, int])
• sample_weight – defaults to 1.0

Returns

Classifier: self

predict_one

Predict the label of a set of features x.

Parameters

• x (dict)
• kwargs

Returns

typing.Union[bool, str, int, NoneType]: The predicted label.

predict_proba_one

Predict the probability of each label for a dictionary of features x.

Parameters

• x

Returns

A dictionary that associates a probability which each label.

References

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1. Junwei Pan, Jian Xu, Alfonso Lobos Ruiz, Wenliang Zhao, Shengjun Pan, Yu Sun, and Quan Lu, 2018, April. Field-weighted Factorization Machines for Click-Through Rate Prediction in Display Advertising. In Proceedings of the 2018 World Wide Web Conference on World Wide Web. International World Wide Web Conferences Steering Committee, (pp. 1349–1357). ↩