FwFMRegressor

Field-weighted Factorization Machine for regression.

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

  Default → 10

  Dimensionality of the factorization or number of latent factors.

• weight_optimizer

  Type → optim.base.Optimizer | None

  Default → None

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

• latent_optimizer

  Type → optim.base.Optimizer | None

  Default → None

  The sequential optimizer used for updating the latent factors.

• int_weight_optimizer

  Type → optim.base.Optimizer | None

  Default → None

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

• loss

  Type → optim.losses.RegressionLoss | None

  Default → None

  The loss function to optimize for.

• sample_normalization

  Default → False

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

• l1_weight

  Default → 0.0

  Amount of L1 regularization used to push weights towards 0.

• l2_weight

  Default → 0.0

  Amount of L2 regularization used to push weights towards 0.

• l1_latent

  Default → 0.0

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

• l2_latent

  Default → 0.0

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

• intercept

  Default → 0.0

  Initial intercept value.

• intercept_lr

  Type → optim.base.Scheduler | float

  Default → 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

  Type → optim.initializers.Initializer | None

  Default → None

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

• latent_initializer

  Type → optim.initializers.Initializer | None

  Default → None

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

• clip_gradient

  Default → 1000000000000.0

  Clips the absolute value of each gradient value.

• seed

  Type → int | None

  Default → 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'}, 8),
    ({'user': 'Alice', 'item': 'Terminator'}, 9),
    ({'user': 'Alice', 'item': 'Star Wars'}, 8),
    ({'user': 'Alice', 'item': 'Notting Hill'}, 2),
    ({'user': 'Alice', 'item': 'Harry Potter '}, 5),
    ({'user': 'Bob', 'item': 'Superman'}, 8),
    ({'user': 'Bob', 'item': 'Terminator'}, 9),
    ({'user': 'Bob', 'item': 'Star Wars'}, 8),
    ({'user': 'Bob', 'item': 'Notting Hill'}, 2)
)

model = facto.FwFMRegressor(
    n_factors=10,
    intercept=5,
    seed=42,
)

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

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

5.236501

report = model.debug_one({'Bob': 1, 'Harry Potter': 1})

print(report)

Name                                    Value      Weight     Contribution
                            Intercept    1.00000    5.23426        5.23426
Bob(Harry Potter) - Harry Potter(Bob)    1.00000    0.00224        0.00224
                         Harry Potter    1.00000    0.00000        0.00000
                                  Bob    1.00000    0.00000        0.00000

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

Fits to a set of features x and a real-valued target y.

Parameters

• x — 'dict'
• y — 'base.typing.RegTarget'
• sample_weight — defaults to 1.0

Returns

Regressor: self

predict_one

Predict the output of features x.

Parameters

• x

Returns

The prediction.

---

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). ↩