FMRegressor¶

Factorization Machine for regression.

The model equation is defined as:

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

Where \(\mathbf{v}_j\) 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.

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.
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.

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.FMRegressor(
    n_factors=10,
    intercept=5,
    seed=42,
)

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

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

5.236504

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    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'
w — defaults to 1.0

predict_one

Predict the output of features x.

Parameters

x

Returns

The prediction.