HOFMRegressor

Higher-Order Factorization Machine for regression.

The model equation is defined as:

\[\hat{y}(x) = w_{0} + \sum_{j=1}^{p} w_{j} x_{j} + \sum_{l=2}^{d} \sum_{j_1=1}^{p} \cdots \sum_{j_l=j_{l-1}+1}^{p} \left(\prod_{j'=1}^{l} x_{j_{j'}} \right) \left(\sum_{f=1}^{k_l} \prod_{j'=1}^{l} v_{j_{j'}, f}^{(l)} \right)\]

For more efficiency, this model automatically one-hot encodes strings features considering them as categorical variables.

Parameters

• degree – defaults to 3

  Polynomial degree or model order.

• 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 thatthe intercept is handled separately.

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

  The sequential optimizer used for updating the latent factors.

• loss (optim.losses.RegressionLoss) – 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.

Examples

>>> from river import facto

>>> dataset = (
...     ({'user': 'Alice', 'item': 'Superman', 'time': .12}, 8),
...     ({'user': 'Alice', 'item': 'Terminator', 'time': .13}, 9),
...     ({'user': 'Alice', 'item': 'Star Wars', 'time': .14}, 8),
...     ({'user': 'Alice', 'item': 'Notting Hill', 'time': .15}, 2),
...     ({'user': 'Alice', 'item': 'Harry Potter ', 'time': .16}, 5),
...     ({'user': 'Bob', 'item': 'Superman', 'time': .13}, 8),
...     ({'user': 'Bob', 'item': 'Terminator', 'time': .12}, 9),
...     ({'user': 'Bob', 'item': 'Star Wars', 'time': .16}, 8),
...     ({'user': 'Bob', 'item': 'Notting Hill', 'time': .10}, 2)
... )

>>> model = facto.HOFMRegressor(
...     degree=3,
...     n_factors=10,
...     intercept=5,
...     seed=42,
... )

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

>>> model.predict_one({'user': 'Bob', 'item': 'Harry Potter', 'time': .14})
5.311745

>>> report = model.debug_one({'user': 'Bob', 'item': 'Harry Potter', 'time': .14})

>>> print(report)
Name                                  Value      Weight     Contribution
                          Intercept    1.00000    5.23495        5.23495
                           user_Bob    1.00000    0.11436        0.11436
                               time    0.14000    0.03185        0.00446
                    user_Bob - time    0.14000    0.00884        0.00124
user_Bob - item_Harry Potter - time    0.14000    0.00117        0.00016
                  item_Harry Potter    1.00000    0.00000        0.00000
           item_Harry Potter - time    0.14000   -0.00695       -0.00097
       user_Bob - item_Harry Potter    1.00000   -0.04246       -0.04246

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 (numbers.Number)
• sample_weight – defaults to 1.0

Returns

Regressor: self

predict_one

Predict the output of features x.

Parameters

• x

Returns

The prediction.

References

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1. Rendle, S., 2010, December. Factorization machines. In 2010 IEEE International Conference on Data Mining (pp. 995-1000). IEEE. ↩