BiasedMF

Biased Matrix Factorization for recommender systems.

The model equation is defined as:

\[\hat{y}(x) = \bar{y} + bu_{u} + bi_{i} + \langle \mathbf{v}_u, \mathbf{v}_i \rangle\]

Where \(bu_{u}\) and \(bi_{i}\) are respectively the user and item biases. The last term being simply the dot product between the latent vectors of the given user-item pair:

\[\langle \mathbf{v}_u, \mathbf{v}_i \rangle = \sum_{f=1}^{k} \mathbf{v}_{u, f} \cdot \mathbf{v}_{i, f}\]

where \(k\) is the number of latent factors.

This model expects a dict input with a user and an item entries without any type constraint on their values (i.e. can be strings or numbers). Other entries are ignored.

Parameters

• n_factors – defaults to 10

  Dimensionality of the factorization or number of latent factors.

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

  The sequential optimizer used for updating the bias weights.

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

  The sequential optimizer used for updating the latent weights.

• loss (optim.base.Loss) – defaults to None

  The loss function to optimize for.

• l2_bias – defaults to 0.0

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

• l2_latent – defaults to 0.0

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

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

  Weights initialization scheme.

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

  Latent factors initialization scheme.

• clip_gradient – defaults to 1000000000000.0

  Clips the absolute value of each gradient value.

• seed – defaults to None

  Random number generation seed. Set this for reproducibility.

Attributes

• global_mean (stats.Mean)

  The target arithmetic mean.

• u_biases (collections.defaultdict)

  The user bias weights.

• i_biases (collections.defaultdict)

  The item bias weights.

• u_latents (collections.defaultdict)

  The user latent vectors randomly initialized.

• i_latents (collections.defaultdict)

  The item latent vectors randomly initialized.

• u_bias_optimizer (optim.base.Optimizer)

  The sequential optimizer used for updating the user bias weights.

• i_bias_optimizer (optim.base.Optimizer)

  The sequential optimizer used for updating the item bias weights.

• u_latent_optimizer (optim.base.Optimizer)

  The sequential optimizer used for updating the user latent weights.

• i_latent_optimizer (optim.base.Optimizer)

  The sequential optimizer used for updating the item latent weights.

Examples

>>> from river import optim
>>> from river import reco

>>> 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 = reco.BiasedMF(
...     n_factors=10,
...     bias_optimizer=optim.SGD(0.025),
...     latent_optimizer=optim.SGD(0.025),
...     latent_initializer=optim.initializers.Normal(mu=0., sigma=0.1, seed=71)
... )

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

>>> model.predict_one(user='Bob', item='Harry Potter')
6.489025

Methods

learn_one

Fits a user-item pair and a real-valued target y.

Parameters

• user (Union[str, int])
• item (Union[str, int])
• y (Union[numbers.Number, bool])
• x (dict) – defaults to None

predict_one

Predicts the target value of a set of features x.

Parameters

• user (Union[str, int])
• item (Union[str, int])
• x (dict) – defaults to None

Returns

typing.Union[numbers.Number, bool]: The predicted preference from the user for the item.

rank

Rank models by decreasing order of preference for a given user.

Parameters

• user (Union[str, int])
• items (Set[Union[str, int]])
• x (dict) – defaults to None

References

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1. Paterek, A., 2007, August. Improving regularized singular value decomposition for collaborative filtering. In Proceedings of KDD cup and workshop (Vol. 2007, pp. 5-8) ↩

2. Matrix factorization techniques for recommender systems ↩