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

clone

Return a fresh estimator with the same parameters.

The clone has the same parameters but has not been updated with any data. This works by looking at the parameters from the class signature. Each parameter is either - recursively cloned if it's a River classes. - deep-copied via copy.deepcopy if not. If the calling object is stochastic (i.e. it accepts a seed parameter) and has not been seeded, then the clone will not be idempotent. Indeed, this method's purpose if simply to return a new instance with the same input parameters.

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

---

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 ↩