# Basic and Utility Algorithms¶

The lenskit.algorithms.basic module contains baseline and utility algorithms for nonpersonalized recommendation and testing.

## Personalized Mean Rating Prediction¶

class lenskit.algorithms.basic.Bias(items=True, users=True, damping=0.0)

A user-item bias rating prediction algorithm. This implements the following predictor algorithm:

$s(u,i) = \mu + b_i + b_u$

where $$\mu$$ is the global mean rating, $$b_i$$ is item bias, and $$b_u$$ is the user bias. With the provided damping values $$\beta_{\mathrm{u}}$$ and $$\beta_{\mathrm{i}}$$, they are computed as follows:

\begin{align*} \mu & = \frac{\sum_{r_{ui} \in R} r_{ui}}{|R|} & b_i & = \frac{\sum_{r_{ui} \in R_i} (r_{ui} - \mu)}{|R_i| + \beta_{\mathrm{i}}} & b_u & = \frac{\sum_{r_{ui} \in R_u} (r_{ui} - \mu - b_i)}{|R_u| + \beta_{\mathrm{u}}} \end{align*}

The damping values can be interpreted as the number of default (mean) ratings to assume a priori for each user or item, damping low-information users and items towards a mean instead of permitting them to take on extreme values based on few ratings.

Parameters: items – whether to compute item biases users – whether to compute user biases damping (number or tuple) – Bayesian damping to apply to computed biases. Either a number, to damp both user and item biases the same amount, or a (user,item) tuple providing separate damping values.
predict(model, user, items, ratings=None)

Compute predictions for a user and items. Unknown users and items are assumed to have zero bias.

Parameters: model (BiasModel) – the trained model to use. user – the user ID items (array-like) – the items to predict ratings (pandas.Series) – the user’s ratings (indexed by item id); if provided, will be used to recompute the user’s bias at prediction time. scores for the items, indexed by item id. pandas.Series
train(data)

Train the bias model on some rating data.

Parameters: data (DataFrame) – a data frame of ratings. Must have at least user, item, and rating columns. a trained model with the desired biases computed. BiasModel
class lenskit.algorithms.basic.BiasModel

Trained model for the Bias algorithm.

mean

the global mean.

Type: double
items

the item means.

Type: pandas.Series
users

the user means.

Type: pandas.Series

## Fallback Predictor¶

The Fallback rating predictor is a simple hybrid that takes a list of composite algorithms, and uses the first one to return a result to predict the rating for each item.

A common case is to fill in with Bias when a primary predictor cannot score an item.

class lenskit.algorithms.basic.Fallback(*algorithms)

The Fallback algorithm predicts with its first component, uses the second to fill in missing values, and so forth.

load_model(file)

Save a trained model to a file.

Parameters: path (str) – the path to file from which to load the model. the re-loaded model (of an implementation-defined type).
predict(model, user, items, ratings=None)

Compute predictions for a user and items.

Parameters: model – the trained model to use. Either None or the ratings matrix if the algorithm has no concept of training. user – the user ID items (array-like) – the items to predict ratings (pandas.Series) – the user’s ratings (indexed by item id); if provided, they may be used to override or augment the model’s notion of a user’s preferences. scores for the items, indexed by item id. pandas.Series
save_model(model, path)

Save a trained model to a file or directory. The default implementation pickles the model.

Algorithms are allowed to use any format for saving their models, including directories.

Parameters: model – the trained model. path (str) – the path at which to save the model.
train(ratings)

Train the model on rating/consumption data. Training methods that require additional data may accept it as additional parameters or via class members.

Parameters: ratings (pandas.DataFrame) – rating data, as a matrix with columns ‘user’, ‘item’, and ‘rating’. The user and item identifiers may be of any type. the trained model (of an implementation-defined type).

## Memorized Predictor¶

The Memorized recommender is primarily useful for test cases. It memorizes a set of rating predictions and returns them.

class lenskit.algorithms.basic.Memorized(scores)

Bases: object

The memorized algorithm memorizes scores & repeats them.