Bias
The lenskit.algorithms.bias module contains the personalized mean rating prediction.
- class lenskit.algorithms.bias.Bias(items=True, users=True, damping=0.0)
Bases:
PredictorA 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.
- mean_
The global mean rating.
- Type
double
- item_offsets_
The item offsets (\(b_i\) values)
- Type
- user_offsets_
The item offsets (\(b_u\) values)
- Type
- fit(ratings, **kwargs)
Train the bias model on some rating data.
- Parameters
ratings (DataFrame) – a data frame of ratings. Must have at least user, item, and rating columns.
- Returns
the fit bias object.
- Return type
- transform(ratings, *, indexes=False)
Transform ratings by removing the bias term. This method does not recompute user (or item) biases based on these ratings, but rather uses the biases that were estimated with
fit().- Parameters
ratings (pandas.DataFrame) – The ratings to transform. Must contain at least
user,item, andratingcolumns.indexes (bool) – if
True, the resulting frame will includeuidxandiidxcolumns containing the 0-based user and item indexes for each rating.
- Returns
A data frame with
ratingtransformed by subtracting user-item bias prediction.- Return type
- inverse_transform(ratings)
Transform ratings by removing the bias term.
- transform_user(ratings)
Transform a user’s ratings by subtracting the bias model.
- Parameters
ratings (pandas.Series) – The user’s ratings, indexed by item. Must have at least item as index and rating column.
- Returns
The transformed ratings and the user bias.
- Return type
- inverse_transform_user(user, ratings, user_bias=None)
Un-transform a user’s ratings by adding in the bias model.
- Parameters
user – The user ID.
ratings (pandas.Series) – The user’s ratings, indexed by item.
user_bias (float or None) – If None, it looks up the user bias learned by fit.
- Returns
The user’s de-normalized ratings.
- Return type
- fit_transform(ratings, **kwargs)
Fit with ratings and return the training data transformed.
- predict_for_user(user, items, ratings=None)
Compute predictions for a user and items. Unknown users and items are assumed to have zero bias.
- Parameters
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.
- Returns
scores for the items, indexed by item id.
- Return type
- property user_index
Get the user index from this (fit) bias.
- property item_index
Get the item index from this (fit) bias.