""" Algorithm predicting a random rating.
"""
import numpy as np
from .algo_base import AlgoBase
[docs]class NormalPredictor(AlgoBase):
"""Algorithm predicting a random rating based on the distribution of the
training set, which is assumed to be normal.
The prediction :math:`\\hat{r}_{ui}` is generated from a normal distribution
:math:`\\mathcal{N}(\\hat{\\mu}, \\hat{\\sigma}^2)` where :math:`\\hat{\\mu}` and
:math:`\\hat{\\sigma}` are estimated from the training data using Maximum
Likelihood Estimation:
.. math::
\\hat{\\mu} &= \\frac{1}{|R_{train}|} \\sum_{r_{ui} \\in R_{train}}
r_{ui}\\\\\\\\\
\\hat{\\sigma} &= \\sqrt{\\sum_{r_{ui} \\in R_{train}}
\\frac{(r_{ui} - \\hat{\\mu})^2}{|R_{train}|}}
"""
def __init__(self):
AlgoBase.__init__(self)
def fit(self, trainset):
AlgoBase.fit(self, trainset)
num = sum(
(r - self.trainset.global_mean) ** 2
for (_, _, r) in self.trainset.all_ratings()
)
denum = self.trainset.n_ratings
self.sigma = np.sqrt(num / denum)
return self
def estimate(self, *_):
return np.random.normal(self.trainset.global_mean, self.sigma)