There are some rows and columns with empty values and the goal would be for the model to learn how to fill in these values.

San Diego State University

Movielens dataset contains millions of movie ratings data, namely, these are the combination of movie and user IDs and numerical rating. This dataset can be used to practice for recommendation problems. 

MovieLens Data for Collaborative Filtering

 ``` python
from fastai.collab import *
from fastai.tabular.all import *
path = untar_data(URLs.ML_100k)

ratings = pd.read_csv(path/'u.data', delimiter='\t', 
                                        header=None,
                                         names='user','movie','rating','timestamp'])


```

Load Data

Crosstab Representation

What does the term **latent factors** refer to ? Latent factors are those factors which are important in order to make recommendation predictions, but these factors are not directly given to the model, they are learned during training. That's why they are called **latent**. 

First step for is to randomly initialize the parameters. These parameters would be the set of latent factors for each user and movie. The number of latent factors can be explicitly chosen.

Second step is to make predictions using our latent factors. 

Third step is to calculate loss. 

Then the optimization starts in order to minimize the loss. 

Learning the Latent Factors (collaborative filtering)

Latent Factors with Crosstab

```python
class DotProductBias(Module):
  def __init__(self, n_users, n_movies, n_factors, y_range=(0,5.5)):
    self.user_factors = Embedding(n_users, n_factors)
    self.user_bias = Embedding(n_users, 1)
    self.movie_factors = Embedding(n_movies, n_factors)
    self.movie_bias = Embedding(n_movies, 1)
    self.y_range = y_range
  def forward(self, x):
    users = self.user_factors(x[:,0])
    movies = self.movie_factors(x[:,1])
    res = (users * movies).sum(dim=1, keepdim=True)
    res += self.user_bias(x[:,0]) + self.movie_bias(x[:,1])
    return sigmoid_range(res, *self.y_range)

model = DotProductBias(n_users, n_movies, 50)
learn = Learner(dls, model, loss_func=MSELossFlat())
learn.fit_one_cycle(5, 5e-3)

```

Learn Before

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