# PyTorch for Recommenders 101

Recommenders, generally associated with e-commerce, sift though a huge inventory of available items to find and recommend ones that a user will like. Different from search, recommenders rely on historical data to tease out user preference. How does a recommender accomplish this? In this post we explore building simple recommendation systems in PyTorch using the Movielens 100K data, which has 100,000 ratings (1-5) that 943 users provided on 1682 movies.

## Matrix Factorization We first build a traditional recommendation system based on matrix factorization. The input data is an interaction matrix where each row represents a user and each column represents an item. The rating assigned by a user for a particular item is found in the corresponding row and column of the interaction matrix. This matrix is generally large but sparse; there are many items and users but a single user would only have interacted with a small subset of items. Matrix factorization decomposes this larger matrix into two smaller matrices - the first one maps users into a set of factors and the second maps items into the same set of factors. Multiplying these two smaller matrices together gives an approximation to the original matrix, with values for empty elements inferred. To predict a rating for a user-item pair, we simply multiply the row representing the user from the first matrix with the column representing the item from the second matrix.

In PyTorch we can implement a version of matrix factorization by using the embedding layer to “map” users into a set of factors. The number of factors determine the size of the embedding vector. Similarly we map items into their own embedding layer. Both user and item embeddings have the same size. To predict a user-item rating, we multiply the user embeddings with item embeddings and sum to obtain one number. The following code draws from Ethan Rosenthal’s work on matrix factorization in PyTorch.

``````import torch

class MatrixFactorization(torch.nn.Module):
def __init__(self, n_users, n_items, n_factors=20):
super().__init__()
# create user embeddings
self.user_factors = torch.nn.Embedding(n_users, n_factors,
sparse=True)
# create item embeddings
self.item_factors = torch.nn.Embedding(n_items, n_factors,
sparse=True)

def forward(self, user, item):
# matrix multiplication
return (self.user_factors(user)*self.item_factors(item)).sum(1)

def predict(self, user, item):
return self.forward(user, item)

``````

To fit the matrix factorization model we need to pick a loss function and an optimizer. In this example we use the average squared distance between the prediction and the actual value as a loss function, this is known as mean-squared error. We then try to minimize this loss by using stochastic gradient descent. The code below shows how the model is fitted in four steps: i) pass in a user-item pair, ii) forward pass to compute the predicted rating, iii) compute the loss, and iv) backpropagate to compute gradients and update the weights.

``````model = MatrixFactorization(n_users, n_items, n_factors=20)
loss_fn = torch.nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(),
lr=1e-6)

for user, item in zip(users, items):
# get user, item and rating data
rating = Variable(torch.FloatTensor([ratings[user, item]]))
user = Variable(torch.LongTensor([int(user)]))
item = Variable(torch.LongTensor([int(item)]))

# predict
prediction = model(user, item)
loss = loss_fn(prediction, rating)

# backpropagate
loss.backward()

# update weights
optimizer.step()
``````

We train this model on the Movielens dataset with ratings scaled between [0, 1] to help with convergence. Applied on the test set, we obtain a root mean-squared error(RMSE) of 0.66. This means that on average, the difference between our prediction and the actual value is 0.66!

## Dense Feedforward Neural Network

Given the underwhelming performance of our matrix factorization model, we try a simple feedforward recommendation system instead. The input to this neural network is a pair of user and item represented by their IDs. Both user and item IDs first pass through an embedding layer. The output of the embedding layer, which are two embedding vectors, are then concatenated into one and passed into a linear network. The output of the linear network is one dimensional - representing the rating for the user-item pair. The model is fit the same way as the matrix factorization model and uses the standard PyTorch approach of forward passing, computing the loss, backpropagating and updating weights.

``````import torch
import torch.nn.functional as F
from torch import nn

class DenseNet(nn.Module):

def __init__(self, n_users, n_items, n_factors, H1, D_out):
"""
Simple Feedforward with Embeddings
"""
super().__init__()
# user and item embedding layers
self.user_factors = torch.nn.Embedding(n_users, n_factors,
sparse=True)
self.item_factors = torch.nn.Embedding(n_items, n_factors,
sparse=True)
# linear layers
self.linear1 = torch.nn.Linear(n_factors*2, H1)
self.linear2 = torch.nn.Linear(H1, D_out)

def forward(self, users, items):
users_embedding = self.user_factors(users)
items_embedding = self.item_factors(items)
# concatenate user and item embeddings to form input
x = torch.cat([users_embedding, items_embedding], 1)
h1_relu = F.relu(self.linear1(x))
output_scores = self.linear2(h1_relu)
return output_scores

def predict(self, users, items):
# return the score
output_scores = self.forward(users, items)
return output_scores

``````

Once again, we train this model on the Movielens dataset with ratings scaled between [0, 1] to help with convergence. Applied on the test set, we obtain a root mean-squared error(RMSE) of 0.28, a substantial improvement!

## Sequence based Recommendation System

Finally we build a recommendation system that takes into account the sequence of item interactions. The heart of this is a Long Short-Term Memory (LSTM) cell, a variant of Recurrent Neural Networks (RNN) with faster convergence and better long term memory. The input to this system is a history of item interactions and their corresponding ratings. In the following example of an input, we show a sequence of item interaction of length 10 (arbitrarily chosen) and the corresponding rating. Elements in the first array correspond to items(movies), and elements in the second array correspond to ratings. We see that, for example, movie 209 has a rating of 4, and movie 32 has a rating of 5. Sequences shorter than 10 are padded with zeros.

``````In : training_data
Out:
(array([209,  32, 189, 242, 171, 111, 256,   5,  74, 102], dtype=int32),
array([4, 5, 3, 5, 5, 5, 4, 3, 1, 2], dtype=int32))
``````

Items are passed through an embedding layer before going into the LSTM. The output of the LSTM is then fed into a linear layer with an output dimension of one. The LSTM has 2 hidden states, one for short term memory and one for long term. Both states need to be initialized.

PyTorch expects LSTM inputs to be a three dimensional tensor. The first dimension is the length of the sequence itself, the second represents the number of instances in a mini-batch, the third is the size of the actual input into the LSTM. Using our training data example with sequence of length 10 and embedding dimension of 20, input to the LSTM is a tensor of size 10x1x20 when we do not use mini batches. For a mini-batch size of 2, each forward pass will have two sequences, and the input to the LSTM needs to have a dimension of 10x2x20. LSTMs take variable input sequence lengths but for batch training purposes the input data is generally processed(with padding if necessary) to have a fixed length.

``````import torch
import torch.nn as nn

class LSTMRating(nn.Module):

def __init__(self, embedding_dim, hidden_dim, num_items, num_output):
super().__init__()
self.hidden_dim = hidden_dim
self.item_embeddings = nn.Embedding(num_items, embedding_dim)
self.lstm = nn.LSTM(embedding_dim, hidden_dim)
self.linear = nn.Linear(hidden_dim, num_output)
self.hidden = self.init_hidden()

def init_hidden(self):
# initialize both hidden layers
return (Variable(torch.zeros(1, 1, self.hidden_dim)),
Variable(torch.zeros(1, 1, self.hidden_dim)))

def forward(self, sequence):
embeddings = self.item_embeddings(sequence)
output, self.hidden = self.lstm(embeddings.view(len(sequence), 1, -1),
self.hidden)
rating_scores = self.linear(output.view(len(sequence), -1))
return rating_scores

def predict(self, sequence):
rating_scores = self.forward(sequence)
return rating_scores

``````

Once the neural network is defined, we fit the training data using stochastic gradient descent with a mean squared error loss function.

``````embedding_dim = 64
hidden_dim = 128
n_output = 1

# add one to represent padding when there is not enough history
model = LSTMRating(embedding_dim, hidden_dim, n_items+1, n_output)
loss_fn = nn.MSELoss()
optimizer = optim.SGD(model.parameters(), lr=0.1)

for sequence, target_ratings in training_data:
# initialize hidden layers
model.hidden = model.init_hidden()
# convert sequence to PyTorch variables
sequence_var = Variable(torch.LongTensor(sequence.astype('int64')))
# forward pass
ratings_scores = model(sequence_var)
target_ratings_var = Variable(torch.FloatTensor(target_ratings.astype('float32')))
# compute loss
loss = loss_fn(ratings_scores, target_ratings_var)
# backpropagate
loss.backward()
# update weights
optimizer.step()

``````

Similar to other models, we train the LSTM-based model on the Movielens dataset with ratings scaled between [0, 1] to help with convergence. Applied on the test set, we obtain a root mean-squared error(RMSE) of 0.43 - the LSTM model underperforms the dense feed forward network.

## Post-amble

The models discussed in this post are basic building blocks for a recommendation system in PyTorch. There are no bells and whistles and we did not attempt to fine tune any hyperparameters. Our first pass result suggests that the dense network performs best, followed by the LSTM network and finally the matrix factorization model. The root mean-squared error (RMSE) are 0.28, 0.43 and 0.66 respectively on the Movielens 100K dataset with ratings scaled between [0, 1]. We thought PyTorch was fun to use; models can be built and swapped out relatively easily. When we did encounter errors, most of them were triggered by incorrect data types.

For more on recommendations, please see our Semantic Recommendations report, where we focus on how machines can better understand content!

Older

## Latest posts

##### Nov 15, 2020 · post by Figure 1: Overview of representation learning methods. TLDR; Good representations of data (e.g., text, images) are critical for solving many tasks (e.g., search or recommendations). Deep representation learning yields state of the art results when used to create these representations. In this article, we review methods for representation learning and walk through an example using pretrained models. Introduction Deep Neural Networks (DNNs) have become a particularly useful tool in building intelligent systems that simplify cognitive tasks for users.
##### Jun 22, 2020 · post by Given a question and a passage, the task of Question Answering (QA) focuses on identifying the exact span within the passage that answers the question. Figure 1: In this sample, a BERTbase model gets the answer correct (Achaemenid Persia). Model gradients show that the token “subordinate ..” is impactful in the selection of an answer to the question “Macedonia was under the rule of which country?". This makes sense .. good for BERTbase.
##### Jun 16, 2020 · notebook by A deep dive into computing QA predictions and when to tell BERT to zip it! In our last post, Building a QA System with BERT on Wikipedia, we used the HuggingFace framework to train BERT on the SQuAD2.0 dataset and built a simple QA system on top of the Wikipedia search engine. This time, we’ll look at how to assess the quality of a BERT-like model for Question Answering.
##### May 19, 2020 · notebook by So you’ve decided to build a QA system. You want to start with something simple and general so you plan to make it open domain using Wikipedia as a corpus for answering questions. You want to use the best NLP that your compute resources allow (you’re lucky enough to have access to a GPU) so you’re going to focus on the big, flashy Transformer models that are all the rage these days.
##### Apr 28, 2020 · notebook by Welcome to the first edition of the Cloudera Fast Forward blog on Natural Language Processing for Question Answering! Throughout this series, we’ll build a Question Answering (QA) system with off-the-shelf algorithms and libraries and blog about our process and what we find along the way. We hope to wind up with a beginning-to-end documentary that provides:
##### Apr 1, 2020 · newsletter by At Cloudera Fast Forward, one of the mechanisms we use to tightly couple machine learning research with application is through application development projects for both internal and external clients. The problems we tackle in these projects are wide ranging and cut across various industries; the end goal is a production system that translates data into business impact. What is Enterprise Grade Machine Learning? Enterprise grade ML, a term mentioned in a paper put forth by Microsoft, refers to ML applications where there is a high level of scrutiny for data handling, model fairness, user privacy, and debuggability.

### Popular posts

##### Oct 30, 2019 · newsletter
Exciting Applications of Graph Neural Networks
##### Nov 14, 2018 · post
Federated learning: distributed machine learning with data locality and privacy
##### Apr 10, 2018 · post
PyTorch for Recommenders 101
##### Oct 4, 2017 · post
First Look: Using Three.js for 2D Data Visualization
##### Aug 22, 2016 · whitepaper
Under the Hood of the Variational Autoencoder (in Prose and Code)
##### Feb 24, 2016 · post
"Hello world" in Keras (or, Scikit-learn versus Keras)

# Reports

In-depth guides to specific machine learning capabilities

# Prototypes

Machine learning prototypes and interactive notebooks

## NeuralQA

A usable library for question answering on large datasets.
https://neuralqa.fastforwardlabs.com

## Explain BERT for Question Answering Models

Tensorflow 2.0 notebook to explain and visualize a HuggingFace BERT for Question Answering model.
##### Notebooks

Ongoing posts and code documenting the process of building a question answering model.
https://qa.fastforwardlabs.com

## Interpretability Revisited: SHAP and LIME

Explore how to use LIME and SHAP for interpretability.