Recommendations in Keras using triplet loss

Note: a much richer set of neural network recommender models is available as Spotlight.

Along the lines of BPR [1].

[1] Rendle, Steffen, et al. "BPR: Bayesian personalized ranking from implicit feedback." Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence. AUAI Press, 2009.

This is implemented (more efficiently) in LightFM (https://github.com/lyst/lightfm). See the MovieLens example (https://github.com/lyst/lightfm/blob/master/examples/movielens/example.ipynb) for results comparable to this notebook.

Set up the architecture

A simple dense layer for both users and items: this is exactly equivalent to latent factor matrix when multiplied by binary user and item indices. There are three inputs: users, positive items, and negative items. In the triplet objective we try to make the positive item rank higher than the negative item for that user.

Because we want just one single embedding for the items, we use shared weights for the positive and negative item inputs (a siamese architecture).

This is all very simple but could be made arbitrarily complex, with more layers, conv layers and so on. I expect we'll be seeing a lot of papers doing just that.

"""
Triplet loss network example for recommenders
"""

from __future__ import print_function

import numpy as np

from keras import backend as K
from keras.models import Model
from keras.layers import Embedding, Flatten, Input, merge
from keras.optimizers import Adam

import data
import metrics

def identity_loss(y_true, y_pred):

    return K.mean(y_pred - 0 * y_true)

def bpr_triplet_loss(X):

    positive_item_latent, negative_item_latent, user_latent = X

    # BPR loss
    loss = 1.0 - K.sigmoid(
        K.sum(user_latent * positive_item_latent, axis=-1, keepdims=True) -
        K.sum(user_latent * negative_item_latent, axis=-1, keepdims=True))

    return loss

def build_model(num_users, num_items, latent_dim):

    positive_item_input = Input((1, ), name='positive_item_input')
    negative_item_input = Input((1, ), name='negative_item_input')

    # Shared embedding layer for positive and negative items
    item_embedding_layer = Embedding(
        num_items, latent_dim, name='item_embedding', input_length=1)

    user_input = Input((1, ), name='user_input')

    positive_item_embedding = Flatten()(item_embedding_layer(
        positive_item_input))
    negative_item_embedding = Flatten()(item_embedding_layer(
        negative_item_input))
    user_embedding = Flatten()(Embedding(
        num_users, latent_dim, name='user_embedding', input_length=1)(
            user_input))

    loss = merge(
        [positive_item_embedding, negative_item_embedding, user_embedding],
        mode=bpr_triplet_loss,
        name='loss',
        output_shape=(1, ))

    model = Model(
        input=[positive_item_input, negative_item_input, user_input],
        output=loss)
    model.compile(loss=identity_loss, optimizer=Adam())

    return model

Using Theano backend.

Load and transform data

We're going to load the Movielens 100k dataset and create triplets of (user, known positive item, randomly sampled negative item).

The success metric is AUC: in this case, the probability that a randomly chosen known positive item from the test set is ranked higher for a given user than a ranomly chosen negative item.

latent_dim = 100
num_epochs = 10

# Read data
train, test = data.get_movielens_data()
num_users, num_items = train.shape

# Prepare the test triplets
test_uid, test_pid, test_nid = data.get_triplets(test)

model = build_model(num_users, num_items, latent_dim)

# Print the model structure
print(model.summary())

# Sanity check, should be around 0.5
print('AUC before training %s' % metrics.full_auc(model, test))

____________________________________________________________________________________________________
Layer (type)                     Output Shape          Param #     Connected to                     
====================================================================================================
positive_item_input (InputLayer) (None, 1)             0                                            
____________________________________________________________________________________________________
negative_item_input (InputLayer) (None, 1)             0                                            
____________________________________________________________________________________________________
user_input (InputLayer)          (None, 1)             0                                            
____________________________________________________________________________________________________
item_embedding (Embedding)       (None, 1, 100)        168300      positive_item_input[0][0]        
                                                                   negative_item_input[0][0]        
____________________________________________________________________________________________________
user_embedding (Embedding)       (None, 1, 100)        94400       user_input[0][0]                 
____________________________________________________________________________________________________
flatten_7 (Flatten)              (None, 100)           0           item_embedding[0][0]             
____________________________________________________________________________________________________
flatten_8 (Flatten)              (None, 100)           0           item_embedding[1][0]             
____________________________________________________________________________________________________
flatten_9 (Flatten)              (None, 100)           0           user_embedding[0][0]             
____________________________________________________________________________________________________
loss (Merge)                     (None, 1)             0           flatten_7[0][0]                  
                                                                   flatten_8[0][0]                  
                                                                   flatten_9[0][0]                  
====================================================================================================
Total params: 262700
____________________________________________________________________________________________________
None
AUC before training 0.50247407966

Run the model

Run for a couple of epochs, checking the AUC after every epoch.

for epoch in range(num_epochs):

    print('Epoch %s' % epoch)

    # Sample triplets from the training data
    uid, pid, nid = data.get_triplets(train)

    X = {
        'user_input': uid,
        'positive_item_input': pid,
        'negative_item_input': nid
    }

    model.fit(X,
              np.ones(len(uid)),
              batch_size=64,
              nb_epoch=1,
              verbose=0,
              shuffle=True)

    print('AUC %s' % metrics.full_auc(model, test))

Epoch 0
AUC 0.905896400776
Epoch 1
AUC 0.908241780938
Epoch 2
AUC 0.909650205748
Epoch 3
AUC 0.910820451523
Epoch 4
AUC 0.912184845152
Epoch 5
AUC 0.912632057958
Epoch 6
AUC 0.91326604222
Epoch 7
AUC 0.913786881853
Epoch 8
AUC 0.914638438854
Epoch 9
AUC 0.915375014253

The AUC is in the low-90s. At some point we start overfitting, so it would be a good idea to stop early or add some regularization.