Matrix Factorization (MF) part 2: Getting Fancy

Demonstrates matrix factorization with MXNet on the MovieLens 100k dataset. This is an extension of part 1 where we try fancy optimizers and network structures.

You need to have python package pandas and bokeh installed (pip install pandas bokeh).



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import mxnet as mx
from movielens_data import get_data_iter, max_id
from matrix_fact import train



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# If MXNet is not compiled with GPU support (e.g. on OSX), set to [mx.cpu(0)]
# Can be changed to [mx.gpu(0), mx.gpu(1), ..., mx.gpu(N-1)] if there are N GPUs
ctx = [mx.gpu(0)]



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train_test_data = get_data_iter(batch_size=100)
max_user, max_item = max_id('./ml-100k/u.data')
(max_user, max_item)

Linear MF

Same as before, but this time with the Adam optimizer which will often converge much faster than SGD w/ momentum as we used before. You should see this model over-fitting quickly.



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def plain_net(k):
    # input
    user = mx.symbol.Variable('user')
    item = mx.symbol.Variable('item')
    score = mx.symbol.Variable('score')
    # user feature lookup
    user = mx.symbol.Embedding(data = user, input_dim = max_user, output_dim = k) 
    # item feature lookup
    item = mx.symbol.Embedding(data = item, input_dim = max_item, output_dim = k)
    # predict by the inner product, which is elementwise product and then sum
    pred = user * item
    pred = mx.symbol.sum_axis(data = pred, axis = 1)
    pred = mx.symbol.Flatten(data = pred)
    # loss layer
    pred = mx.symbol.LinearRegressionOutput(data = pred, label = score)
    return pred

net1 = plain_net(64)
mx.viz.plot_network(net1)



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results1 = train(net1, train_test_data, num_epoch=25, learning_rate=0.001, optimizer='adam', ctx=ctx)

Neural Network (non-linear) MF

The non-linear model converges strangely with Adam.



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def get_one_layer_mlp(hidden, k):
    # input
    user = mx.symbol.Variable('user')
    item = mx.symbol.Variable('item')
    score = mx.symbol.Variable('score')
    # user latent features
    user = mx.symbol.Embedding(data = user, input_dim = max_user, output_dim = k)
    user = mx.symbol.Activation(data = user, act_type='relu')
    user = mx.symbol.FullyConnected(data = user, num_hidden = hidden)
    # item latent features
    item = mx.symbol.Embedding(data = item, input_dim = max_item, output_dim = k)
    item = mx.symbol.Activation(data = item, act_type='relu')
    item = mx.symbol.FullyConnected(data = item, num_hidden = hidden)
    # predict by the inner product
    pred = user * item
    pred = mx.symbol.sum_axis(data = pred, axis = 1)
    pred = mx.symbol.Flatten(data = pred)
    # loss layer
    pred = mx.symbol.LinearRegressionOutput(data = pred, label = score)
    return pred

net2 = get_one_layer_mlp(64, 64)
mx.viz.plot_network(net2)



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results2 = train(net2, train_test_data, num_epoch=20, learning_rate=0.001, optimizer='adam', ctx=ctx)

Deep Neural Network (Residual Network / ResNet)

Borrowing ideas from Deep Residual Learning for Image Recognition (He, et al.) to build a complex deep network that is aggressively regularized to avoid over-fitting, but still achieves good performance.



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def get_multi_layer_dropout_resnet(hidden, k):
    # input
    user = mx.symbol.Variable('user')
    item = mx.symbol.Variable('item')
    score = mx.symbol.Variable('score')
    # user latent features
    user1 = mx.symbol.Embedding(data = user, input_dim = max_user, output_dim = k)
    user = mx.symbol.FullyConnected(data = user1, num_hidden = hidden)
    user = mx.symbol.Activation(data = user, act_type='relu')
    user = mx.symbol.Dropout(data=user, p=0.5)
    user = mx.symbol.FullyConnected(data = user, num_hidden = hidden)
    user2 = user + user1
    user2 = mx.symbol.Dropout(data=user2, p=0.5)
    user = mx.symbol.FullyConnected(data = user2, num_hidden = hidden)
    user = mx.symbol.Activation(data = user, act_type='relu')
    user = mx.symbol.Dropout(data=user, p=0.5)
    user = mx.symbol.FullyConnected(data = user, num_hidden = hidden)
    user = user + user2
    # item latent features
    item1 = mx.symbol.Embedding(data = item, input_dim = max_item, output_dim = k)
    item = mx.symbol.FullyConnected(data = item1, num_hidden = hidden)
    item = mx.symbol.Activation(data = item, act_type='relu')
    item = mx.symbol.Dropout(data=item, p=0.5)    
    item = mx.symbol.FullyConnected(data=item, num_hidden = hidden)
    item2 = item + item1
    item2 = mx.symbol.Dropout(data=item2, p=0.5)    
    item = mx.symbol.FullyConnected(data = item2, num_hidden = hidden)
    item = mx.symbol.Activation(data = item, act_type='relu')
    item = mx.symbol.Dropout(data=item, p=0.5)    
    item = mx.symbol.FullyConnected(data=item, num_hidden = hidden)
    item = item + item2
    # predict by the inner product
    pred = user * item
    pred = mx.symbol.sum_axis(data = pred, axis = 1)
    pred = mx.symbol.Flatten(data = pred)
    # loss layer
    pred = mx.symbol.LinearRegressionOutput(data = pred, label = score)
    return pred
net3 = get_multi_layer_dropout_resnet(64, 64)
mx.viz.plot_network(net3)



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# Larger batch size makes GPU more efficient for this complex model
train_test_data2 = get_data_iter(batch_size=200) 
results3 = train(net3, train_test_data2, num_epoch=25, learning_rate=0.001, optimizer='adam', ctx=ctx)

Visualizing results

Compare accuracy and training time across the models.



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import bokeh
import bokeh.io
import bokeh.plotting
bokeh.io.output_notebook()
import pandas as pd

def viz_lines(fig, results, legend, color):
    df = pd.DataFrame(results._data['eval'])
    fig.line(df.elapsed,df.RMSE, color=color, legend=legend, line_width=2)
    df = pd.DataFrame(results._data['train'])
    fig.line(df.elapsed,df.RMSE, color=color, line_dash='dotted', alpha=0.1)

fig = bokeh.plotting.Figure(x_axis_type='datetime', x_axis_label='Training time', y_axis_label='RMSE')
viz_lines(fig, results1, "Linear MF", "orange")
viz_lines(fig, results2, "MLP", "blue")
viz_lines(fig, results3, "ResNet", "red")

bokeh.io.show(fig)



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