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%matplotlib inline

Compare Stochastic learning strategies for MLPClassifier

This example visualizes some training loss curves for different stochastic learning strategies, including SGD and Adam. Because of time-constraints, we use several small datasets, for which L-BFGS might be more suitable. The general trend shown in these examples seems to carry over to larger datasets, however.

Note that those results can be highly dependent on the value of learning_rate_init.

In [ ]:

import warnings

import matplotlib.pyplot as plt

from sklearn.neural_network import MLPClassifier
from sklearn.preprocessing import MinMaxScaler
from sklearn import datasets
from sklearn.exceptions import ConvergenceWarning

# different learning rate schedules and momentum parameters
params = [{'solver': 'sgd', 'learning_rate': 'constant', 'momentum': 0,
           'learning_rate_init': 0.2},
          {'solver': 'sgd', 'learning_rate': 'constant', 'momentum': .9,
           'nesterovs_momentum': False, 'learning_rate_init': 0.2},
          {'solver': 'sgd', 'learning_rate': 'constant', 'momentum': .9,
           'nesterovs_momentum': True, 'learning_rate_init': 0.2},
          {'solver': 'sgd', 'learning_rate': 'invscaling', 'momentum': 0,
           'learning_rate_init': 0.2},
          {'solver': 'sgd', 'learning_rate': 'invscaling', 'momentum': .9,
           'nesterovs_momentum': True, 'learning_rate_init': 0.2},
          {'solver': 'sgd', 'learning_rate': 'invscaling', 'momentum': .9,
           'nesterovs_momentum': False, 'learning_rate_init': 0.2},
          {'solver': 'adam', 'learning_rate_init': 0.01}]

labels = ["constant learning-rate", "constant with momentum",
          "constant with Nesterov's momentum",
          "inv-scaling learning-rate", "inv-scaling with momentum",
          "inv-scaling with Nesterov's momentum", "adam"]

plot_args = [{'c': 'red', 'linestyle': '-'},
             {'c': 'green', 'linestyle': '-'},
             {'c': 'blue', 'linestyle': '-'},
             {'c': 'red', 'linestyle': '--'},
             {'c': 'green', 'linestyle': '--'},
             {'c': 'blue', 'linestyle': '--'},
             {'c': 'black', 'linestyle': '-'}]

def plot_on_dataset(X, y, ax, name):
    # for each dataset, plot learning for each learning strategy
    print("\nlearning on dataset %s" % name)

    X = MinMaxScaler().fit_transform(X)
    mlps = []
    if name == "digits":
        # digits is larger but converges fairly quickly
        max_iter = 15
        max_iter = 400

    for label, param in zip(labels, params):
        print("training: %s" % label)
        mlp = MLPClassifier(random_state=0,
                            max_iter=max_iter, **param)

        # some parameter combinations will not converge as can be seen on the
        # plots so they are ignored here
        with warnings.catch_warnings():
            warnings.filterwarnings("ignore", category=ConvergenceWarning,
  , y)

        print("Training set score: %f" % mlp.score(X, y))
        print("Training set loss: %f" % mlp.loss_)
    for mlp, label, args in zip(mlps, labels, plot_args):
        ax.plot(mlp.loss_curve_, label=label, **args)

fig, axes = plt.subplots(2, 2, figsize=(15, 10))
# load / generate some toy datasets
iris = datasets.load_iris()
X_digits, y_digits = datasets.load_digits(return_X_y=True)
data_sets = [(,,
             (X_digits, y_digits),
             datasets.make_circles(noise=0.2, factor=0.5, random_state=1),
             datasets.make_moons(noise=0.3, random_state=0)]

for ax, data, name in zip(axes.ravel(), data_sets, ['iris', 'digits',
                                                    'circles', 'moons']):
    plot_on_dataset(*data, ax=ax, name=name)

fig.legend(ax.get_lines(), labels, ncol=3, loc="upper center")