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SGD Convex Loss Functions in Scikit-learn

A plot that compares the various convex loss functions supported by sklearn.linear_model.SGDClassifier

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Version

In [1]:
import sklearn
sklearn.__version__
Out[1]:
'0.18.1'

Imports

In [2]:
print(__doc__)

import plotly.plotly as py
import plotly.graph_objs as go

import numpy as np
Automatically created module for IPython interactive environment

Calculations

In [3]:
def modified_huber_loss(y_true, y_pred):
    z = y_pred * y_true
    loss = -4 * z
    loss[z >= -1] = (1 - z[z >= -1]) ** 2
    loss[z >= 1.] = 0
    return loss


xmin, xmax = -4, 4
xx = np.linspace(xmin, xmax, 100)
lw = 2

Plot Results

In [4]:
trace1 = go.Scatter(x=[xmin, 0, 0, xmax], 
                  y=[1, 1, 0, 0], 
                  mode='lines',
                  line=dict(color='gold', width=lw),
                  name="Zero-one loss")

trace2 = go.Scatter(x=xx, 
                    y=np.where(xx < 1, 1 - xx, 0), 
                    mode='lines',
                    line=dict(color='teal', width=lw),
                    name="Hinge loss")

trace3 = go.Scatter(x=xx, 
                    y=-np.minimum(xx, 0), 
                    mode='lines',
                    line=dict(color='yellowgreen', width=lw),
                    name="Perceptron loss")

trace4 = go.Scatter(x=xx, 
                    y=np.log2(1 + np.exp(-xx)), 
                    mode='lines',
                    line=dict(color='cornflowerblue', width=lw),
                    name="Log loss")

trace5 = go.Scatter(x=xx, 
                    y=np.where(xx < 1, 1 - xx, 0) ** 2, 
                    mode='lines',
                    line=dict(color='orange', width=lw),
                    name="Squared hinge loss")

trace6 = go.Scatter(x=xx, 
                    y=modified_huber_loss(xx, 1), 
                    mode='lines',
                    line=dict(color='darkorchid', width=lw, dash='dash'),
                    name="Modified Huber loss")

data = [trace1, trace2, trace3, trace4, trace5, trace6]

layout = go.Layout(xaxis=dict(title=r"Decision function <i>f(x)</i>", 
                              zeroline=False, showgrid=False),
                   yaxis=dict(title="<i>L(y, f(x))</i>", range=[0, 8],
                              showgrid=False),
                   hovermode='closest')

fig = go.Figure(data=data, layout=layout)
In [5]:
py.iplot(fig)
Out[5]:
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