Quantile MLPRegressor

scikit-learn does not have a quantile regression for multi-layer perceptron. mlinsights implements a version of it based on the scikit-learn model. The implementation overwrites method _backprop.

We first generate some dummy data.

import numpy
from pandas import DataFrame
import matplotlib.pyplot as plt
from sklearn.neural_network import MLPRegressor
from mlinsights.mlmodel import QuantileMLPRegressor


X = numpy.random.random(1000)
eps1 = (numpy.random.random(900) - 0.5) * 0.1
eps2 = (numpy.random.random(100)) * 10
eps = numpy.hstack([eps1, eps2])
X = X.reshape((1000, 1))
Y = X.ravel() * 3.4 + 5.6 + eps

clr = MLPRegressor(hidden_layer_sizes=(30,), activation="tanh")
clr.fit(X, Y)

MLPRegressor(activation='tanh', hidden_layer_sizes=(30,))

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clq = QuantileMLPRegressor(hidden_layer_sizes=(30,), activation="tanh")
clq.fit(X, Y)

QuantileMLPRegressor(activation='tanh', hidden_layer_sizes=(30,))

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data = dict(X=X.ravel(), Y=Y, clr=clr.predict(X), clq=clq.predict(X))
df = DataFrame(data)
df.head()

	X	Y	clr	clq
0	0.379957	6.937997	7.492150	6.949007
1	0.076410	5.860495	6.348967	5.788681
2	0.292278	6.559855	7.178483	6.630396
3	0.755102	8.211254	8.671232	8.156544
4	0.637990	7.733815	8.331789	7.806592

fig, ax = plt.subplots(1, 1, figsize=(10, 4))
choice = numpy.random.choice(X.shape[0] - 1, size=100)
xx = X.ravel()[choice]
yy = Y[choice]
ax.plot(xx, yy, ".", label="data")
xx = numpy.array([[0], [1]])
y1 = clr.predict(xx)
y2 = clq.predict(xx)
ax.plot(xx, y1, "--", label="L2")
ax.plot(xx, y2, "--", label="L1")
ax.set_title("Quantile (L1) vs Square (L2) for MLPRegressor")
ax.legend()

<matplotlib.legend.Legend object at 0x7f75565b6c80>