Show Sidebar Hide Sidebar

Prediction Intervals for Gradient Boosting Regression in Scikit-learn

This example shows how quantile regression can be used to create prediction intervals.

New to Plotly?

Plotly's Python library is free and open source! Get started by downloading the client and reading the primer.
You can set up Plotly to work in online or offline mode, or in jupyter notebooks.
We also have a quick-reference cheatsheet (new!) to help you get started!

Version

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

Imports

This tutorial imports GradientBoostingRegressor.

In [2]:
print(__doc__)

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

import numpy as np
import matplotlib.pyplot as plt

from sklearn.ensemble import GradientBoostingRegressor
Automatically created module for IPython interactive environment

Calculation

In [3]:
np.random.seed(1)
def f(x):
    """The function to predict."""
    return x * np.sin(x)

First the noiseless case

In [4]:
X = np.atleast_2d(np.random.uniform(0, 10.0, size=100)).T
X = X.astype(np.float32)

# Observations
y = f(X).ravel()

dy = 1.5 + 1.0 * np.random.random(y.shape)
noise = np.random.normal(0, dy)
y += noise
y = y.astype(np.float32)

Mesh the input space for evaluations of the real function, the prediction and its MSE

In [5]:
xx = np.atleast_2d(np.linspace(0, 10, 1000)).T
xx = xx.astype(np.float32)

alpha = 0.95

clf = GradientBoostingRegressor(loss='quantile', alpha=alpha,
                                n_estimators=250, max_depth=3,
                                learning_rate=.1, min_samples_leaf=9,
                                min_samples_split=9)

clf.fit(X, y)

# Make the prediction on the meshed x-axis
y_upper = clf.predict(xx)

clf.set_params(alpha=1.0 - alpha)
clf.fit(X, y)

# Make the prediction on the meshed x-axis
y_lower = clf.predict(xx)

clf.set_params(loss='ls')
clf.fit(X, y)

# Make the prediction on the meshed x-axis
y_pred = clf.predict(xx)

Plot Results

Plot the function, the prediction and the 90% confidence interval based on the MSE

In [6]:
def data_to_plotly(k):
    data = []
    
    for i in range(0, len(k)):
        data.append(k[i][0])
    
    return data
    
In [7]:
sinx = go.Scatter(x=data_to_plotly(xx), y=data_to_plotly(f(xx)),
                  mode='lines',
                  line=dict(color='black', dash='dash'),
                  name='f(x) = xsin(x)'
                 )

observations = go.Scatter(x=data_to_plotly(X), y=y,
                          mode='markers',
                          marker=dict(color='blue', size=10),
                          name='Observations'
                         )

prediction = go.Scatter(x=data_to_plotly(xx), y=y_pred,
                        name='Prediction',
                        mode='lines',
                        line=dict(color='red')
                       )

trace = go.Scatter(x=data_to_plotly(np.concatenate([xx, xx[::-1]])),
                   y=np.concatenate([y_upper, y_lower[::-1]]),
                   showlegend=False,
                   line=dict(color='blue'),
                   name='90% prediction interval',
                   fill='tozeroy'
                  )

layout = go.Layout(xaxis=dict(title='x'),
                   yaxis=dict(title='f(x)')
                   )
fig = go.Figure(data=[trace, sinx, observations, prediction], layout=layout)
In [8]:
py.iplot(fig)
Out[8]:
Still need help?
Contact Us

For guaranteed 24 hour response turnarounds, upgrade to a Developer Support Plan.