获取SciPy的gaussian_kde函数使用的带宽 [英] Getting bandwidth used by SciPy's gaussian_kde function

问题描述

我正在使用SciPy的

您可以通过这种方式进行检查，如果您使用新功能(例如使用sklearn)创建kde:

从sklearn.neighbors

 导入KernelDensitydef kde_sklearn(x，x_grid，带宽):kde_skl = KernelDensity(带宽=带宽)kde_skl.fit(x [:, np.newaxis])#score_samples()返回样本的对数似然log_pdf = kde_skl.score_samples(x_grid [:, np.newaxis])pdf = np.exp(log_pdf)返回pdf 

现在使用上面的相同代码，您将得到:

  plot(x_grid，kde_sklearn(sample，x_grid，f)) 

  plot(x_grid，kde_sklearn(sample，x_grid，bw)) 

I'm using SciPy's stats.gaussian_kde function to generate a kernel density estimate (kde) function from a data set of x,y points.

This is a simple MWE of my code:

import numpy as np
from scipy import stats

def random_data(N):
    # Generate some random data.
    return np.random.uniform(0., 10., N)

# Data lists.
x_data = random_data(100)
y_data = random_data(100)

# Obtain the gaussian kernel.
kernel = stats.gaussian_kde(np.vstack([x_data, y_data]))

Since I'm not setting a bandwidth manually (via the bw_method key), the function defaults to using Scott's rule (see function's description). What I need is to obtain this bandwidth value set automatically by the stats.gaussian_kde function.

I've tried using:

print kernel.set_bandwidth()

but it always returns None instead of a float.

解决方案

Short answer

The bandwidth is kernel.covariance_factor() multiplied by the std of the sample that you are using.

(This is in the case of 1D sample and it is computed using Scott's rule of thumb in the default case).

Example:

from scipy.stats import gaussian_kde
sample = np.random.normal(0., 2., 100)
kde = gaussian_kde(sample)
f = kde.covariance_factor()
bw = f * sample.std()

The pdf that you get is this:

from pylab import plot
x_grid = np.linspace(-6, 6, 200)
plot(x_grid, kde.evaluate(x_grid))

You can check it this way, If you use a new function to create a kde using, say, sklearn:

from sklearn.neighbors import KernelDensity
def kde_sklearn(x, x_grid, bandwidth):
    kde_skl = KernelDensity(bandwidth=bandwidth)
    kde_skl.fit(x[:, np.newaxis])
    # score_samples() returns the log-likelihood of the samples
    log_pdf = kde_skl.score_samples(x_grid[:, np.newaxis])
    pdf = np.exp(log_pdf)
    return pdf

Now using the same code from above you get:

plot(x_grid, kde_sklearn(sample, x_grid, f))

plot(x_grid, kde_sklearn(sample, x_grid, bw))

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