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I have a bimodal distribution for the range [-0.1, 0.1] which can be viewed here:

enter image description here

I want to train/fit a Kernel Density Estimation (KDE) on the bimodal distribution as shown in the picture and then, given any other distribution say a uniform distribution such as:

# a uniform distribution between the same range [-0.1, 0.1]-
u_data = np.random.uniform(low = -0.1, high = 0.1, size = (1782,))

I want to be able to use the trained KDE to 'predict' how many of the data points from the given data distribution (say, 'u_data') belong to the target bimodal distribution.

I tried the following code but it doesn't work out:

# Here 'a' is the numpy array containing target bimodal distribution.

# Generate random samples-
kde_samples = {}

for kernel in ['tophat', 'gaussian']:
    # Train a kernel on bimodal data distribution 'a'-
    kde = KernelDensity(kernel=kernel, bandwidth=0.2).fit(a.reshape(-1, 1))

    # Try and generate 300 random samples from trained model-
    kde_samples[kernel] = np.exp(kde.sample(300))



# Visualize data distribution using histograms-
plt.hist(a, bins=20, label = 'original distribution')
# sns.distplot(a, kde = True, bins = 20, label = 'original distribution')
plt.hist(kde_samples['gaussian'], bins = 20, label = 'KDE: Gaussian')
plt.hist(kde_samples['tophat'], bins = 20, label = 'KDE: tophat')

plt.title("KDE: Data distribution")
plt.xlabel("weights")
plt.ylabel("frequency")
plt.legend(loc = 'best')
plt.show()

This gives the following visualization:

KDE different kernels

Two things are wrong:

  1. The range of the generated samples are wrong!
  2. The distribution of generated data is NOT bimodal

How can I therefore: train/fit a Kernel Density Estimation (KDE) on the bimodal distribution and then, given any other distribution (say a uniform or normal distribution) be able to use the trained KDE to 'predict' how many of the data points from the given data distribution belong to the target bimodal distribution.

I am using Python 3.8 and sklearn 0.22.

Thanks!

Arun
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  • Why don't you plot the KDE itself onto the histogram first, to see how good the fit is? And you can't really expect the range to stay the same when you transform the values with the exponential function, can you? – Arne Apr 27 '20 at 12:14
  • @Arne how do I plot the KDE onto the histogram? I am new to sklearn KDE, can you post some code? – Arun Apr 27 '20 at 12:31
  • See here: https://stackoverflow.com/questions/33323432/add-kde-on-to-a-histogram – Arne Apr 27 '20 at 12:50

0 Answers0