ParzenWindow

Performing non-parametric Parzen Window estimation on the 'ted_main.csv' dataset, both from scratch and using built-in functions. The duration column of the dataset is extracted to estimate its distribution using Parzen Window with Gaussian kernel.

From Scratch

Here is the implementation of the Parzen Window with Gaussian kernel from scratch.

def ParzenWindow_est(x,x_samples,h):
	k=0
	for xi in x_samples:
		k += norm.pdf((x-xi)/h,loc=0,scale=1)
	p=k/(len(x_samples)*h)
	return p

Below are the results of the distribution estimation for various window widths (h).

h	10	[20, 50, 100]
Estimation

Window width (h) is also known as the smoothing factor. As you can observe, increasing h leads to a smoother distribution.

With Built-in Functions

from sklearn.neighbors import KernelDensity

The table below displays the sample set sizes, ranging from 250 samples to the entire dataset, with increments of 250.

10% of the Dataset	20% of the Dataset	29% of the Dataset	39% of the Dataset	49% of the Dataset
59% of the Dataset	69% of the Dataset	78% of the Dataset	88% of the Dataset	98% of the Dataset

It can be inferred that the larger the sample set, the smoother the distribution becomes, eventually converging to the actual distribution.