Non Parametric Density Estimation

For this project, we generate a dataset for three classes each with 500 samples from three Gaussian distribution described below:

$$ class1:\quad\mu = \binom{2}{5} \qquad \sum = \begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix} $$

$$ class2:\quad\mu = \binom{8}{1} \qquad \sum = \begin{pmatrix} 3 & 1 \\ 1 & 3 \end{pmatrix} $$

$$ class3:\quad\mu = \binom{5}{3} \qquad \sum = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix} $$

Use generated data and estimate the density without pre-assuming a model for the distribution which is done by a non-parametric estimation. Implement the Histogram PDF estimation methods using h=0.09,0.3,0.6. Estimate P(X) and Plot the true and estimated PDF.

True Density 3D

Histogram Density 3D

It is clear that as 'h' is larger, the histogram becomes more general and we lose details, and as 'h' is smaller, some bins may be empty and discontinuous.