# Is kernel density estimation a GMM with uniform mixture weight?

recall that for a Gaussian Mixture Model, the density of p(x) (multivariate) is $$P(x) = \Sigma_{i=1}^{C}\pi(c_i)\mathcal{N}(\mu_i,\Sigma_i)$$

On the other hand, non-parametric density estimation using kernel can be stated as follows, $$P(x)=\frac{1}{N}\Sigma_{i=1}^{N}\frac{1}{(2\pi h^2)^\frac{D}{2}}exp(-\frac{||x-x_n||^2}{2h^2})$$

where N is total number of data we have and D is the dimension we're in, and h is window size.

It seems to me that non-parametric estimation is just a GMM with uniformly distributed prior. But I can't find any justification.

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