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If aren't they synonymous, what distinguishes the one from the other? Is probability density estimation a certain kind of generative model? Can any generative model be regarded as density estimation?

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Density estimation is generally seen as a nonparametric goal: rather than using specific families such as the Gamma family or the Normal family, density estimation procedures can arrive at any shape. I haven't seen anyone use the name "density estimation" for a parametric procedure, presumably because then it's just parameter estimation.

By contrast, generative models often have parametric components; for example, the Latent Dirichlet Allocation model uses the Dirichlet distribution.

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  • $\begingroup$ Thanks. Here Prof. Ng introduces EM as a way of doing density estimation, wouldn't that be a parametric goal? youtu.be/ZZGTuAkF-Hw?list=PLA89DCFA6ADACE599&t=1279 $\endgroup$ – Lenar Hoyt Jan 12 '16 at 22:28
  • $\begingroup$ I guess it's a fuzzy boundary. Nonparametric procedures sometime use mixtures of Gaussians -- just with one Gaussian per data point. They might even be used generatively; that's sort of the idea behind the bootstrap. I would never call LDA "density estimation", even though it can yield a density estimate. $\endgroup$ – eric_kernfeld Jan 13 '16 at 20:57

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