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what is the difference in training and testing between the Gaussian and Mixture of Gaussians? Are they the same except one is unimodal and one is multimodal?

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  • Training / learning / estimate a Gaussian (using maximize likelihood) is an relative easy task. There are some proof behind the conclusion, but the conclusion is simple. We can use the empirical mean and empirical variance as our estimated parameters. For example, if we have 1000 data that is measuring a person's weight, we can just get the sample mean $\mu$ and variance $\sigma^2$ and say our model is $\mathcal{N}(\mu,\sigma^2)$

  • Training a mixture of Gaussian is not as easy as single Gaussian. We need to use algorithms to get the parameters, such as Expectation Maximization. For example, if we have 1000 data that is measuring a person's weight but want to fit a mixture Gaussian with 2 genders, we need to run an algorithm to do that, to get $5$ parameters $\mu_1,\sigma_1^2,\mu_2,\sigma_2^2,\theta$, where $\theta$ is the proportion between two Gaussian.

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