This CMU Machine Learning Text Book is talking about naive bayes.

Of course we must also estimate the priors on Y as well

$π_k = P(Y = y_k)$

The above model summarizes a Gaussian Naive Bayes classifier, which assumes that the data X is generated by a mixture of class-conditional (i.e., dependent on the value of the class variable Y) Gaussians.

Does mixture here mean is a Gaussian mixture model, which is a probabilistic model that assumes all the data points are generated from a mixture of a finite number of Gaussian distributions with unknown parameters?


Exactly! Each class conditional density, i.e. $p_{X|Y}(x|y_k)$ is in Gaussian form, and the overall distribution is the distribution of $X$, i.e. $$p_X(x)=\sum p_{X|Y}(x|y_k)\pi_k$$

...which assumes that the data X is generated by... $[p_X(x)]$


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