# Unsupervised Learning We can express our data distribution by marginalizing [[Latenent Variable Models|latent variables]] (unobserved targets/values that make it easier to understand the data). This allows us to model the data with more tractable joint distributions with simpler components to understand: $ \begin{aligned} z \text { continuous: } p(\boldsymbol{x}) & =\int p(\boldsymbol{x}, \boldsymbol{z}) d \boldsymbol{z}=\int p(\boldsymbol{x} \mid \boldsymbol{z}) p(\boldsymbol{z}) d \boldsymbol{z} \\ \boldsymbol{z} \text { discrete: } p(\boldsymbol{x}) & =\sum_{\boldsymbol{z}} p(\boldsymbol{x}, \boldsymbol{z})=\sum_{\boldsymbol{z}} p(\boldsymbol{x} \mid \boldsymbol{z}) p(\boldsymbol{z}) \end{aligned} $ --- ## References