15 Discrete Latent Variables
Chapter 11
We have seen how complex distributions can be constructed by combining multiple simple distributions and how the resulting models can be described by directed graphs. In addition to the observed variables, which form part of the data set, such models often introduce additional hidden, or latent, variables. These might correspond to specific quantities involved in the data generation process, such as the unknown orientation of an object in three-dimensional space in the case of images, or they may be introduced simply as modelling constructs to allow much richer models to be created. If we define a joint distribution over observed and latent variables, the corresponding distribution of the observed variables alone is obtained by marginalization. This allows relatively complex marginal distributions over observed variables to be expressed in terms of more tractable joint distributions over the expanded space of observed and latent variables. In this chapter, we will see that marginalizing over discrete latent variables gives
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