Probabilistic Models

Probabilistic Models

A probabilistic model asserts how observations from a natural phenomenon arise. The model is a joint distribution \[\begin{aligned} p(\mathbf{x}, \mathbf{z})\end{aligned}\] of observed variables $(\mathbf{x})$ corresponding to data, and latent variables $(\mathbf{z})$ that provide the hidden structure to generate from $(\mathbf{x})$. The joint distribution factorizes into two components.

The likelihood \[\begin{aligned} p(\mathbf{x} \mid \mathbf{z})\end{aligned}\] is a probability distribution that describes how any data $(\mathbf{x})$ depend on the latent variables $(\mathbf{z})$. The likelihood posits a data generating process, where the data $(\mathbf{x})$ are assumed drawn from the likelihood conditioned on a particular hidden pattern described by $(\mathbf{z})$.

The prior \[\begin{aligned} p(\mathbf{z})\end{aligned}\] is a probability distribution that describes the latent variables present in the data. It posits a generating process of the hidden structure.

For details on how to specify a model in Edward, see the model API. We describe several examples in detail in the tutorials.