A latent variable model represents unobserved variables alongside observed variables. The latent variables capture hidden conditions or causes that help explain how observed data arise. section 2.3.2
The observed joint distribution omits latent variables, while the full joint distribution includes both. Marginalizing over the latent variables recovers the distribution of observable outcomes. section 2.3.2
A latent variable model can support several modeling workflows:
- Represent hidden factors such as a document’s topic, a person’s inclination to act, or the strength of a physical object. section 2.3.2
- Specify a data-generating process in which latent initial conditions produce observed variables through deterministic or probabilistic mechanisms. section 2.3.2
- Extend a structural causal model by treating exogenous variables as latent proxies for unmodeled causes and assigning each endogenous variable a latent parent. section 6.1.6
Hidden impact in a window-breaking process
Suppose two observed variables record whether Jenny and Brian throw rocks, while window_breaks is also observed. A hidden strength_of_impact variable depends on who throws, and window_strength determines whether the window breaks. The code implements this process and returns only the observed outcomes.
