1. A computer-implemented method for using a hidden-variable model to generate enhanced action messages, the method comprising: accessing, at a prediction subsystem of a computer system, a set of action messages, each action message of the set of action messages including a set of key/value pairs and an identification of an action assigned to the action message by an abstraction layer, the action representing an actual or inferred user interaction with at least part of a website; extracting, from an action message in the set of action messages, a website identifier, the action message being associated with a user device; determining a session identifier for the action message; identifying, at the prediction subsystem and based on the website identifier, a current predictive model configured to generate action predictions, the current predictive model being configured to process a representation one or more past action observations to estimate one or more hidden variables and to generate output data corresponding to a subsequent-action prediction based on the one or more hidden variables; processing, at the prediction subsystem, input data representing the action identified in the action message using the current predictive model to estimate the one or more hidden variables and to generate the output data corresponding to the subsequent-action prediction; generating, at the prediction subsystem, an enhanced action message for the action message, at least part of the enhanced action message including prediction information corresponding to the output data, the prediction information representing a likelihood of subsequently detecting, in association with the user device, one or more user interactions with the website that correspond to a particular type of event or action; and outputting, from the prediction subsystem, the enhanced action message to an enhanced-action-message sink, the enhanced-action-message sink including one or both of a downstream subsystem of the computer system and a remote system.