Modeling Language Process as Hierarchical Adaptive Random Distributions

Modeling the process of language is particularly challenging due to its complex nature and the continuous changes required to ensure its relevance. The process of constructing words from a set of characters or sentences from a set of words, among others, is intrinsically hierarchical and conditional. Consequently, we conceptualize the design as recursive, where each level of the process depends on the outcomes of the lower level, and so on. At each level, the process can be seen as a random experiment which involves sequentially selecting one item at a time until a terminal item is reached, where each item is itself a random experiment to be constructed at the lower level. Given that each experiment is inherently conditional, we primarily model this process in discrete intervals. Then at each trial of the experiment, we characterize the selection probability on observed outcomes from previous trials. This enables us to analyze when a specific item is most likely to occur and how the selection probability evolves over successive trials. The cost of the estimation step is reduced through sampling. Finally, the estimation of the variance of the parameter estimate is provided.