We propose in~\cite{AleCriGhi26} a novel extension of the Indian Buffet Process (IBP) that introduces explicit probabilistic dependence among features in multi-factorial innovation processes. In contrast to classical IBP models \cite{GG06,GG11}, where feature inclusion events are independent, our model allows the inclusion of a feature to influence the inclusion probabilities of others, providing a framework to study interacting latent factors in a mathematically tractable setting.

We develop a rigorous probabilistic formulation and derive asymptotic results for key quantities, including the total number of observed features $D_t$, the averaged number of features per agent/item $\overline{T}_t$, the averaged feature inclusion probability $\overline{P}_t$, the averaged number of agents/items per feature $\overline{K}_t$, as well as feature-specific quantities such as inclusion probability $P_t(j)$ and popularity $K_{t,j}$ for an observed feature $j$. While the asymptotic growth of $D_t$ coincides with that of the classical three-parameter IBP \cite{TG}, the interacting structure induces novel asymptotic phenomena in both averaged and feature-specific quantities, including power-law behavior and non-linear growth in feature popularity, not observed in the standard IBP.

Our theoretical results include strong laws of large numbers and central limit theorems for these quantities, providing probabilistic guarantees and detailed characterization of the stochastic behavior of the system. This model offers a combination of analytical tractability, interpretability, and flexibility, allowing the study of multi-feature systems with explicit interactions, while extending the asymptotic theory of classical IBP models to settings with dependent feature allocations.