A Dependent Feature Allocation Model Based on Random Fields

We introduce a flexible framework for modeling dependent feature allocations. Our approach addresses limitations in traditional nonparametric methods by directly modeling the logit-probability surface of the feature paintbox, enabling the explicit incorporation of covariates and complex but tractable dependence structures. The core of our model is a Gaussian Markov Random Field (GMRF), which we use to robustly decompose the latent field, separating a structural component based on the baseline covariates from intrinsic, unstructured heterogeneity. This structure is not a rigid grid but a sparse k-nearest neighbors graph derived from the latent geometry in the data, ensuring high-dimensional tractability. We extend this framework to a dynamic spatio-temporal process, allowing item effects to evolve via an Ornstein-Uhlenbeck process. Feature correlations are captured using a low-rank factorization of their joint prior. We demonstrate our model’s utility by applying it to a polypharmacy dataset, successfully inferring latent health conditions from patient drug profiles.

💡 Research Summary

This paper introduces a novel framework for dependent feature allocation that departs from traditional non‑parametric approaches such as the Indian Buffet Process (IBP). Instead of treating feature probabilities as independent Beta‑distributed random variables, the authors embed the entire binary feature matrix into a continuous probability surface defined on the unit square (