source: arxiv statistics ml: deep gaussian processes on directed acyclic graphs
level: research
many real-world systems can be described as functions connected along a directed acyclic graph, such as causal mechanisms, multi-fidelity engineering models, or gene regulatory networks. these functions are often observed only partially, with noisy and irregularly sampled data, making it hard to reconstruct the full process, propagate uncertainty, or perform inference. to address this, the authors place gaussian process priors over the functions, leading to a model called deep gaussian processes on dags.
the paper provides a theoretical analysis of how information flows through such models. it examines prior collapse, where the model loses sensitivity to inputs as depth increases, and shows how graph structure and intermediate observations can prevent this. the authors derive almost-sure lower bounds on the depth at which inputs remain distinguishable, identify kernel classes that satisfy these bounds, and prove that with enough intermediate data, information can be preserved even in deep graphs.
this work offers a principled way to handle complex, structured data where relationships are not simply sequential but follow a directed acyclic topology. by combining the flexibility of deep gaussian processes with the constraints of a dag, the model can capture intricate dependencies while providing uncertainty estimates. the theoretical results give practical guidance on when and how such models can be reliably used, avoiding the common pitfall of losing meaningful signal in deep architectures.
why it matters: it provides a theoretically grounded method for modeling complex, graph-structured processes with uncertainty, useful in causal inference, multi-fidelity simulations, and systems biology.
source: arxiv statistics ml: deep gaussian processes on directed acyclic graphs