Probabilistic inference is tractable in low‑treewidth graphical models but becomes infeasible for high‑treewidth structures. Existing approaches improve efficiency by exploiting explicit parametric patterns such as symmetries, which limits their applicability to models that already exhibit those patterns. To overcome this restriction we introduce a framework where tractability is governed by latent parametric structure rather than by an a‑priori explicit one.
We first re‑parameterise a graphical model as a specific tensor‑network form that we call a base tensor network. This representation has two key properties: (1) the inference cost is dominated by the parametric structure of a single tensor – the base tensor. We identify several tractable classes of base tensors that allow the whole network to be contracted efficiently; (2) decomposing the base tensor yields a new collection of base tensor networks, turning inference into the task of decomposing the base tensor into tractable components with sufficient parametric structure, a process we term parametric tensor decomposition.
By exploiting hidden structure inside the base tensor, the framework enables efficient probabilistic inference for a much broader range of graphical models without requiring explicit structural assumptions.
Review