Probabilistic inference improved through base tensor networks
On Probabilistic Inference Through Parametric Tensor Decomposition in Base Tensor Networks
Artificial Intelligence
Summary
Probabilistic inference helps computers make smart guesses based on uncertain information, but it’s usually only easy with simple models. The paper’s authors introduce a new way to reorganize these models into a 'base tensor network' that captures hidden patterns. By breaking down this network into smaller parts with familiar structures, it becomes easier to compute even in complex cases. This method allows efficient reasoning that was previously limited to simpler or specially-structured problems.
What this means in practice
- •For machine learning engineers: Improve inference efficiency on complex probabilistic models lacking explicit structures by using parametric tensor decompositions.
- •For computer vision developers: Enable more efficient probabilistic reasoning in image analysis tasks that rely on high-treewidth graphical models without known symmetries.
Authors
Sagad Hamid, Tanya Braun
Abstract
Probabilistic inference is generally only tractable in low-treewidth graphical models, limiting its effective applicability in high-treewidth settings. Many existing methods improve efficiency by exploiting specific parametric structure, such as symmetries. However, they typically require such structure to be explicitly present, limiting their applicability to a broader range of graphical models. To address this limitation, we propose a framework where tractable inference is controlled by latent parametric structure exploitation, rather than requiring it to be explicitly present a priori. Our approach first reparameterises a graphical model as a specific tensor network representation, which we call a base tensor network. This representation yields two key properties that allow inference tractability to be controlled by parametric structure: 1) First, the complexity of inference is mainly determined by the parametric structure of a single tensor, called the base tensor. We characterise several tractable classes of base tensors for which the entire base tensor network can be contracted efficiently. 2) Second, decomposing the base tensor yields again a collection of base tensor networks. This allows inference to be naturally reduced to decomposing the base tensor into tractable components with sufficient parametric structure. We call this procedure parametric tensor decomposition. By exploiting parametric structure within the base tensor, our framework enables a novel view on inference beyond settings where such structure is explicitly present.