Characterize structural compatibility conditions for Markov-network biochemical classifiers

Determine the conditions that define structural compatibility between chosen input-edge assignments, output-node selections, and input datasets in Markov jump-process network classifiers by characterizing the feasible region of such assignments, for example in terms analogous to constrained optimization.

Background

The authors introduce structural compatibility to describe when a specific choice of input edges, output nodes, and dataset labels can, in principle, be solved by training the Markov network. Some assignments lead to fundamental mismatches—independent of training—due to how inputs influence spanning trees contributing to output nodes.

They explicitly defer a systematic analysis of this issue, suggesting it can be posed as identifying a feasible region, akin to constrained optimization, to predict solvable classification assignments for a given graph topology and input/output mapping.