HORDCOIN: A Software Library for Higher Order Connected Information and Entropic Constraints Approximation

Abstract Background and objective Quantifying higher-order statistical dependencies in multivariate biomedical data is essential for understanding collective dynamics in complex systems such as neuronal populations. The connected information framework provides a principled decomposition of the total information content into contributions from interactions of increasing order. However, its application has been limited by the computational complexity of conventional maximum entropy formulations. In this work, we present a generalised formulation of connected information based on maximum entropy problems constrained by entropic quantities. Methods The entropic-constraint approach, contrasting with the original constraints based on marginals or moments, transforms the original nonconvex optimisation into a tractable linear program defined over polymatroid cones. This simplification enables efficient, robust estimation even under undersampling conditions. Results We present theoretical foundations, algorithmic implementation, and validation through numerical experiments and real-world data. Applications to symbolic sequences, large-scale neuronal recordings, and DNA sequences demonstrate that the proposed method accurately detects higher-order interactions and remains stable even with limited data. Conclusions The accompanying open-source software library, HORDCOIN (Higher ORDer COnnected INformation), provides user-friendly tools for computing connected information using both marginal- and entropy-based formulations. Overall, this work bridges the gap between abstract information-theoretic measures and practical biomedical data analysis, enabling scalable investigation of higher-order dependencies in neurophysiological and other complex biological systems such as the genome.