Horseshoe sparsity and Kolmogorov complexity

Establish a rigorous mathematical relationship between coefficient sparsity induced by the horseshoe prior in K-GAM models and Kolmogorov complexity (program-length) notions of minimal description for functions or data.

Background

The paper observes a conceptual parallel between sparsity (few nonzero coefficients under horseshoe priors) and minimal program descriptions in Kolmogorov complexity.

While the analogy is compelling, the authors emphasize that a formal, mathematical link is lacking and remains to be established.

References

The analogy highlights a shared principle (parsimony) but the mathematical relationship between coefficient sparsity and program length remains open.

— Bell's Inequality, Causal Bounds, and Quantum Bayesian Computation: A Unified Framework  (2603.28973 - Polson et al., 30 Mar 2026) in Section 5, following Proposition “Horseshoe sparsity in K-GAM” (Connection to Kolmogorov complexity)