Empirical radius formulas for canonical neutron stars from bidirectionally selecting EOS features in extended Bayesian analyses of observational data

Given the significant advancement in Bayesian inference of nuclear Equation of State (EOS) from gravitational wave and X-ray observations of neutron stars (NSs), especially since GW170817, is there a data-driven and robust empirical formula for the radius $R_{1.4}$ of canonical NSs in terms of the characteristic EOS parameters (features)? What is the single most important but currently poorly known EOS parameter for determining the $R_{1.4}$? We study these questions by extending the traditional Bayesian analysis which normally ends at presenting the marginalized posterior probability distribution functions (PDFs) of individual EOS parameters and their correlations (or sometimes only the Pearson correlation coefficients which are only reliably useful when the variables are linearly correlated while they are actually often not). Using three regression model-building methodologies: bidirectional step-wise feature selection, Least Absolute Shrinkage Selection Operator (LASSO) regression, and neural network regression on a large set of posterior EOSs and the corresponding $R_{1.4}$ values inferred from earlier comprehensive Bayesian analyses of NS observational data, we systematically and rigorously develop the most probable $R_{1.4}$ formulas with varying statistical accuracy and technical complexity. The most important EOS parameters for determining $R_{1.4}$ are found consistently in each of the feature/model selection processes to be (in order of decreasing importance): curvature $K_{sym}$, slope $L$, skewness $J_{sym}$ of nuclear symmetry energy, skewness $J_{0}$, incompressibility $K_{0}$ of symmetric nuclear matter, and the magnitude $E_{sym} (\rho_0)$ of symmetry energy at the saturation density $\rho_0$ of nuclear matter.