  Morphology and structure of galaxies reflect their star formation and
assembly histories. We use the framework of mutual information ($\mathrm{MI}$)
to quantify interdependence among several structural variables and to rank them
according to their relevance for predicting specific star formation rate (SSFR)
by comparing the $\mathrm{MI}$ of the predictor variables with SSFR and
penalizing variables that are redundant. We apply this framework to study $\sim
3,700$ face-on star-forming galaxies (SFGs) with varying degrees of bulge
dominance and central concentration and with stellar mass $M_\star \approx
10^9\,M_\odot - 5\times 10^{11}\,M_\odot$ at redshift $z = 0.02-0.12$. We use
the Sloan Digital Sky Survey (SDSS) Stripe 82 deep $i$-band imaging data, which
improve measurements of asymmetry and bulge dominance indicators. We find that
star-forming galaxies are a multi-parameter family. In addition to $M_\star$,
asymmetry emerges as the most powerful predictor of SSFR residuals of SFGs,
followed by bulge prominence/concentration. Star-forming galaxies with higher
asymmetry and stronger bulges have higher SSFR at a given $M_\star$. The
asymmetry reflects both irregular spiral arms and lopsidedness in seemingly
isolated SFGs and structural perturbations by galaxy interactions or mergers.
