Surface roughness is key in determining a material's performance. It plays a critical role in determining properties like adhesion and friction, but achieving quantitative predictions from topographic measurements has remained challenging. Here, we demonstrate how statistical machine learning can establish strong correlations between roughness measurements and surface properties, enabling predictive data-driven models. Our approach is based on a novel class of statistical descriptors, called scale-dependent roughness parameters (SDRPs), which capture surface roughness across multiple scales and allow combining multiple measurements on the same specimen into single statistical descriptor. These SDRPs are used as features in Gaussian process classifiers and regressors to predict surface properties. We apply this to predict friction coefficients in shoe-floor interactions, modeling the complex tribosystem of viscoelastic rubber soles sliding on rough surfaces, enhancing our understanding of friction behavior in practical applications.