Laser powder bed fusion (L-PBF) parts often require post-processing prior to use in engineering applications to improve mechanical properties and modify the as-built surface topography. The ability to tune the L-PBF process parameters to obtain designer as-built surface topography could reduce the need for post-processing. However, the relationship between the as-built surface topography and the L-PBF process parameters is currently not well-understood. In this paper, we derive data-driven models from surface topography data and L-PBF process parameters using machine learning (ML) algorithms. The prediction accuracy of the data-driven models derived from ML algorithms exceeds that of the multivariate regression benchmark because the latter does not always capture the complex relationship between the as-built surface topography parameters and the corresponding L-PBF process parameters in a single best-fit equation. Data-driven models based on decision tree (interpretable) and artificial neural network (non-interpretable) algorithms display the highest prediction accuracy. We also show experimental evidence that thermocapillary convection and melt track overlap are important drivers of the formation of as-built surface topography.