Vortex-induced vibration (VIV) of long flexible cylinders in deep water involves a large number of physical variables, such as Strouhal number, Reynolds number, mass ratio, damping parameter etc. Among all the variables, it is essential to identify the most important parameters for robust VIV response prediction. In this paper, machine learning techniques were applied to iteratively reduce the dimension of VIV related parameters. The crossflow vibration amplitude was chosen as the prediction target. A neural network was used to build nonlinear mappings between a set of up to seventeen input parameters and the predicted crossflow vibration amplitude. The data used in this study came from 38-meter-long bare cylinders of 30 and 80 mm diameters, which were tested in uniform and sheared flows at Marintek in 2011. A baseline prediction using the full set of seventeen parameters gave a prediction error of 12%. The objective was then to determine the minimum number of input parameters that would yield approximately the same level of prediction accuracy as the baseline prediction. Feature selection techniques including both forward greedy feature selection and combinatorial search were implemented in a neural network model with two hidden layers. A prediction error of 13% was achieved using only six of the original seventeen input parameters. The results provide insight as to those parameters which are truly important in the prediction of the VIV of flexible cylinders. It was also shown that the coupling between inline and crossflow vibration has significant influence. It was also confirmed that Reynolds number and the damping parameter, c*, are important for predicting the crossflow response amplitude of long flexible cylinders. While shear parameter was not helpful for response amplitude prediction.