Title: Learning to Generate Columns with Application to Vertex Coloring. Abstract: We present a new column generation approach based on Machine Learning (ML) for solving combinatorial optimization problems. The aim of our method is to generate high-quality columns that belong to an optimal integer solution, in contrast to the traditional approach that aims at solving linear programming relaxations. To achieve this aim, we design novel features to characterize a column, and develop an effective ML model to predict whether a column belongs to an optimal integer solution. We then use the ML model as a filter to select high-quality columns generated from a sampling method and use the selected columns to construct an integer solution.  Our method is computationally fast compared to the traditional methods that generate columns by repeatedly solving a pricing problem. We demonstrate the efficacy of our method on the vertex coloring problem, by empirically showing that the columns selected by our ML model are significantly better, in terms of the integer solution that can be constructed from them, than those selected randomly or based only on their reduced cost. Further, we show that the columns generated by our method can be used as a warm start to boost the performance of a column generation-based heuristic.