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We explore the applications of machine learning techniques in relativistic laser-plasma experiments beyond optimization purposes. We predict the beam charge of electrons produced in a laser wakefield accelerator given the laser wavefront change caused by a deformable mirror. Machine learning enables feature analysis beyond merely searching for an optimal beam charge, showing that specific aberrations in the laser wavefront are favored in generating higher beam charges. Supervised learning models allow characterizing the measured data quality as well as recognizing irreproducible data and potential outliers. We also include virtual measurement errors in the experimental data to examine the model robustness under these conditions. This work demonstrates how machine learning methods can benefit data analysis and physics interpretation in a highly nonlinear problem of relativistic laser-plasma interaction.