A machine learning model was created to predict the electron spectrum generated by a GeV-class laser wakefield accelerator. The model was constructed from variational convolutional neural networks, which mapped the results of secondary laser and plasma diagnostics to the generated electron spectrum. An ensemble of trained networks was used to predict the electron spectrum and to provide an estimation of the uncertainty of that prediction. It is anticipated that this approach will be useful for inferring the electron spectrum prior to undergoing any process that can alter or destroy the beam. In addition, the model provides insight into the scaling of electron beam properties due to stochastic fluctuations in the laser energy and plasma electron density.