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Statistical downscaling of Global Climate Models (GCMs) allows researchers to study local climate change effects decades into the future. A wide range of statistical models have been applied to downscaling GCMs but recent advances in machine learning have not been explored compared to traditional approaches. In this paper, we compare five Perfect Prognosis (PP) approaches, Ordinary Least Squares, Elastic-Net, and Support Vector Machine along with two machine learning methods Multi-task Sparse Structure Learning (MSSL) and Autoencoder Neural Networks. In addition, we introduce a hybrid Model Output Statistics and PP approach by modeling the residuals of Bias Correction Spatial Disaggregation (BCSD) with MSSL. Metrics to evaluate each method's ability to capture daily anomalies, large-scale climate shifts, and extremes are analyzed. Generally, we find inconsistent performance between PP methods in their ability to predict daily anomalies and extremes as well as monthly and annual precipitation. However, results suggest that L-1 sparsity constraints aid in reducing error through internal feature selection. The MSSL+BCSD coupling, when compared with BCSD, improved daily, monthly, and annual predictability but decreased performance at the extremes. Hence, these results suggest that the direct application of state-of-the-art machine learning methods to statistical downscaling does not provide direct improvements over simpler, longstanding approaches.