The outstanding performance of deep learning (DL) for computer vision and natural language processing has fueled increased interest in applying these algorithms more broadly in both research and practice. This study investigates the application of DL techniques to classification of large sparse behavioral data—which has become ubiquitous in the age of big data collection. We report on an extensive search through DL architecture variants and compare the predictive performance of DL with that of carefully regularized logistic regression (LR), which previously (and repeatedly) has been found to be the most accurate machine learning technique generally for sparse behavioral data. At a high level, we demonstrate that by following recommendations from the literature, researchers and practitioners who are not DL experts can achieve world-class performance using DL. More specifically, we report several findings. As a main result, applying DL on 39 big sparse behavioral classification tasks demonstrates a significant performance improvement compared with LR. A follow-up result suggests that if one were to choose the best shallow technique (rather than just LR), there still would often be an improvement from using DL, but that in this case the magnitude of the improvement might not justify the high cost. Investigating when DL performs better, we find that worse performance is obtained for data sets with low signal-from-noise separability—in line with prior results comparing linear and nonlinear classifiers. Exploring why the deep architectures work well, we show that using the first-layer features learned by DL yields better generalization performance for a linear model than do unsupervised feature-reduction methods (e.g., singular-value decomposition). However, to do well enough to beat well-regularized LR with the original sparse representation, more layers from the deep distributed architecture are needed. With respect to interpreting how deep models come to their decisions, we demonstrate how the neurons on the lowest layer of the deep architecture capture nuances from the raw fine-grained features and allow intuitive interpretation. Looking forward, we propose the use of instance-level counterfactual explanations to gain insight into why deep models classify individual data instances the way they do.