Recommender systems are ubiquitous in the domain of e-commerce, used to improve the user experience and to market inventory, thereby increasing revenue for the site. Techniques such as item-based collaborative filtering are used to model users' behavioral interactions with items and make recommendations from items that have similar behavioral patterns. However, there are challenges when applying these techniques on extremely sparse and volatile datasets. On some e-commerce sites, such as eBay, the volatile inventory and minimal structured information about items make it very difficult to aggregate user interactions with an item. In this work, we describe a novel deep learning-based method to address the challenges. We propose an objective function that optimizes a similarity measure between binary implicit feedback vectors between two items. We demonstrate formally and empirically that a model trained to optimize this function estimates the log of the cosine similarity between the feedback vectors. We also propose a neural network architecture optimized on this objective. We present the results of experiments comparing the output of the neural network with traditional item-based collaborative filtering models on an implicit-feedback dataset, as well as results of experiments comparing different neural network architectures on user purchase behavior on eBay. Finally, we discuss the results of an A/B test that show marked improvement of the proposed technique over eBay's existing collaborative filtering recommender system.