Modeling human decision making plays a fundamental role in the design of intelligent systems capable of rich interactions. In this paper we consider the task of choice prediction in settings with multiple alternatives. Cognitive models of decision making can successfully replicate and explain behavioral effects involving uncertainty and interactions among alternatives but are computationally intensive to train. ML approaches excel in terms of choice prediction accuracy, but fail to provide insights on the underlying preference reasoning. We study different degrees of integration of ML and cognitive models for this task. We show, via testing on behavioral data, that our hybrid approach, based on the integration of a neural network and the Multi-attribute Linear Ballistic Accumulator cognitive model, requires significantly less time to train, and allows to capture important cognitive parameters while maintaining similar accuracy to the pure ML approach.