Emerging research frontiers and computational advances have gradually transformed cognitive science into a multidisciplinary and data-driven field. As a result, there is a proliferation of cognitive theories investigated and interpreted from different academic lens and in different levels of abstraction. We formulate this applied aspect of this challenge as the computational cognitive inference, and describe the major routes of computational approaches. To balance the potential optimism alongside the speed and scale of the data-driven era of cognitive science, we propose to inspect this trend in more empirical terms by identifying the operational challenges, societal impacts and ethical guidelines in conducting research and interpreting results from the computational inference in cognitive science.