Impact statement: While many of the successful and highly-visible applications of machine learning are in classification and regression, there are a broad range of applications that don’t naturally fit into these categories and that can potentially benefit significantly from machine learning approaches. In particular, in this paper we focus on continuous-time event data, which is very common in real-world applications but has not yet seen significant attention from the ML research community. There are multiple important problems in society where such data is common and that could benefit from the development of better predictive and simulation, including: • Education: Understanding of individual learning habits of students, especially in online educa- tional programs, could improve and allow for more personalized curricula. • Medicine: Customized tracking and predictions of medical events could save lives and improve patients’ quality of living. • Behavioral Models: Person-specific simulations of their behavior can lead to better systematic understandings of people’s social activities and actions in day-to-day lives. • Cybersecurity: Through the user identification capabilities, our work could aid in cyber-security applications for the purposes of identifying fraud detection and identify theft. Another potential positive broad impact of the work, is that by utilizing amortized VI, our methods do not require further costly training or fine-tuning to accommodate new users, which can potentially produce energy savings and lessen environmental impact in a production setting. On the other hand, as with many machine learning technologies, there is also always the potential for negative impact from a societal perspective. For example, more accurate individualized models for user-generated data could be used in a negative fashion for applications such as surveillance (e.g., to monitor and negatively impact individuals in protected groups). In addition, better predictions and recommendations for products and services, through explicitly conditioning on prior behavior from a user, could potentially further worsen existing privacy concerns.