Modeling Response Time in Digital Human Communication

Our daily lives increasingly involve interactions with other individuals via different communication channels, such as email, text messaging, and social media. In this paper we focus on the problem of modeling and predicting how long it takes an individual to respond to an incoming communication event, such as receiving an email or a text. In particular, we explore the effect on response times of an individual’s temporal pattern of activity, such as circadian and weekly patterns which are typically present in individual data. A probabilistic time-warping approach is used, considering linear time to be a transformation of “effective time,” where the transformation is a function of an individual’s activity rate. We apply this transformation of time to two different types of temporal event models, the first for modeling response times directly, and the second for modeling event times via a Hawkes process. We apply our approach to two different sets of real-world email histories. The experimental results clearly indicate that the transformation-based approach produces systematically better models and predictions compared to simpler methods that ignore circadian and weekly patterns. Current technology allows us to collect large quantities of time-stamped individual-level event data characterizing our “digital behavior” in contexts such as texting, email activity, microblogging, social media interactions, and more — and the volume and variety of this type of data is continually increasing. The resulting time-series of events are rich in behavioral information about our daily lives. Tools for obtaining and visualizing such information are becoming increasingly popular, such as the ability to download your entire email history for mail applications such as Gmail, and various software packages for tracking personal fitness using data from devices such as Fitbit. This paper is focused on modeling the temporal aspects of how an individual (also referred to as the “ego”) responds to others, given a sequence of timestamped events (e.g. communication messages via email or text). What can we learn from the way we respond to others? Are there systematic ∗Currently employed at Google. The research described in this paper was conducted while the author was a graduate student at UC Irvine.   Example of smoothed daily and weekly patterns over two separate individuals’ email histories. ) on the yaxis represents an individual’s typical activity as a function of time. patterns that can be extracted and used predictively? How do our daily sleep and work patterns factor in to our response patterns? These are common issues that arise when modeling communication events, as the ego’s behavior typically changes significantly over the course of a day or week. Examples of such patterns are shown in Figure 1. We propose a novel method for parameterizing these circadian (daily) and weekly patterns, allowing the time dimension to be transformed according to such patterns. This transformation of time will allow models to describe and predict behavioral patterns which are invariant to the ego’s routine patterns. We apply this approach to predicting the ego’s response time to an event. Learning such response patterns is useful not only for identifying relationships between pairs of individuals (Halpin and De Boeck 2013), but also as features for prioritization of events, e.g., the priority inbox implemented in Gmail (Aberdeen, Pacovsky, and Slater 2010). Our experimental results show clear advantages in terms of predictive power when modeling response times in the transformed time domain. τ0 τ1 τ2 t0 t1 t2 ∆0