Modeling user return time using inhomogeneous poisson process

For Intelligent Assistants (IA), user activity is often used as a lag metric for user satisfaction or engagement. Conversely, predictive leading metrics for engagement can be helpful with decision making and evaluating changes in satisfaction caused by new features. In this paper, we propose User Return Time (URT), a fine grain metric for gauging user engagement. To compute URT, we model continuous inter-arrival times between users’ use of service via a log Gaussian Cox process (LGCP), a form of inhomogeneous Poisson process which captures the irregular variations in user usage rate and personal preferences typical of an IA. We show the effectiveness of the proposed approaches on predicting the return time of users on real-world data collected from an IA. Experimental results demonstrate that our model is able to predict user return times reasonably well and considerably better than strong baselines that make the prediction based on past utterance frequency

A Bayesian Point Process Model for User Return Time Prediction in Recommendation Systems

In order to sustain the user-base for a web service, it is important to know the return time of a user to the service. In this work, we propose a point process model which captures the temporal dynamics of the user activities associated with a web service. The time at which the user returns to the service is predicted, given a set of historical data. We propose to use a Bayesian non-parametric model, log Gaussian Cox process (LGCP), which allows the latent intensity function generating the return times to be learnt non-parametrically from the data. It also allows us to encode prior domain knowledge such as periodicity in users return time using Gaussian process kernels. Further, we cap- ture the similarities among the users in their return time by using a multi-task learning approach in the LGCP framework. We compare the performance of LGCP with different kernels on a real- world last.fm data and show their superior performance over standard radial basis function kernel and baseline models. We also found LGCP with multitask learning kernel to provide an improved predictive performance by capturing the user similarity

Impact of non-Poisson activity patterns on spreading processes

Halting a computer or biological virus outbreak requires a detailed understanding of the timing of the interactions between susceptible and infected individuals. While current spreading models assume that users interact uniformly in time, following a Poisson process, a series of recent measurements indicate that the inter-contact time distribution is heavy tailed, corresponding to a temporally inhomogeneous bursty contact process. Here we show that the non-Poisson nature of the contact dynamics results in prevalence decay times significantly larger than predicted by the standard Poisson process based models. Our predictions are in agreement with the detailed time resolved prevalence data of computer viruses, which, according to virus bulletins, show a decay time close to a year, in contrast with the one day decay predicted by the standard Poisson process based models.Comment: 4 pages, 3 figure

Feller Processes: The Next Generation in Modeling. Brownian Motion, L\'evy Processes and Beyond

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of L\'evy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also L\'evy processes, of which Brownian Motion is a special case, have become increasingly popular. L\'evy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include L\'evy processes and in particular Brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.Comment: 22 pages, including 4 figures and 8 pages of source code for the generation of sample paths of Feller processe