  Access to a large variety of data across a massive population has made it
possible to predict customer purchase patterns and responses to marketing
campaigns. In particular, accurate demand forecasts for popular products with
frequent repeat purchases are essential since these products are one of the
main drivers of profits. However, buyer purchase patterns are extremely diverse
and sparse on a per-product level due to population heterogeneity as well as
dependence in purchase patterns across product categories. Traditional methods
in survival analysis have proven effective in dealing with censored data by
assuming parametric distributions on inter-arrival times. Distributional
parameters are then fitted, typically in a regression framework. On the other
hand, neural-network based models take a non-parametric approach to learn
relations from a larger functional class. However, the lack of distributional
assumptions make it difficult to model partially observed data. In this paper,
we model directly the inter-arrival times as well as the partially observed
information at each time step in a survival-based approach using Recurrent
Neural Networks (RNN) to model purchase times jointly over several products.
Instead of predicting a point estimate for inter-arrival times, the RNN outputs
parameters that define a distributional estimate. The loss function is the
negative log-likelihood of these parameters given partially observed data. This
approach allows one to leverage both fully observed data as well as partial
information. By externalizing the censoring problem through a log-likelihood
loss function, we show that substantial improvements over state-of-the-art
machine learning methods can be achieved. We present experimental results based
on two open datasets as well as a study on a real dataset from a large
retailer.
