Mixed membership RNNs for modeling customer purchases

Models of sequential data such as the recurrent neural network (RNN) often implicitly treat a sequence of data as having a fixed time interval between observations. They also do not account for group-level effects when multiple sequences are observed generated from separate sources. A simple example is user purchasing behavior, where each user generates a unique sequence of purchases and the time between purchases is variable. We propose a model for such sequential data based on the RNN that accounts for varying time intervals between observations in a sequence. We do this by learning a group-level "base" parameter to which each data-generating object can revert as more time passes before the next observation. This requires modeling assumptions about the data that we argue are typically satisfied by consumer purchasing behavior. Our approach is motivated by the mixed membership framework, with Latent Dirichlet Allocation being the canonical example, which we adapt to our dynamic setting. We demonstrate our approach on two consumer shopping datasets: The Instacart set of 3.4 million online grocery orders made by 206K customers and a UK retail set consisting of over 500K orders.