Diffusion-aware Censored Gaussian Processes for Demand Modelling

TL;DR

This paper introduces a novel demand modeling approach combining censored Gaussian processes with graph diffusion to better estimate true demand and account for substitution effects among similar products.

Contribution

It proposes Diffusion-aware Censored Demand Models integrating Tobit likelihood with graph diffusion in Gaussian processes, addressing substitution effects in demand estimation.

Findings

Improved demand recovery in simulated data

More accurate out-of-sample predictions on real-world data

Effectively models substitution effects among similar products

Abstract

Inferring the true demand for a product or a service from aggregate data is often challenging due to the limited available supply, thus resulting in observations that are censored and correspond to the realized demand, thereby not accounting for the unsatisfied demand. Censored regression models are able to account for the effect of censoring due to the limited supply, but they don't consider the effect of substitutions, which may cause the demand for similar alternative products or services to increase. This paper proposes Diffusion-aware Censored Demand Models, which combine a Tobit likelihood with a graph diffusion process in order to model the latent process of transfer of unsatisfied demand between similar products or services. We instantiate this new class of models under the framework of GPs and, based on both simulated and real-world data for modeling sales, bike-sharing demand, and EV charging demand, demonstrate its ability to better recover the true demand and produce more accurate out-of-sample predictions.