  This paper proposes a new approach to sales forecasting for new products with
long lead time but short product life cycle. These SKUs are usually sold for
one season only, without any replenishments. An exponential factorization
machine (EFM) sales forecast model is developed to solve this problem which not
only considers SKU attributes, but also pairwise interactions. The EFM model is
significantly different from the original Factorization Machines (FM) from
two-fold: (1) the attribute-level formulation for explanatory variables and (2)
exponential formulation for the positive response variable. The attribute-level
formation excludes infeasible intra-attribute interactions and results in more
efficient feature engineering comparing with the conventional one-hot encoding,
while the exponential formulation is demonstrated more effective than the
log-transformation for the positive but not skewed distributed responses. In
order to estimate the parameters, percentage error squares (PES) and error
squares (ES) are minimized by a proposed adaptive batch gradient descent method
over the training set. Real-world data provided by a footwear retailer in
Singapore is used for testing the proposed approach. The forecasting
performance in terms of both mean absolute percentage error (MAPE) and mean
absolute error (MAE) compares favourably with not only off-the-shelf models but
also results reported by extant sales and demand forecasting studies. The
effectiveness of the proposed approach is also demonstrated by two external
public datasets. Moreover, we prove the theoretical relationships between PES
and ES minimization, and present an important property of the PES minimization
for regression models; that it trains models to underestimate data. This
property fits the situation of sales forecasting where unit-holding cost is
much greater than the unit-shortage cost.
