Bayesian Intermittent Demand Forecasting for Large Inventories
We present a scalable and robust Bayesian method for demand forecasting in the context of a large e-commerce platform, paying special attention to intermittent and bursty target statistics. Inference is approximated by the Newton-Raphson algorithm, reduced to linear-time Kalman smoothing, which allows us to operate on several orders of magnitude larger problems than previous related work. In a study on large real-world sales datasets, our method outperforms competing approaches on fast and medium moving items.
The paper aims to forecast accurate probability distributions of demand, particularly when the data is count or bursty as in an e-commerce setting. To do this, state space models are extended as in the case of GLMs, with a double logistic link function, and algorithms are proposed for maximum likelihood learning of parameters.
The authors should familarize themselves with the work on State Space Models in statistics: a useful starting point would be Durbin, James, and Siem Jan Koopman. Time series analysis by state space methods. No. 38. Oxford University Press, 2012. There is a big section of the book devoted to non gaussian models, and they would also find discussion on adding regression effects, referred to as "modeling of deterministic part" in the paper, line 27-28. In particular, closely related papers would be:        Fahrmeir, Ludwig, and Stefan Wagenpfeil. "Penalized likelihood estimation and iterative Kalman smoothing for non-Gaussian dynamic regression models." Computational Statistics and Data Analysis 24.3 (1997): 295-320.    Durbin, James, and Siem Jan Koopman. "Time series analysis of non‐Gaussian observations based on state space models from both classical and Bayesian perspectives." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 62.1 (2000): 3-56.    The above papers discuss how finding the mode reduces to kalman Smoothing, and simplifying the non-gaussian likelihood by linearising it around its mode.     Its hard for me to judge the paper without any discussion on relation with very closely related papers. However, based on my understanding a lot of the technical contributions of the paper are well known. More detailed comments follow below.     1.) How is the proposed method bayesian ?    2.) The abstract says you pay special attention to "intermittent and burst" items, but then at the end, it is mentioned that improvements are for fast and medium moving items. Isnt this contradictory ? How can an item be both intermittent and fast moving at the same time ?     3.)12-13. "Classical forecasting methods produce gaussian distrbutions only": not true. See the references I cited.    4.)18-19. very crucial point. should have been emphasized and elaborated on more.    5.) line 28: again not true representation of related work.    6.)Discussion in 3.1 and 3.2, are very hard to follow. Since this is a core and crucial technical contribution of the paper, its important to be presented in a clear way.    7.) Eq. (3) is non-standard, and most people with Math/Statistics background would find it puzzling since measurement error is completely skipped. I know this notation is from one of the references, but it would be better to follow standard notation which is more widely followed.    8.)Section 5.1 is fairly obvious and can be skipped.