Forecasting of Commercial Sales with Large Scale Gaussian Processes

Abstract

This paper argues that there has not been enough discussion in the field of applications of Gaussian Process for the fast moving consumer goods industry. Yet, this technique can be important as it e.g., can provide automatic feature relevance determination and the posterior mean can unlock insights on the data. Significant challenges are the large size and high dimensionality of commercial data at a point of sale. The study reviews approaches in the Gaussian Processes modeling for large data sets, evaluates their performance on commercial sales and shows value of this type of models as a decision-making tool for management.

When Gaussian Process Meets Big Data: A Review of Scalable GPs

“…∈ [0, 1] is an inverse link function 26 that squashes f into the class probability space. Differently, the multi-class GPC (MGPC) [228] with y ∈ {1, · · · , C} is f c ∼ GP(0, k c ), p(y|f ) = Categorical(π(f )), (37) where {f c } C c=1 are independent latent functions 27 for C classes, and f = [f 1 , · · · , f C ] T : R d → R C . 28 Due to the non-Gaussian likelihood, exact inference for GPC however is intractable, thus requiring approximate inference, the key of which approximates the non-Gaussian posterior p(f |y) ∝ p(y|f )p(f ) with a Gaussian q(f |y) [227].…”

“…This sidesteps the non-Gaussian likelihood. A more principled way however is adopting GPCs in (36) and (37), and combining approximate inference, e.g., laplace approximation, EP and VI, with the sparse strategies in section III-C to derive scalable GPCs [90], [233]- [237]. 29 The main challenges of scalable GPC, especially MGPC, are: (i) the intractable inference and posterior, and (ii) the high training complexity for a large C. For the first issue, the stochastic GPC derives the model evidence expressed as the integration over an one-dimensional Gaussian distribution, which can be adequately calculated using Gaussian-Hermite quadrature [234], [238].…”

“…When organizing the inducing points into Kronecker structure, sparse approximations can further reduce the complexity to O(n) [18], [34]. In the meantime, by reorganizing the variational lower bound, stochastic optimization is available for sparse approximations with a remarkable complexity of O(m 3 ) [1], [35], [36], enabling the regression with million-and even billion-sized data points [36], [37].…”

“…The survey[16] at 14 years ago focuses on the prior approximations, which is just a part of our review in section III-C1. The recent comparison and survey[37],[44] provide however a quick and rough review without detailed analysis.…”

Demand Forecasting Techniques for Build-to-Order Lean Manufacturing Supply Chains

“…The aims and backgrounds of this research is to present a technique for data pre-processing accessible to non-technical business experts. Traditional forecasting methods are still being used primarily by over 40% of demand planners in the industry, [10], and the use of novel machine learning methods is a promising area with little academic research and insufficient efforts to expose practitioners to them, [24] [25].…”