All Times ET
Keywords: bayesian neural networks, causality, structural equation models, KL divergence
We extend the empirical results from the structural equation model (SEM) published in the paper "Assortment Planning for Retail Buying, Retail Store Operations, and Firm Performance" [1] by implementing the directed acyclic graph of the SEM as a causal Bayesian neural network. The neural network is shown to converge more quickly when the node with the weakest SEM path is removed, with barely any difference in final validation loss. However, this occurs only when variational inference is provided by perturbing the neural network weights using the Kullback-Leibler divergence with Flipout layers. In contrast, results are inconclusive when variational inference is provided by perturbing weights using Monte Carlo sampling at the output layer with the Vadam optimizer. The implication is that removing the node with the weakest causal connection reduces the KL divergence and therefore speeds up neural network convergence in a Bayesian neural network that relies on it to provide variational inference.