We consider a seller who can dynamically adjust the price of a product at the individual customer level, by utilizing information about customers’ characteristics encoded as a $d$-dimensional feature vector. We assume a personalized demand model, parameters of which depend on $s$ out of the $d$ features. The seller initially does not know the relationship…

Adaptive gradient-based optimizers such as AdaGrad and Adam are among the methods of choice in modern machine learning. These methods maintain second-order statistics of each model parameter, thus doubling the memory footprint of the optimizer. In behemoth-size applications, this memory overhead restricts the size of the model being used as well as the number of…

Bayesian inference for non-Gaussian state-space models is a ubiquitous problem with applications ranging from geophysical data assimilation to mathematical finance. We will discuss how deterministic couplings between probability distributions enable new solutions to this problem. We first consider filtering in high-dimensional models with nonlinear (potentially chaotic) dynamics and sparse observations in space and time. While…