Characterize Training-to-Deployment Stress Coverage

Determine whether a corruption law used for training StochLOB, denoted by q_t, adequately covers a deployment stress law ν, particularly with respect to the radial and angular mismatch between the training corruption distribution and realized limit-order-book shocks.

Background

StochLOB trains a deterministic limit-order-book trend classifier using isotropic Gaussian scale-mixture corruptions whose random scale produces heavy-tailed or jump-like perturbations. The paper notes that robustness under an unseen deployment stress distribution depends not only on the training-side loss but also on a coverage constant involving the chi-squared divergence between the deployment stress law ν and the training corruption law q_t.

The paper further decomposes this mismatch into radial and angular components. Heavy-tailed corruption can improve radial coverage of large residuals, but isotropic noise may fail to represent the signed, cross-level, and state-dependent directions of actual order-book stress. In the high-dimensional LOB setting, the angular Rényi-divergence term may become dominant, so it remains unresolved whether a training corruption law that is useful in the auxiliary score-matching task also provides sufficient coverage for the stress distribution encountered at deployment.