Abstract In this paper we address the computational aspects of uniformly accurate numerical methods for solving highly oscillatory evolution equations. particular, introduce an approximation strategy that allows construction arbitrary high-order using solely right-hand side differential equation. No derivative vector field is required, while uniform accuracy retained. The then applied to two di...

Summary Modern methods for Bayesian regression beyond the Gaussian response setting are often computationally impractical or inaccurate in high dimensions. In fact, as discussed recent literature, bypassing such a trade-off is still an open problem even routine binary models, and there limited theory on quality of variational approximations high-dimensional settings. To address this gap, we stu...