A Quasi-Monte Carlo Method Based on Neural Autoregressive Flow

This paper proposes a novel transport quasi-Monte Carlo framework that combines randomized quasi-Monte Carlo sampling with a neural autoregressive flow architecture for efficient sampling and integration over complex, high-dimensional distributions. The method constructs a sequence of invertible transport maps to approximate the target density by decomposing it into a series of lower-dimensional marginals. Each sub-model leverages normalizing flows parameterized via monotonic beta-averaging transformations and is optimized using forward Kullback-Leibler (KL) divergence. To enhance computational efficiency, a hidden-variable mechanism that transfers optimized parameters between sub-models is adopted. Numerical experiments on a banana-shaped distribution demonstrate that this new approach outperforms standard Monte Carlo-based normalizing flows in both sampling accuracy and integral estimation. Further, the model is applied to A-share stock return data and shows reliable predictive performance in semiannual return forecasts, while accurately capturing covariance structures across assets. The results highlight the potential of transport quasi-Monte Carlo (TQMC) in financial modeling and other high-dimensional inference tasks.