Quantum-Bayesian Structural Time-Series Machine Learning with Skew-Normal Innovations

AbstractThis study provides a comprehensive empirical benchmark of quantum, classical, and Bayesian machine learning approaches for regression under challenging small-sample conditions with multicollinear features and skew-normal innovations. We systematically compare nine algorithms—including three quantum methods (Quantum Circuit Learning, Quantum Error Regression, Quantum Kernel Methods),four classical machine learning techniques (Lasso, Ridge, Random Forest, Gradient Boosting, Support Vector Regression), and Bayesian Structural Time Series— across two sample size regimes (n=30 and n=80) with five features. Outcome of the study revealed robust sample-size-dependent performance hierarchies in regularized linear methods (Lasso, Ridge) and Bayesian paradigms which ordinarily subsist in small-sample regimes of (n=30), with RMSE values of 4.46-5.74, while non-linear ensemble methods (Random Forest) exhibited superiority with moderate samples (n=80, RMSE: 2.07). Quantum machine learning methods had overtimes underperform classical benchmarks when exhibiting 91% higher error rates at small sample size of n=30, this may be due to classical method learned the noise, though Quantum Circuit Learning exhibited substantial convergence toward classical performance at n=80 (only 25% worse than best model),thus higher sample sizes thresholds will be better off for quantum-classical parity.