Ibrahim Laklaa.

Abstract

Five classifiers, from logistic regression to an MLP, on 8,000 synthetic borrowers, explained by a consensus of feature importances. Alongside, a European call priced by Black-Scholes, by Monte Carlo on 200,000 antithetic GBM paths and by a neural network trained on 50,000 analytical prices, with Greeks and convergence analysis.

Abstract

A from-scratch reimplementation of Song et al. (ICLR 2021) in PyTorch and JAX. Using the analytic score of a Gaussian mixture isolates integrator error from model error: the probability-flow ODE is the most accurate integrator yet the least robust to a learned score, discretisation error shows up as a width error rather than mode collapse, and the Langevin corrector only pays in high dimension.

Abstract

A synthetic benchmark where the Bayes posterior is known in closed form turns uncertainty quantification into a falsifiable experiment. Total uncertainty is split exactly into epistemic and aleatoric parts with MC dropout and deep ensembles, calibration is reported with bootstrap intervals, and six experiments test recovery, data scaling, temperature scaling under shift, OOD detection and deferral.

Abstract

Fidelity quantum kernels in Qiskit (Z, ZZ, Pauli feature maps) and a projected quantum kernel, benchmarked against RBF, linear, polynomial and random Fourier feature baselines over 10 seeds with bootstrap intervals and McNemar tests. Classical kernels win by about 17 points on MNIST 3 vs 5, and kernel concentration and barren plateaus are reproduced empirically.

Abstract

Detects latent market regimes with an HMM, a Gaussian mixture and spectral clustering on 13 engineered features, then conditions five allocation methods on the regime. Walk-forward backtests over 2009-2023: GMM-conditioned Markowitz doubles the Sharpe ratio of static Markowitz, and CVaR optimisation cuts the maximum drawdown by 69 % versus equal weight.