Blog

Kernel design for financial time series — Matern roughness, locally periodic composition, spectral mixtures — and the marginal likelihood as a regularizer that needs no validation set. Plus the honest list of what still has to be measured before any of it is tradeable.

Operator learning maps whole function spaces, not points — how the Fourier Neural Operator parameterizes a PDE solution operator in frequency space, what that buys for option pricing, and which of its claims still need measuring on real hardware.

Flash Attention makes a 23,400-step trading context computationally free — tiling, online softmax, and an IO bound of N^2 d^2 / M. Whether that longer context makes the model better is a separate question, and it has to be measured, not asserted.

Three things about trading ensembles this blog has not covered: why the covariance term — not model count — dominates ensemble error, how stacking works as a signal-combination layer with out-of-fold meta-features, and whether turnover netting across many signals actually reduces execution cost.

Every model on this blog so far answers 'what predicts what?'. Double ML answers 'what causes what?' — with a standard error you can defend. The partially linear model, Neyman orthogonality, purged cross-fitting on order book data, and an honest account of why a valid DML confidence interval survives exactly one pre-specified question.

Every backtest on this blog estimates a conditional mean. Causal forests estimate a conditional treatment effect instead — tau(x) rather than mu(x) — with honest splitting, an adaptive-kernel weight representation, and a calibration test that tells you whether the heterogeneity you found is real.

Every sizing rule on this blog treats uncertainty as one number. MC Dropout and deep ensembles split it into model ignorance and market noise — and those two deserve different position sizes.