部落格

Return-direction classifiers are imbalanced problems, and 0.5 is the wrong decision threshold. Comparing scale_pos_weight, focal loss, and precision-constrained threshold optimization on crypto data — plus the engineering differences between XGBoost, LightGBM, and CatBoost.

DCC-GARCH tells you when crypto dependence tightens. Transfer entropy tells you which way it points. A directed information-flow measure, its null calibration, and an honest account of what it does and does not add over average pairwise correlation.

Reconstructing trade direction from OHLCV, bar history, or venues without an aggressor flag — the classic rules, the stale-quote problem, bulk volume classification, and how to measure them against crypto's free ground truth.

Sequence models fed tick data still assume regular spacing. Three ways to tell a Transformer when a tick actually happened — learnable-timescale continuous encoding, ODE-RNN latent state, and delta_t as a plain feature — and the ablation that decides between them.

This series has priced the selection route to a false edge — DSR prices the winner, PBO prices the search. Neither touches confounding: the strategy that made money because volatility doubled the week you deployed it. The Synthetic Control Method builds a weighted counterfactual from a donor pool of untouched instruments and gives you a falsification criterion and a placebo p-value.

How to evaluate a predictive distribution honestly — CRPS as a proper scoring rule, the PIT histogram as a calibration diagnostic, and DeepAR sampling in GluonTS.

Putting the Heston, free-boundary, and jump-diffusion pricing PDEs into a neural network loss — the log-price residual, the mixed-partial autograd trick, and what still needs measuring.

How PCMCI's two-stage MCI test recovers directed causal links between crypto assets where correlation and bivariate Granger cannot — the construction, the tigramite pipeline, and the real-data study it still needs.

Turning raw book updates into a signed flow quantity: the CKS event decomposition, multi-level OFI with PCA reduction, and Lee-Ready trade classification — plus an honest accounting of what the headline R-squared actually measures.

Neural ODEs, Neural SDEs and continuous normalizing flows for irregularly-sampled market data — and the one ablation that decides whether continuous dynamics are worth their solver cost.

Does jointly predicting return, volume, and volatility actually help? Measuring loss-balancing schemes and diagnosing negative transfer through gradient cosine similarity — with a classical baseline and purged walk-forward folds.

Magnitude and structured pruning, the Lottery Ticket Hypothesis, movement pruning, distillation and 2:4 sparsity — the methods behind shrinking a trading model, and what still has to be measured before any of it ships.

Our VWAP article shipped a static, weekly-refit volume curve and called the forecaster the weakest link. This is the follow-up: a Bayesian intraday updater run against the same 500-parent BTCUSDT harness, with the IS delta conditioned on realized curve error.

Dynamic Mode Decomposition fits a linear operator to nonlinear market dynamics. The only question that matters: do the fitted modes persist from one window to the next, and does the rolling spectral radius lead realised volatility? Here is the measurement protocol and the code to run it.

The blog's standing answer to the accuracy-vs-latency tension is a two-stage fast/slow split. Distillation is a different answer: train one small model to mimic the ensemble. The KD loss, temperature, born-again nets, early exits for a variable latency budget, and the distill-to-FPGA pipeline — plus the measurements that would decide whether it beats the two-stage split.

Selection bias in the search is not the only way a regression fools you. When the regressor is correlated with the error, more data makes the estimate more confidently wrong. Instrumental variables applied to the one endogeneity problem this blog has already left open: permanent impact from net taker flow.

Fitting a self-exciting point process to real crypto trade tape: where the three numbers (mu, alpha, beta) come from, how to estimate the branching ratio n, whether the exponential kernel survives a goodness-of-fit test, and how much n moves when you change the estimation window.

Hamiltonian Neural Networks are provably stable — but stability is worthless if the conserved quantity does not exist. Learning a scalar H via autograd, symplectic integration, and the falsification test that decides whether a financial (q, p) pair is canonical at all.

Granger causality on crypto prices done two ways — differenced returns and Toda-Yamamoto on levels — with a correct Wald implementation, an effective-N corrected causality matrix, and a rolling-stability test of whether the lag is tradeable at all.

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.

Automated feature generation (tsfresh, Featuretools), budget-aware model search (FLAML's cost-frugal optimizer), and the WorldQuant formulaic alpha factory — the parts of the research pipeline this blog's search-and-overfit arc never covered, and what the arc's own results say about them.

Every leveraged position advertises the price at which it must be sold. How to build the on-chain liquidation depth chart and the CEX liquidation heatmap, model cascade dynamics as a reproduction number, and trade forced flow as a signal instead of only fearing it as a risk.

An active v3 LP is running a market-making book with gas costs and no cancel button. Size ranges from a GARCH vol forecast, frame rebalancing as fee-gain vs realized-cost, derive the position delta from tick math and hedge it with perps, and understand JIT liquidity and the honest pitfalls of backtesting LP from on-chain data.

MEV stopped being a lone bot and became an assembly line: searcher, builder, relay, proposer. A technical walk through proposer-builder separation, MEV-Boost's sealed-bid block auction, why the searcher's margin gets bid away, order-flow auctions as the new moat, and how Solana's Jito model differs.

Finding an on-chain arbitrage cycle is the easy half. The hard half is winning the sealed-bid priority auction against every other searcher who found the same cycle. A technical breakdown of atomicity, flash loans, backrunning, and where arb profit actually survives — including non-atomic CEX-DEX.

Impermanent loss, concentrated-liquidity leverage, and loss-versus-rebalancing derived from first principles. The closed forms, the σ²/8 result, per-block markout, and the exact fee-versus-volatility condition under which an LP actually beats holding.

Almgren-Chriss 與 VWAP 只負責設定切片預算——執行的勝負卻在戰術層決出。升級計時器、maker-taker 盈虧平衡數學、Binance/OKX/CME 上 amend 與 cancel-replace 的佇列語義、冰山訂單的反訊號洩露,以及一套 Python 逐切片狀態機。

用依賴於規模、波動率和流動性的成本曲線取代恆定的 bps 滑點:平方根定律、從 TCA 成交或公開資料擬合曲線、市場狀態壓力乘數,以及為什麼你的策略排行榜會重新洗牌。

為什麼加密 SOR 比股票路由更難：沒有合併行情、幻影流動性、預注資本。一套帶數學與 Python 的凸路由最佳化、maker 感知的戰術，以及來自你自己 TCA 的分場所 markout 排行榜。