Verdict: PARTIAL alignment. The method detects non-linear dependence as advertised, but its built-in significance machinery over-rejects on financial data by a factor of 2-3. Usable as a secondary check; not a drop-in production replacement.
Hub trail: /CLAUDE.md โ findings โ audits โ audit hub โ aggregated-hsic/
What this method does, in plain English
It maps every data point into a high-dimensional "kernel space" โ a coordinate system where curved relationships look more like straight lines โ then checks whether the two variables stay correlated in that space. It does this at four different "zoom levels" (kernel bandwidths) and combines the verdicts, so you don't have to commit to one zoom level. The number it outputs is a p-value: small means "these variables really are dependent"; large means "looks like they could be independent."
Minimum p-value across 4 kernel bandwidths, per audit pair. Pairs where Spearman called them "independent" are highlighted.
| Pair | Prior audit | Spearman ฯ | HSICAgg p_min | Flag at ฮฑ=0.05? |
|---|---|---|---|---|
| ofi โ turnover_imbalance | REDUNDANT-PERFECT | +1.000 | 0.0050 | YES |
| vwap โ close | REDUNDANT-PERFECT | +0.967 | 0.0050 | YES |
| vwap โ open | REDUNDANT-PERFECT | +0.993 | 0.0050 | YES |
| buy_volume โ sell_volume | REDUNDANT-HIGH | +0.718 | 0.0050 | YES |
| ofi โ aggression_ratio | REDUNDANT-MODERATE | +0.793 | 0.0050 | YES |
| vwap_close_deviation โ price_impact | REDUNDANT-MODERATE | โ0.020 | 0.0199 | YES |
| kyle_lambda_proxy โ ofi | ORTHOGONAL | โ0.170 | 0.0050 | YES |
| kyle_lambda_proxy โ buy_volume | ORTHOGONAL | +0.049 | 0.0050 | YES |
| Paper claim | How we tested | Result |
|---|---|---|
| HSIC = 0 iff X โฅ Y (for universal kernels) | Synthetic independent Gaussians at N=500 | p_min = 0.49 โ |
| Catches non-linear dependence (Y = Xยฒ) | Synthetic Y = Xยฒ + noise | p_min at floor 0.005 โ |
| Aggregation removes bandwidth burden | Per-bandwidth p-values on pair 6: 0.025, 0.020, 0.060, 0.090 | Aggregation doing work โ |
| Significance correctly calibrated at ฮฑ | IAAFT surrogate Type-I rate on pairs 7+8 | 10% / 13% vs nominal 5% โ |
What "Type-I error inflation" means
If a statistical test is "calibrated at ฮฑ=0.05", it should incorrectly call independent things "dependent" only 5% of the time. We measured what it actually does on financial data and found it does that 10-13% of the time โ so it's twice as trigger-happy as advertised. The fix is to use a stricter threshold (ฮฑ=0.01 or 0.02) to get a true 5% false-positive rate. The reason this happens: the original papers assumed the data is "independent and identically distributed", but financial returns are bumpy and autocorrelated. That breaks the calibration math.
Flagged every pair Chatterjee flagged. Conceptually it measures the right thing. Useful for cross-method corroboration.
Raw p-values over-reject by 2-3ร. Production use needs hand-tightened ฮฑ to maintain intended Type-I rate.
~140ร slower than Chatterjee for comparable verdicts. Panel-wide broadening would be 4 hours vs 41 sec.
Provenance: committed in 5d44f419 ยท "Gate 0.5 spike for Aggregated HSIC + validation methodology in FRAMEWORK"