Empirical substrate

WESAD dataset

TSST: Trier Social Stress Test

A validated laboratory stressor (Kirschbaum 1993). Two main phases before an evaluative panel:

Drives reliable +15–25 bpm sympathetic tachycardia + cortisol surge. The cardiac signal the watch can in principle see. Social-evaluative threat → SAM + HPA co-activation.

Why 15 subjects, not 16?

WESAD recorded 16 subjects; S12 excluded here for data quality (sustained ECG / wrist-signal artefact in the relevant windows). 15 usable.

Applied consistently across agreement, effect-size, and LOSO classification analyses.

Feature set

The 8 pseudo-HRV features

60 s windows, 30 s stride. HR → pseudo-IBI: \(\text{IBI} \approx 60000 / \text{HR}\).

Class	Feature
Level	mean HR
	mean pseudo-IBI
Dispersion	\(\sigma_{HR}\)
	HR range
	\(CV_{HR}\)
	\(\sigma_{\text{pseudo-IBI}}\) (SDNN proxy)
Dynamics	HR slope
	pseudo-RMSSD

"pseudo-" is not cosmetic: these are 1 Hz HR statistics, not clinical HRV (Camm et al. 1996).

The 8 features collapse to ≈ 3 effective axes: level / dispersion / slope. Mean HR vs Mean IBI r = −0.985.

Why 60 s windows, 30 s stride?

Classical HRV uses 5-min stationary records, but at 1 Hz that is 300 samples per window, and the TSST stress phase is shorter than 5 min. 60 s balances: enough beats to estimate dispersion, short enough to track state change. 50% overlap → CIs bootstrap subjects, not windows.

8 features or 3? Gini importance

Pseudo-RMSSD is informationally inside the dispersion cluster (\(r \approx 0.77\text{–}0.91\) with \(\sigma_{HR}\) / range).

Result A, the honest negative

Pseudo-HRV ≠ ECG-HRV

Feature vs ECG	Bias	r	ICC(2,1)
Mean HR	−3.04 bpm	0.73	≈ 0.70 (pooled)
Mean pseudo-IBI	+20 ms	0.76*	≈ 0.74*
\(\sigma_{\text{pseudo-IBI}}\) vs SDNN	large	low	0.02
pseudo-RMSSD vs RMSSD	> 120 ms LoA	0.13	0.00

* mostly arithmetic inverse of HR; not an independent HRV signal

For absolute HRV measurement, the 1 Hz stream fails, and we can say exactly by how much.

Pooled ICC 0.70 but median 0.40: why?

The pooled ICC absorbs between-subject HR spread (different people sit at different resting HR).

It reflects ranking different people similarly, not tracking within-person state changes. Strip the between-subject variance and the median per-subject ICC falls to 0.40.

So even mean HR is not window-level interchangeable with ECG.

What could a better wrist signal do?

Wrist PRV from the raw 64 Hz Empatica signal (not downsampled):

A 64 Hz wrist signal partly recovers variability, but Garmin does not expose it to third parties.

Conceptual centrepiece

Why both are true: the paradox

Agreement and classification answer different questions.

Why keep pseudo-RMSSD at all?

Discriminative at window level (d = 0.60) but informationally redundant with σ_HR / HR range (r ≈ 0.77–0.91).

Dropped for deployment at only −1.1 pp cost. Kept in the paper to complete the agreement story: without it the "pseudo" honesty argument has a hole.

Result C, the headline

LOSO classification

Most of this is a calibrated tachycardia detector. The other five features add ≈ 1 pp.   Context: WESAD wrist 70.0% (3-class), not like-for-like.

One feature → 77%

A single within-subject z-scored mean-HR feature already reaches 77.0% BA / 84.4% AUC. Add one dispersion feature → 78.0%. The five IBI/variability features together add ≈ 1 pp.

How does this compare?

Different task, different signal, different evaluation: not a direct comparison, only context.

Honest failure mode

Per-subject heterogeneity

Per-subject balanced accuracy ranges 42.11% (S2) → 92.83% (S11), a 50.7 pp spread, the central empirical finding.

• 11 / 15 above 70%.
• 4 near or below chance (S2, S9, S15, S6).
• ~25% of users would get unreliable output with no warning.
• S2 AUC = 55%: the signal itself is weak, not a threshold problem (no model recovers what the stream doesn't contain).

Plausibly ~15–20% of healthy people are blunted responders (Dickerson 2004).

Confidence cross-check

Calibration + ARIMA confidence

Probability calibration

Raw SVM probabilities already usable: Brier Skill Score 0.397; isotonic → 0.403 (negligible; a safety measure, not a skill gain).

Enables abstention: flag 0.4 < p̂ < 0.6 as "uncertain".

ARIMA cross-check

Forecast each subject's baseline HR into stress; count windows outside 95% PI → anomaly detection rate (ADR).

Per-subject ADR vs SVM accuracy: r = 0.742.

Responder type	ADR	SVM acc.
Strong	> 50%	87.9%
Weak	≤ 10%	52.2%

A 35.7 pp gap: a confidence signal derivable from baseline HR alone. N=15, 95% CI [0.37, 0.91]; internal consistency check, not independent validation.

How is ADR computed?

Per subject: fit ARIMA on baseline HR, forecast into stress period, count 60-s windows whose mean HR falls outside the 95% prediction interval → ADR.

Also a directionality finding: HR stabilises against anticipatory drift once stress begins.

Proposed confidence gate

Two branches over the same 1 Hz HR stream:

1. calibrated stress probability from the classifier;
2. baseline ARIMA anomaly flag from the 95% prediction interval.

This is a deployment proposal motivated by WESAD, not an on-device validated feature.