HB-PVI: A Hierarchical Bayesian Personalization and Value-of-Information Framework for Complex Activity Recognition

Hammed A. Olayinka

cs.LGSep 4, 2026

HB-PVI: A Hierarchical Bayesian Personalization and Value-of-Information Framework for Complex Activity Recognition

Authors: Hammed A. Olayinka

Organizations: Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609 USA

Abstract

Personalization can improve activity-recognition performance, but participant-specific gains are heterogeneous, and every additional calibration label has an acquisition cost. This study presents HB-PVI, a hierarchical Bayesian personalization and value-of-information framework jointly modeling participant heterogeneity, the benefit and harm of four personalization mechanisms, and the economic value of an additional label, for the 47-participant MUSIC-CAR complex-activity cohort. A leakage-safe, leave-one-participant-out evaluation combines a sequential-Monte-Carlo participant-effect updater with a Student- $t$ hierarchical gain model and a one-step expected-value-of-sample-information (EVSI) stopping rule. Adapter personalization produced small positive mean F1 gains, growing from 0.00099 at one label to 0.00198 at ten, while adapter-plus-head and prototype-residual personalization were negative on average. Under the primary practical-benefit threshold ( $Δ_{\min}=0.01$ ) and cost setting, one-step EVSI was zero at every decision state, so the policy purchased no labels and retained population inference for all 47 participants, matching always-stop exactly (region-of-practical-equivalence probability $=1$ ). Relative to fixed ten-shot adapter personalization, this reduced labeling by 100% while keeping the posterior mean F1 loss at 0.00217 (95% credible interval, 0.00048 to 0.00389), with posterior probability 0.9992 of remaining below the 0.005 tolerance. HB-PVI was utility-optimal in 199 of 216 cost-threshold settings and in every setting at or above the primary label cost. These results argue for a population-first deployment policy whenever personalization gains are small relative to labeling, computation, and harm costs, and show that value-of-information reasoning, not raw predictive accuracy, should drive personalization decisions in health-sensing applications.

Figures & tables

Action	Shot	Mean gain	Pos. (%)	Ben. (%)	Harm (%)
Adapter	1	$+0.00099$	61.7	8.5	4.3
Adapter	10	$+0.00198$	72.3	10.6	4.3
Head	1	$+0.00109$	51.1	14.9	8.5
Head	10	$+0.00037$	55.3	19.1	10.6
Adapter+head	1	$-0.00236$	44.7	17.0	21.3
Adapter+head	10	$-0.00449$	48.9	21.3	25.5

TABLE I: Action-specific personalization gain at 1 and 10 purchased labels (percentages of 47 participants)

Fig. 1: Action-specific personalization outcomes across purchased labels. (A) Mean sample-level F1 gain relative to population inference, with 95% intervals. (B) Percentage of participants with meaningful benefit ( $g>0.01$ ). (C) Percentage with meaningful harm ( $g<-0.01$ ).

Study	Backbone	Personalization	Mean F1
MUSIC-CAR baseline [ 4 ]	Feature+XGBoost	None	0.588
P-HART [ 1 ]	P-HART transf.	None	0.880
P-HART [ 1 ]	P-HART transf.	6-shot adapter	0.926
HB-PVI (this study)	P-HART-style a	None (population)	0.904
HB-PVI (this study)	P-HART-style a	Adapter, 6 shots	0.905
HB-PVI (this study)	P-HART-style a	Adapter, 10 shots	0.906

TABLE II: Population and personalized mean F1 across related studies on the same cohort or sensor modality

Action	MAE	RMSE	Cov. (%)	Brier g>0	Brier g>.01
Adapter	0.00565	0.00824	91.9	0.2695	0.0915
Head	0.00958	0.01321	91.1	0.2721	0.1257
Adapter+head	0.01396	0.01857	88.9	0.2940	0.1318
Prototype-resid.	0.00325	0.00546	95.3	0.1860	0.0002

TABLE III: Held-out gain-model prediction and calibration by action

Fig. 2: Population-only F1 versus adapter F1 at (A) 1, (B) 6, and (C) 10 purchased labels, all 47 participants (Table ). Points scatter closely around the $y=x$ line at every shot count, and meaningful-benefit (green) and meaningful-harm (red) cases both occur at low and high baseline F1 alike, illustrating that realized gain is not predictable from population-only performance ( $r=-0.06$ at 10 shots.

Fig. 3: Fixed-order one-step EVSI and stopping decisions. (A) Mean EVSI under the primary setting; no state-level decision continued. (B) Labels purchased across the three practical-gain thresholds. (C) Action selected at stopping under the primary $\Delta_{\min}=0.01$ setting.

Comparator	Util.	$\Delta$ mean	95% CrI	$P(\Delta\!>\!0)$
Fixed adapter@1	$-0.00434$	$+0.00387$	(0.00054, 0.00723)	0.9892
Fixed adapter@6	$-0.00894$	$+0.00820$	(0.00492, 0.01157)	1.0000
Fixed adapter@10	$-0.01129$	$+0.01017$	(0.00703, 0.01343)	1.0000

TABLE IV: Realized comparator utility and posterior paired-utility difference (HB-PVI minus comparator)

$c_{L}$	0	0.0005	0.001	0.0025	0.005	0.01
HB-PVI optimal (%)	61.1	91.7	100.0	100.0	100.0	100.0

TABLE V: Percentage of the 36 computation-and-harm-penalty settings, per label cost

c_{L}

, in which HB-PVI was utility-optimal (across all

\Delta_{\min}

)

Fig. 4: Cost sensitivity and F1 preservation with zero calibration labels. (A) Percentage of computation-cost and harm-penalty settings in which HB-PVI was utility-optimal, by label cost and practical-gain threshold; the dotted vertical line marks the primary label cost. (B) Bayesian and bootstrap estimates of mean F1 loss from purchasing zero labels rather than using fixed adapter personalization at 1, 6, or 10 shots. The dashed vertical line marks the F1-loss tolerance of 0.005, and the annotations report the posterior probability that the mean loss remained below this tolerance.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Parameter	Prior
Model I (hierarchical multi-label prediction)
$\alpha_{k}$ (activity intercept)	$\mathcal{N}(0,2.5^{2})$
$\beta_{kq}$ (representation coef.)	Regularized horseshoe: $\beta_{kq}=\beta^{\mathrm{raw}}_{kq}\tau_{\beta,k}\tilde{\omega}_{kq}$ , $\tilde{\omega}_{kq}=c\,\omega_{kq}/\sqrt{c^{2}+(\tau_{\beta,k}\omega_{kq})^{2}}$ , $c=0.5$
$\beta^{\mathrm{raw}}_{kq}$	$\mathcal{N}(0,1)$
$\omega_{kq}$ (local shrinkage)	$\mathcal{N}^{+}(0,1)$
$\tau_{\beta,k}$ (global shrinkage)	$\mathcal{N}^{+}(0,0.10^{2})$

Appendix

Table S1: Prior specifications for Model I and Model II

Gate	Result (47/47 folds)
Minimum distinct population-posterior ancestors per state	$\geq 400$ : passed
Minimum final joint-particle ESS per state	$\geq 400$ : passed
Zero missing direct-state predictor keys	Passed
Zero missing participant-effect predictor keys	Passed
Enriched-state completeness (517/517 fold-shot states)	Passed

Appendix

Table S2: Validation gates for the sequential updater, evaluated on all 47 outer folds

Predictor	Domain
Shot count	Primary predictor
Ensemble mutual information (mean)	Ensemble uncertainty
Ensemble predictive entropy (mean)	Ensemble uncertainty
Ensemble predictive variance (mean)	Ensemble uncertainty
Purchased-label cardinality (mean)	Purchased-label summary
Purchased-label pattern diversity	Purchased-label summary

Appendix

Table S3: Sequential-state predictor dictionary used in Model II

Quantity	Value(s)
Practical-gain thresholds $\Delta_{\min}$	$\{0,\ 0.005,\ 0.01\}$
Eligibility constraint	$P(g>\Delta_{\min})\geq 0.90$ , $P(g<0)\leq 0.10$
Label-cost grid $c_{L}$	$\{0,\ 0.0005,\ 0.001,\ 0.0025,\ 0.005,\ 0.01\}$
Adapter computation-cost grid $c_{C}$	$\{0,\ 0.0005,\ 0.001\}$
Population computation cost	$0$ (fixed)
Harm-penalty grid $c_{R}$	$\{0,\ 0.005,\ 0.01,\ 0.02\}$

Appendix

Table S4: EVSI cost specification

Action	Shot	Mean F1 (95% CI)	Gain	Ben. $>$ .01 (%)	Harm $<-$ .01 (%)
Adapter	1	0.9052 (0.8810, 0.9272)	$+0.00099$	8.5	4.3
	2	0.9053 (0.8792, 0.9271)	$+0.00109$	8.5	4.3
	3	0.9053 (0.8797, 0.9270)	$+0.00105$	10.6	6.4
	4	0.9054 (0.8810, 0.9274)	$+0.00121$	8.5	4.3
	5	0.9055 (0.8807, 0.9270)	$+0.00124$	8.5	4.3
	6	0.9054 (0.8808, 0.9262)	$+0.00118$	8.5	4.3

Appendix

Table S5: Action-specific mean F1 and gain by shot (all 10 shots; percentages of 47 participants)

Shot	Min	Q1	Median	Q3	Max
1	$-0.02188$	$-0.00168$	$+0.00125$	$+0.00369$	$+0.02083$
6	$-0.02486$	$-0.00214$	$+0.00164$	$+0.00469$	$+0.01932$
10	$-0.02650$	$-0.00058$	$+0.00203$	$+0.00533$	$+0.01678$

Appendix

Table S6: Distribution of realized adapter gain across 47 participants, by shot count

Fold	Population F1	Adapter F1@1	Adapter F1@6	Adapter F1@10	Gain@10
000	0.5664	0.5606	0.5621	0.5777	+0.0113
001	0.7462	0.7505	0.7471	0.7482	+0.0020
002	0.6804	0.6811	0.6772	0.6699	-0.0105
003	0.7883	0.7887	0.7902	0.7885	+0.0002
004	0.7906	0.7687	0.7669	0.7641	-0.0265
005	0.9203	0.9158	0.9183	0.9203	+0.0000

Appendix

Table S7: Exact participant-specific population and adapter F1 scores, all 47 participants

Figure S1: Held-out gain-model prediction and calibration. (A) Prediction error (MAE, RMSE) by action. (B–C, E) Reliability curves comparing predicted and observed frequencies for positive gain, gain $>0.01$ , and negative gain (five probability bins per action-event combination; bins with $<10$ held-out observations omitted). (D) Empirical coverage of the nominal 95% predictive interval by action, with the 95% reference line.

Comparator	Div.	Max treedepth	Max $\widehat{R}$	Min bulk ESS	Min tail ESS
Always-stop	—	—	—	—	— a
Fixed adapter@1	0	0	1.0012	5871	5802
Fixed adapter@6	0	0	1.0007	5224	5909
Fixed adapter@10	0	0	1.0008	4099	3495

Appendix

Table S8: Paired-comparison posterior diagnostics (HB-PVI minus comparator)

$c_{L}$	HB-PVI best (%)	Runner-up policy (count)
0.0000	66.7	fixed_adapter_10 (4)
0.0005	91.7	fixed_adapter_1 (1)
0.0010	100.0	—
0.0025	100.0	—
0.0050	100.0	—
0.0100	100.0	—

Appendix

Table S9: HB-PVI utility-optimality by practical-gain threshold and label cost

Figure S2: HB-PVI utility-optimality (%) across the full label-cost ( $c_{L}$ ) and harm-penalty ( $c_{R}$ ) grid, averaged over the three computation-cost ( $c_{C}$ ) settings, for each practical-gain threshold. HB-PVI is never preferred only in the single cell where both costs are zero; it is preferred in a minority of settings only when exactly one of the two costs is zero and the other is at its lowest tested nonzero level; everywhere else in the grid, HB-PVI is optimal in 100% of cases.

Reference	Post. $\tau$	Post. $\nu$	Max $\widehat{R}$	Min bulk ESS	Min tail ESS
Fixed adapter@1	0.00490	4.52	1.0011	3001	3300
Fixed adapter@6	0.00468	3.70	1.0009	4014	4088
Fixed adapter@10	0.00510	5.75	1.0007	4159	4349

Appendix

Table S10: Label-efficiency posterior diagnostics (Bayesian Student-

t

model)

$c_{L}$	Mean EVSI at stop	Max EVSI observed	Mean labels purchased
0.0000	0.00405	0.00411	10.0
0.0005	0.00405	0.00411	10.0
0.0010	0.00405	0.00411	10.0
0.0025	0.00956	0.01012	1.0
0.0050	0.00956	0.01012	1.0
0.0100	0.00956	0.01012	1.0

Appendix

Table S11: Positive one-step EVSI decisions, grouped by label cost (all at

\Delta_{\min}=0

;

n=12

decisions per row)

#	Objective	Status
1	$P$ (mean utility $>$ best existing policy) $>0.95$ without worse calibration	Not met
2	$\geq$ 25% fewer labels with $P$ (F1 loss $<$ 0.005) $>0.90$	Met
3	Materially improved prospective harmful-personalization identification	Not established
4	Practical equivalence supporting simpler policy, ROPE $P>0.90$	Met (ROPE $P=1$ )
5	Heterogeneity estimate changes deployment recommendation	Supported

Appendix

Table S12: Study objectives and outcomes

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