Target-Aware State-Adaptive $p$-Dirichlet Graph Neural Regression for Non-Invasive Body-Composition Estimation

Nadejda Drenska; Matthew Lemoine; Gowri Priya Sunkara; Yu Wang; Sri Lakshmi Sravani Devarakonda; Steven B. Heymsfield

cs.LGAug 30, 2026

Target-Aware State-Adaptive $p$ -Dirichlet Graph Neural Regression for Non-Invasive Body-Composition Estimation

Authors: Nadejda Drenska, Matthew Lemoine, Gowri Priya Sunkara, Yu Wang, Sri Lakshmi Sravani Devarakonda, Steven B. Heymsfield

Organizations: Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA. · Pennington Biomedical Research Center(PBRC), Baton Rouge, LA 70808, USA.

Abstract

Accurate estimation of body-composition outcomes, including body fat percentage (BFP), bone mineral density (BMD), and appendicular lean mass (ALM), is important for evaluating metabolic, skeletal, and muscular health. Direct assessment using dual-energy X-ray absorptiometry (DXA), however, requires specialized equipment and involves ionizing radiation. We propose a target-aware, state-adaptive $p$ -Dirichlet energy-flow graph neural regression ( $p$ SADE-GNR) framework for estimating these outcomes from non-invasive anthropometric measurements. A neural encoder maps participant representations to hidden states that are propagated over an outcome-specific participant-similarity graph by a state-adaptive forward-Euler discretization of the graph $p$ -Dirichlet energy flow. Graph distances weight each original or latent coordinate by its normalized absolute training-fold correlation with the outcome. Using clinical data from the Pennington Biomedical Research Center and five-fold cross-validation, the correlation-weighted model using the original standardized measurements achieved the lowest root mean squared error in all nine primary outcome-cohort combinations and outperformed previously reported support vector regression or least-squares support vector regression reference values in eight of nine comparisons. Autoencoder, variational-autoencoder, and Gaussian-mixture variational-autoencoder representations generally did not improve primary-outcome prediction or reduce computational cost. In an exploratory age-prediction analysis including ALM, BMD, and BFP as predictors, the correlation-weighted GMVAE model achieved the lowest mean error in all three cohorts. These results support target-aware, state-adaptive $p$ -Dirichlet graph neural regression for non-invasive body-composition estimation.

Figures & tables

Figure 1: Schematic of the graph

p

-Dirichlet energy-flow module used in this study. At each iteration, the representation at vertex

i

is updated by an explicit Euler step in the negative-gradient direction of the graph

p

-Dirichlet energy with a fixed step size

\mu

. After

T

flow steps, the propagated representation is averaged with the initial representation and passed to a scalar linear regression layer where each

H^{(k)}=[h_{i}^{(k)}]_{i\in V}

Figure 2: Schematic comparison of three $p$ -Dirichlet Energy-Flow Graph Neural Regression ( $p$ SADE-GNR) pipelines. (1) $L^{2}$ - $p$ SADE-GNR: standardized anthropometric measurements are used directly to construct a mutual $k$ -nearest-neighbor graph using Euclidean distance. (2) cc- $L^{2}$ – $p$ SADE-GNR: each standardized measurement is weighted according to its training-set correlation with the prediction target, producing a target-specific correlation-weighted distance before graph construction. (3) AE- $L^{2}$ - $p$ SADE-GNR: a deterministic autoencoder first maps the anthropometric measurements to a lower-dimensional latent representation, from which the graph is constructed using Euclidean distance. In all three configurations, the resulting participant-similarity graph is processed by the same $p$ -SADE-GNR architecture. Appendicular lean mass (ALM), bone mineral density (BMD), and body fat percentage (BFP) are predicted as separate single-target regression tasks.

Figure 3: Schematic comparison of the two correlation-weighted variational pipelines. (4) VAE-cc- $L^{2}$ – $p$ SADE-GNR: a variational autoencoder maps the standardized anthropometric measurements to a continuous latent space, and the posterior-mean representation is used for graph construction. Latent coordinates are weighted according to their training-set correlations with the current target, yielding a target-aware correlation-weighted distance. (5) GMVAE-cc- $L^{2}$ – $p$ SADE-GNR: a Gaussian-mixture variational autoencoder represents each participant by the posterior expectation over mixture-specific latent means, after which latent-coordinate correlations are used to define the target-aware distance. In both configurations, the weighted distance determines a mutual $k$ -nearest-neighbor participant graph and its distance-based edge weights. The graph is then processed by the $p$ SADE-GNR to predict ALM, BMD, or BFP, with one outcome modeled at a time.

Panel of Figure 4 — Figure 4: Two-dimensional UMAP embeddings of the Pennington data colored by standardized ALM. Left: standardized raw anthropometric features. Middle: VAE latent representation. Right: GMVAE expected latent representation. The same ALM color scale is used across all three panels. UMAP was used for exploratory visualization only.

Panel of Figure 5 — Figure 5: Two-dimensional UMAP embeddings of the Pennington data colored by standardized Age. Left: standardized raw anthropometric features. Middle: VAE latent representation. Right: GMVAE expected latent representation. The same Age color scale is used across all three panels. UMAP was used for exploratory visualization only.

Panel of Figure 6 — Figure 6: Exploratory MAPPER graphs for the standardized raw-feature representation (left), VAE posterior-mean representation (middle), and GMVAE expected latent representation (right). Each node represents a cluster within a pullback-cover element, and an edge indicates that two clusters share at least one participant. Node color denotes the mean standardized ALM of the participants in the cluster, using a common color scale across panels; node size denotes the relative size of the cluster. The MAPPER graphs are descriptive and are distinct from the participant-similarity graphs used by the prediction model.

Figure 7: Absolute Pearson correlations between the non-invasive anthropometric predictors and ALM, BMD, BFP, and Age in the combined Pennington cohort. The figure is a descriptive full-cohort summary and is separate from the training-fold correlations used to construct the correlation-weighted prediction graphs.

Target	Sex	$p$ SADE-GNR		VAE- $p$ SADE-GNR		GMVAE- $p$ SADE-GNR		Autoencoder	Results from [ 1 ]	$p$ GNN
		$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$
ALM	Male	6.27 $\pm$ 0.99	4.24 $\pm$ 0.34	7.75 $\pm$ 0.87	7.66 $\pm$ 0.88	7.27 $\pm$ 1.12	7.23 $\pm$ 1.38	8.09 $\pm$ 0.83	6.30 (SVR)	11.86 $\pm$ 1.68
	Female	8.49 $\pm$ 1.31	5.51 $\pm$ 1.19	9.90 $\pm$ 0.71	9.95 $\pm$ 0.58	8.95 $\pm$ 1.04	8.65 $\pm$ 1.33	10.19 $\pm$ 0.64	6.03 (LSSVR)	12.51 $\pm$ 1.06
	Combined	7.53 $\pm$ 0.68	4.77 $\pm$ 0.42	9.85 $\pm$ 0.81	9.60 $\pm$ 1.01	8.08 $\pm$ 0.84	7.87 $\pm$ 0.72	10.58 $\pm$ 1.03	7.83 (SVR)	13.91 $\pm$ 0.52
BMD	Male	6.84 $\pm$ 0.47	6.63 $\pm$ 0.64	7.75 $\pm$ 1.21	7.85 $\pm$ 1.48	6.83 $\pm$ 0.73	6.95 $\pm$ 0.63	7.93 $\pm$ 0.97	6.97 (SVR)	9.32 $\pm$ 1.39
	Female	7.95 $\pm$ 1.11	7.58 $\pm$ 0.78	8.99 $\pm$ 1.13	8.89 $\pm$ 1.06	8.15 $\pm$ 1.25	7.99 $\pm$ 0.85	9.31 $\pm$ 0.77	7.05 (LSSVR)	9.34 $\pm$ 0.73

Table 1: Average 5-fold

\mathrm{RMSE}_{\mathrm{relativepct}}

are the percentage values across ALM, BMD, and BFP prediction tasks. The underlined values in bold indicate the lowest

\mathrm{RMSE}_{\mathrm{relativepct}}

within each target and sex group.

Target	Sex	$p$ SADE-GNR		VAE- $p$ SADE-GNR		GMVAE- $p$ SADE-GNR		Autoencoder	$p$ GNN
		$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$
ALM ( $kg$ )	Male	1.46 $\pm$ 0.26	0.99 $\pm$ 0.10	1.81 $\pm$ 0.24	1.79 $\pm$ 0.25	1.69 $\pm$ 0.28	1.68 $\pm$ 0.34	1.88 $\pm$ 0.20	2.76 $\pm$ 0.43
	Female	1.39 $\pm$ 0.22	0.90 $\pm$ 0.20	1.62 $\pm$ 0.13	1.62 $\pm$ 0.09	1.46 $\pm$ 0.20	1.41 $\pm$ 0.24	1.66 $\pm$ 0.09	2.04 $\pm$ 0.18
	Combined	1.50 $\pm$ 0.13	0.95 $\pm$ 0.07	1.96 $\pm$ 0.17	1.91 $\pm$ 0.20	1.61 $\pm$ 0.14	1.57 $\pm$ 0.11	2.11 $\pm$ 0.20	2.77 $\pm$ 0.13
BMD ( $\mathrm{gm/cm^{2}}$ )	Male	0.07 $\pm$ 0.01	0.07 $\pm$ 0.01	0.08 $\pm$ 0.01	0.09 $\pm$ 0.02	0.07 $\pm$ 0.01	0.08 $\pm$ 0.01	0.09 $\pm$ 0.01	0.10 $\pm$ 0.01
	Female	0.08 $\pm$ 0.01	0.08 $\pm$ 0.01	0.09 $\pm$ 0.01	0.09 $\pm$ 0.01	0.08 $\pm$ 0.01	0.08 $\pm$ 0.01	0.09 $\pm$ 0.01	0.09 $\pm$ 0.01

Table 2: Average 5-fold

\mathrm{RMSE}_{\mathrm{orig}}

values for the same

p

SADE-GNR-based models on ALM, BMD, and BFP as those reported in Table 1 . The values are expressed in the original units of the corresponding target variables. The underlined values indicate the lowest

\mathrm{RMSE}_{\mathrm{orig}}

within each sex group.

Target	Sex	$p$ SADE-GNR		VAE- $p$ SADE-GNR		GMVAE- $p$ SADE-GNR		Autoencoder	$p$ GNN
		$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$
Age (years) with ALM, BMD, BFP	Male	9.84 $\pm$ 1.54	9.08 $\pm$ 1.41	11.44 $\pm$ 2.28	10.94 $\pm$ 2.03	8.01 $\pm$ 2.00	7.99 $\pm$ 1.96	10.02 $\pm$ 1.60	13.75 $\pm$ 0.94
	Female	11.58 $\pm$ 0.95	11.73 $\pm$ 1.28	14.67 $\pm$ 1.13	15.42 $\pm$ 1.77	11.34 $\pm$ 1.42	10.82 $\pm$ 1.62	14.75 $\pm$ 1.44	16.72 $\pm$ 1.93
	Combined	11.13 $\pm$ 1.00	11.26 $\pm$ 0.88	13.50 $\pm$ 0.75	13.29 $\pm$ 0.65	11.12 $\pm$ 1.00	10.90 $\pm$ 1.17	13.82 $\pm$ 1.74	15.25 $\pm$ 0.93
Age (years) without ALM, BMD, BFP	Male	9.84 $\pm$ 1.55	9.08 $\pm$ 1.44	11.57 $\pm$ 2.21	10.93 $\pm$ 1.84	9.58 $\pm$ 2.52	9.44 $\pm$ 2.57	10.48 $\pm$ 1.30	13.69 $\pm$ 1.01
	Female	11.53 $\pm$ 1.05	11.73 $\pm$ 1.26	14.69 $\pm$ 1.24	15.45 $\pm$ 1.10	11.36 $\pm$ 1.72	11.17 $\pm$ 1.11	14.67 $\pm$ 1.39	16.38 $\pm$ 2.29

Table 3: Average 5 fold

\mathrm{RMSE}_{orig}

values across Age prediction tasks. The underlined values indicate the lowest RMSE within each target and sex group.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 8: Toy illustration of the MAPPER algorithm. A filter function is chosen to project the dataset, overlapping regions are formed in the projected space, clustering is performed within each preimage, and clusters with shared data points are connected in the resulting graph.

Runtime Measure	$p$ SADE-GNR		VAE- $p$ SADE-GNR		GMVAE- $p$ SADE-GNR		Autoencoder	Results from [ 1 ]
	$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$	$\mathbf{cc\text{-}L^{2}}$	$\mathbf{L^{2}}$	SVR	LSSVR
Device	CUDA GPU	CUDA GPU	CUDA GPU	CUDA GPU	CUDA GPU	CUDA GPU	CUDA GPU	CPU	CPU
Total Runtime	1h 26m 22s	10h 45m 35s	2h 07m 07s	13h 55m 50s	1h 27m 08s	11h 06m 52s	1h 6m	1m 50s	52.2s
Runtime (s)	5122.68s	38735.39s	7451.77s	49670.56s	5228.16s	39558.12s	3665.96	110s	52.2s

Appendix

Table 4: Average computational cost per cross-validation fold for the

p

SADE-GNR-based methods for the combined three datasets: Male, Female, and Combined. The reported runtime represents the mean wall-clock time required to complete one fold of the complete hyperparameter search across the Male, Female, and Combined datasets. All proposed methods were executed on the same CUDA GPU computing environment, while the SVR and LSSVR runtimes are taken from [ 1 ] , where experiments were performed on a CPU.

Biomarker	Unit of Measure
Age	Years
Gender	Male/Female
ALM	Kilograms (kg)
BMD	Grams / Square Centimeters (gm/cm 2 )
BFP	Percentage (%)
Height	Centimeters (cm)

Appendix

Table 5: This is a table outlining all of the biomarkers used along with the units of measure.

Feature	ALM	BMD	BFP	Age
Height (cm)	0.8504	0.8043	0.1119	0.4559
Weight (kg)	0.8879	0.7422	0.2980	0.5299
Abdomen Circumference	0.6765	0.5963	0.5589	0.5727
Ankle Circumference Left	0.7226	0.4857	0.2241	0.2228
Arm Length Left	0.7829	0.7495	0.0543	0.3971
Arm Volume Left	0.8605	0.7584	0.1514	0.4827

Appendix

Table 6: Feature correlations with ALM, BMD, BFP, and Age.

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