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

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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

arXiv:2608.29496v1Aug 30, 2026cs.LG

TL;DR

DXA provides reference body-composition measurements but requires dedicated equipment, trained personnel, and in-person acquisition, motivating lower-burden estimation. The paper proposes target-aware pSADE-GNR and finds correlation-weighted raw measurements strongest across primary tasks, while GMVAE leads exploratory age prediction.

Problem
DXA requires dedicated equipment, trained personnel, and an in-person protocol, motivating lower-burden predictors for body-composition outcomes.
Method
pSADE-GNR propagates encoded participant states over outcome-specific graphs using a state-adaptive forward-Euler discretization of graph p-Dirichlet energy flow.
Results
The correlation-weighted raw-feature model achieved the lowest cross-validated RMSE in all nine primary target–cohort settings and lower normalized RMSE than published SVR or LSSVR references in eight of nine comparisons.
Takeaways & Limitations
Target-aware graph construction provided the strongest overall primary-task performance, whereas GMVAE representations led exploratory age prediction across male, female, and combined cohorts.
Takeaways & Limitations
Experiments used data from a single research center with internal five-fold cross-validation and lacked external validation and individual prediction intervals.

Abstract

from arXiv · show

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.

1 Introduction

The paper addresses non-invasive estimation of ALM, BFP, and BMD by constructing outcome-specific participant-similarity graphs and propagating representations with pSADE-GNR. Across primary tasks, target-aware raw-feature graphs performed best overall, while learned representations helped in exploratory age prediction.

ALM, BFP, and BMD estimation should be evaluated using errors in original units, not association measures alone.The relevant units are kilograms for ALM, percentage points for BFP, and g/cm2 for BMD.
DXA provides reference body-composition measurements but requires dedicated equipment, trained personnel, and in-person acquisition.
pSADE-GNR constructs a separate target-aware graph by weighting anthropometric coordinates with training-fold target correlations.This prevents held-out target values from entering graph construction.
The correlation-weighted model using original standardized measurements achieved the lowest RMSE in all nine primary outcome–cohort comparisons.It also produced numerically lower RMSE than reported SVR or LSSVR benchmarks in eight of nine comparisons.
For exploratory age prediction, the GMVAE-based model achieved the lowest mean RMSE in male, female, and combined cohorts.Age is treated as biological age unless otherwise stated.
Increasing latent-representation complexity did not necessarily improve graph-based regression, and learned representations were not central to primary prediction.

2 Related Work

Prior work shows that compact measurements and digital body shape contain predictive information for body composition, while graph-based approaches motivate relational modeling. This study targets the unresolved issue of defining outcome-specific similarity when graph edges are not naturally observed.

Compact anthropometric, demographic, and bioimpedance inputs have been used to predict lean mass, fat mass, ALM, BFP, and BMD.
Digital anthropometry has expanded from 3D surface scans to photographs, smartphone images, and device-agnostic 3D representations.
The closest predecessor used equal biomarker weights and identified principled weighting as a direction for further work.The present study addresses this gap with a training-only correlation-weighted metric for each target.
Patient-similarity networks represent individuals as nodes connected by phenotypic, clinical, or imaging relationships.Their predictive performance can depend strongly on how similarity is defined.
Graph p-Laplacian methods extend quadratic graph smoothness to nonlinear energies used in diffusion, clustering, and semi-supervised learning.The present work develops a distinct diffusion formula based on graph p-Dirichlet energy flow.

3 Background

The background develops graph p-Dirichlet energy flow as a nonlinear propagation mechanism and reviews autoencoder-based latent representations for alternative graph construction. These components motivate comparing raw anthropometric spaces with learned embeddings.

Graph p-Dirichlet energy and gradient flow: Graph models represent participants as vertices and use weighted edges to encode participant similarity for target-smooth regression.
Graph p-Dirichlet energy and gradient flow: Graph p-Dirichlet energy is small when strongly connected vertices have similar representations.
Graph p-Dirichlet energy and gradient flow: Its negative-gradient flow propagates representations through graph edges; p = 2 gives linear heat flow, whereas p ≠ 2 gives nonlinear flow.
Graph p-Dirichlet energy and gradient flow: The study uses finite-step explicit Euler updates as a discretization of graph p-Dirichlet energy flow.The model then applies encoder, residual averaging, and regression components.
Autoencoders and variational representations: A VAE represents observations with a lower-dimensional latent variable and trains an encoder as a variational posterior approximation.
Autoencoders and variational representations: The VAE evidence lower bound combines expected reconstruction log-likelihood with KL regularization toward the prior.
Autoencoders and variational representations: A GMVAE replaces the unimodal Gaussian prior with component-specific Gaussian priors, allowing multiple latent modes.Its component memberships are statistical and should not automatically be interpreted as clinically distinct groups.
Autoencoders and variational representations: VAE and GMVAE embeddings are used to construct alternative participant-similarity graphs for downstream p-Dirichlet-flow regression.

4 Methodology

The methodology constructs target-specific participant graphs from standardized anthropometric or learned representations, then applies state-adaptive p-Dirichlet energy-flow propagation for separate ALM, BMD, and BFP regressions. Correlation weighting uses training-fold associations with each target, while cross-validation and training-only procedures constrain information flow.

State-adaptive p-Dirichlet energy-flow graph neural regression: A neural encoder maps participant representations to hidden states that are propagated on weighted graphs using an adaptive forward-Euler discretization of graph p-Dirichlet energy flow.
Study variables and prediction tasks: ALM, BMD, and BFP are modeled as separate single-target regression tasks rather than through a shared multi-output loss.
Study variables and prediction tasks: Primary body-composition models use chronological age and non-invasive anthropometric measurements while excluding all DXA-derived body-composition variables from inputs.
Raw and learned feature representations: Four graph representations are compared: standardized anthropometric measurements, autoencoder outputs, variational-autoencoder posterior means, and Gaussian-mixture variational-autoencoder posterior expectations.
Participant-similarity graph construction: For each target, feature or latent coordinates are weighted by normalized absolute Pearson correlations estimated only within the training split before constructing target-aware distances and mutual k-nearest-neighbor graphs.
State-adaptive p-Dirichlet energy-flow graph neural regression: The model adds a residual average to retain information from the initial encoded representation, while adaptive normalization supports stable propagation for p > 2.

5 Experimental Results

The experiments compare graph constructions and representations for ALM, BMD, and BFP prediction across sex-specific cohorts. Correlation-weighted raw-feature pSADE-GNR generally performed best, while exploratory visualizations showed target-dependent structure and important interpretive limits.

Exploratory visualization: ALM showed a broad gradient across raw, VAE, and GMVAE UMAP embeddings, whereas Age displayed weaker, more fragmented regional structure with substantial overlap.The GMVAE embedding appeared more branched, but UMAP geometry alone does not establish predictive superiority, biological clustering, or preservation of global distances.
Feature–target correlation structure: The strongest marginal correlation profiles differed by outcome: ALM emphasized body-size measures, BMD showed generally weaker size-related associations, and BFP concentrated on waist, abdominal, hip, seat, and thigh measures.These are descriptive marginal associations, not causal effects or complete measures of predictive importance.
Experimental setup: The study evaluated seven configurations for ALM, BMD, and BFP separately in male, female, and combined cohorts.Performance was summarized using five-fold relative RMSE, with Euclidean, correlation-weighted, AE, VAE, and GMVAE-based graph constructions represented among the configurations.
Primary prediction results: 32.7%, 8.6%, and 39.1% were the ALM normalized-RMSE reductions for male, female, and combined cohorts versus the strongest SVR or LSSVR benchmarks.For BFP, the corresponding reductions were 28.4%, 41.7%, and 34.3%; BMD reductions were 4.9% and 3.2% in male and combined cohorts, while female BMD RMSE was 7.5% higher.
Primary prediction results: Eight of nine primary target–cohort comparisons achieved numerically lower normalized RMSE than the reported SVR or LSSVR benchmarks.The largest gains occurred for ALM and BFP.
Exploratory age prediction: 7.99, 10.82, and 10.90 years were the lowest RMSE values for exploratory age prediction in the male, female, and combined cohorts when ALM, BMD, and BFP were included.The correlation-weighted GMVAE-pSADE-GNR achieved the lowest RMSE in all three cohorts under this predictor setting.

6 Discussion

Target-aware graph construction was the study’s central predictive advantage for primary body-composition outcomes, while GMVAE benefits appeared mainly in exploratory age prediction. The authors caution that significance testing, component isolation, and external validation remain incomplete.

Primary outcomes: The correlation-weighted raw-feature pSADE-GNR achieved the lowest cross-validated RMSE in all nine primary target–cohort settings.It reduced relative RMSE by approximately 7%–40% versus the corresponding unweighted model and was lower than published SVR or LSSVR references in eight of nine comparisons.
Primary outcomes: Target-aware graph construction emphasizes outcome-associated features, adapting participant similarity to distinct ALM, BMD, and BFP correlation profiles.The weights are marginal associations rather than causal or conditional importance measures.
Exploratory age prediction: GMVAE achieved the lowest mean RMSE for exploratory age prediction in male, female, and combined cohorts when DXA-derived ALM, BMD, and BFP were included.Its advantage was less consistent with anthropometry-only predictors and did not improve primary ALM, BMD, or BFP predictions.
Limitations: The experiments do not separately isolate graph propagation and nonlinear p-Laplacian diffusion, and they use one research center with internal five-fold cross-validation.The authors call for independent prospective cohorts, uncertainty quantification, and direct baseline comparisons.

A.1.1 Proof of Proposition 4.1

This proof establishes the stated bound through a case split for zero weights and a Cauchy–Schwarz argument, with equality characterized by proportional weighting.

Case handling: If any b_ℓ is zero for ℓ∈S, then A(b) and K(b) are infinite by convention; otherwise the proof assumes b_ℓ>0.The positive-weight case enables the subsequent ratio construction.
Bound: Cauchy–Schwarz yields K(b)^2 ≤ A(b), with equality for δ_ℓ = β_ℓ/b_ℓ on S and zero elsewhere.This specifies the equality-achieving choice of δ.
Equality conditions: Equality requires all weight to be supported on S and b_ℓ proportional to |β_ℓ| on S.The simplex constraint then uniquely determines the weights.

A.1.2 Proof of Theorem 4.2

The proof bounds one Euler step of the graph p-Dirichlet flow by controlling the Hessian along the Euler segment and then uses homogeneity of the energy.

Euler step: The proof sets g = ∇E_p(H), δ = δ(H), and studies the Euler segment H_s = H − sτg for 0 ≤ s ≤ 1.Here τ is defined as μδ^2−p.
Hessian control: For every U, the edgewise Hessian bound is obtained using the incidence matrix and the operator-norm bound for the p-norm Hessian.This controls the Hessian quadratic form of E_p.
Taylor bound: Taylor’s theorem along the segment uses L = (p − 1)(Rμδ)^(p−2)Λ_w to obtain the stated inequality.The constant L supplies the required smoothness bound along the update path.
Final step: The identity ⟨∇E_p(H), H⟩_F = pE_p(H) implies a nonzero gradient for a nonconstant state on a positive-weight component.This completes the final nonconstancy argument.

A.2 MAPPER

MAPPER projects data, clusters overlapping projected regions, and converts shared cluster membership into a graph for topological visualization.

Projection: MAPPER begins by choosing a filter function that maps high-dimensional data to a lower-dimensional space.Here, Principal Component Analysis constructs the filter using the primary and secondary data axes.
Purpose: The resulting graph summarizes clustering patterns while retaining information about topological structure and local overlap.Figure 8 illustrates the construction with a toy example.
Local clustering: The filter range is covered by overlapping intervals or regions, and clustering is applied within each region’s pre-image.Overlap allows clusters from neighboring regions to share data points.
Graph construction: MAPPER outputs a graph whose vertices are clusters and whose edges connect clusters sharing at least one data point.Vertex size can represent the number of samples in each cluster.

A.3 Uniform Manifold Approximation and Projection (UMAP)

UMAP constructs low-dimensional embeddings by preserving neighborhood structure from high-dimensional data. Its key parameters control the locality of manifold approximation and the compactness of embedding clusters.

A.3 Uniform Manifold Approximation and Projection (UMAP): UMAP is a nonlinear manifold-learning method that constructs low-dimensional embeddings of high-dimensional data.It builds a weighted neighborhood graph in the original feature space and optimizes an embedding that approximates its neighborhood structure.
A.3 Uniform Manifold Approximation and Projection (UMAP): The nneighbors parameter sets neighborhood size, with smaller values emphasizing local structure and larger values incorporating broader global structure.
A.3 Uniform Manifold Approximation and Projection (UMAP): The min dist parameter controls low-dimensional packing, with smaller values allowing denser clusters and larger values producing more spread-out embeddings.
A.3 Uniform Manifold Approximation and Projection (UMAP): Table 4 reports average computational cost per cross-validation fold for pSADE-GNR-based methods across the Male, Female, and Combined datasets.Runtimes are mean wall-clock times for complete hyperparameter searches; proposed methods used the same CUDA GPU environment, while SVR and LSSVR values came from CPU experiments.
A.3 Uniform Manifold Approximation and Projection (UMAP): Tables 5 and 6 document the biomarkers and units used, plus feature correlations with ALM, BMD, BFP, and Age.