Predicting Multiple Clinical Outcomes Related to Functional Recovery and Social Isolation Among Older Adults After Lower-Limb Fracture or Hip Replacement

Older adults recovering after lower-limb fracture or hip replacement may experience complex recovery trajectories. Most of the time, these clinical aspects are studied in isolation, masking their joint impact on recovery. This study used the MAISON-LLF dataset, which contains multimodal sensor and clinical assessment data from 18 older adults recovering in the community after lower-limb fracture or hip replacement. Participants were monitored for up to eight weeks, corresponding to a maximum of 1,008 participant-days of sensor monitoring. Forty-six daily features were extracted from indoor motion, acceleration, step count, heart rate, out-of-home mobility, and sleep data. Five clinical outcomes were assessed every two weeks: the Social Isolation Scale, Oxford Hip Score, Oxford Knee Score, Timed Up and Go test, and 30-second Chair Stand test. We utilize an inherent relationship between multi-modal sensor data and different clinical scores and formulate it as a multi-output regression problem. We tested various machine learning and deep learning single- and multi-output regression algorithms to predict these scores simultaneously. The results showed that predicting clinical scores jointly was better than separately. The tabular DL multi-output regressor, NODE, gave a remarkable performance of MSE=3.96 and MAE=1.02 in comparison to other multi- and single-output regressors. The SHAP feature analysis further showed the importance of including multimodal sensors to provide a good estimate of patients' recovery trajectory. This work may support the simultaneous assessment of functional recovery and social engagement among community-dwelling older adults and ultimately help improve their care and quality of life.

A Factor Graph Approach to Scalable Multi-Output Gaussian Process Regression

Multi-output Gaussian process regression scales cubically in the number of observations times outputs, and dense kernel-matrix methods need bespoke handling whenever different outputs are observed at different inputs. We express multi-output Gaussian process regression as a Forney-style factor graph in which a nearest-neighbor chain orders a fixed candidate set of $C$ inputs into a one-dimensional sequence. Along this chain, latent Matérn processes evolve through linear-Gaussian transition factors, while the linear model of coregionalization mixes $L$ latent processes into $D$ outputs through a deterministic mixing factor and per-output scalar observation factors. Posterior computation reduces to exact Gaussian message passing on the chain at cost $\mathcal{O}(C(DL^2 + L^3))$ after chain construction, and missing observations omit their local factor without any covariance-matrix restructuring. The formulation therefore scales in the number of data samples and in the rate of missing observations, while remaining best suited to candidate sets in low input dimension.We compare the factor-graph formulation against an exact kernel-matrix baseline, a sparse-variational inducing-point baseline, and a nearest-neighbor baseline on a synthetic input-dimension sweep and on electricity time series forecasting. At low input dimension the factor-graph posterior tracks the exact kernel-matrix posterior closely, and the gap grows gradually as input dimension increases while staying competitive with both approximate baselines. On the electricity time series our factor-graph formulation matches all three baselines in forecast accuracy while scaling linearly in the number of data points, where the exact kernel-matrix method becomes infeasible and the inducing-point baseline remains substantially slower.