MT-LLE: Multi-Task Locally Linear Embedding for Interpretable Disease Models from Longitudinal Omics

Constructing interpretable disease models from longitudinal omics data is a central challenge in computational biology. The goal is a low-dimensional representation in which a patient's position encodes their molecular state and clinical severity, and along which disease progression can be read directly. Standard dimensionality reduction methods (e.g., UMAP, variational autoencoders) fall short: they optimize a single generic objective and are blind to clinical labels and to the temporal ordering of measurements. Trajectory inference is therefore applied post-hoc, as a separate step on a space that was never optimized to reveal progression—decoupling representation learning from disease dynamics. We introduce Multi-Task Locally Linear Embedding (MT-LLE), which recasts disease-manifold construction as a multi-task learning problem. A neural Locally Linear Embedding encoder preserves the local geometry of the omics data while enabling inductive inference on unseen patients; on top of it, MT-LLE jointly optimizes five objectives—geometric reconstruction, supervised contrastive organization by clinical stage, embedding forecasting, phenotype forecasting, and clustering—so that representation and progression are learned together rather than in sequence. Naively combining such heterogeneous objectives induces gradient conflicts that distort the molecular geometry. To resolve this, an embedded reinforcement learning (RL) agent treats the vector of current losses as state and the objective weights as actions, using a reward based on improvement in the manifold's overall structure. The agent discovers a staged schedule, establishing global geometry before refining clinical boundaries, rather than forcing all objectives to compete from the outset. To our knowledge, this is the first RL formulation for balancing heterogeneous objectives in manifold learning. We evaluate MT-LLE on two independent chronic obstructive pulmonary disease (COPD) cohorts, SPIROMICS and COPDGene, with the latter held out to assess generalization, across proteomics, metabolomics, and bimodal fusion. The results below are for the highest-resolution setting, SPIROMICS proteomics (162 subjects, 4 longitudinal visits); single-omics proteomics outperformed bimodal fusion, which we attribute to the greater number of visits available without cross-modal alignment. Using an identical frozen-embedding protocol for every method, a linear model reads disease severity (GOLD stage, 0–4) from the MT-LLE embedding 35–40% more accurately than from standard dimensionality reduction (0.53 vs. 0.38 F1-Macro). The gap is starker for progression: forecasting a patient's next-visit severity from their trajectory reaches 0.38 F1-Macro, while unsupervised baselines sit near zero (0.06–0.09 F1-Macro), a temporal signal those methods effectively fail to capture. To isolate the RL agent's contribution, we compare it against a fixed schedule that imposes the same ordering of objectives (geometry first, clinical objectives later) but cannot adapt during training; the learned agent outperforms it by 13–20% across clinical metrics, showing the gains come from adapting the weights to how training unfolds, not merely from ordering the objectives correctly, and at no cost to geometric fidelity. Improvements hold across both cohorts and all molecular layers. Beyond quantitative metrics, the learned manifold supports complementary analyses that surface structure invisible to standard clinical staging: static phenotyping isolates subjects with active molecular pathology despite preserved lung function; trajectory inference maps two mechanistically distinct progression axes; and a kinematic analysis of each patient's speed and acceleration through the manifold identifies subjects whose molecular trajectories accelerate ahead of detectable clinical decline. MT-LLE thus offers a general, adaptively optimized approach to multi-task manifold learning for longitudinal biological data, yielding representations that are simultaneously geometrically faithful, clinically structured, and temporally coherent.