Amortized Bayesian inference for actigraph time sheet data from mobile devices

We develop a general method for amortized Bayesian inference on multilevel models of arbitrary structure. Given a generative model specified as a directed acyclic graph, our method automatically derives valid factorizations of the joint posterior and matching neural network architectures. The key steps, graph expansion and graph inversion, yield an inverse graph that determines how inference networks are stacked and conditioned, producing factorizations that amortize over the number of groups and the number of observations within each group. Unlike approaches that simplify the dependency structure to speed up learning or inference, our method preserves all conditional independence and exchangeability assumptions of the generative model. Across three case studies, it closely matches gold-standard samplers on models with more than 6,500 parameters while reducing inference to a near-instant forward pass once trained.

Foundation models (FMs) trained on large-scale accelerometer data have been proposed as general-purpose feature extractors for health monitoring, but systematic evidence of their advantages is lacking. We present the first comprehensive evaluation of four open-source accelerometer FMs against supervised baselines covering 19 tasks across the domains of activity recognition including activities of daily living, clinical monitoring, and physiological inference. We find task-dependent performance results: supervised models remain competitive with FMs on human action recognition (HAR), with no consistent advantage for either, while selected FMs lead on fall and stress detection and are the most robust to sensor-placement variation. As frozen feature extractors, FMs are strongest for demographic inference, whereas sleep staging performance remains near chance level for all models. The internal FM representations show strong similarity across layers, highlighting potential for future FM improvements. Linear and frozen probing reveals that UniMTS provides the strongest representations and is the only FM that surpasses the supervised baselines without finetuning. Concept discovery analysis shows all models capture high-intensity activities clearly but struggle with sedentary, complex or ambiguous activities. We provide scenario-based deployment recommendations. Furthermore, we identify FM-derived activity profile inference-moving beyond fixed category classification-as a promising research direction.

Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex, large-scale predictive problems. The recent success of deep neural networks and foundation models has now given rise to a new paradigm in statistical modeling, in which Bayesian inference can be amortized through large-scale learned predictors. In amortized inference, substantial computation is required at the beginning to train a neural network, but it can subsequently produce approximate posteriors or predictions at much lower computational cost across a wide range of tasks. While the typical Bayesian inference procedures are computationally expensive due to repeated likelihood calculations and Monte Carlo steps for each new dataset, amortized inference provides a much lower computational cost at deployment. Despite the growing popularity of amortized inference, its statistical interpretation and position within Bayesian inference remain poorly explored. In this paper, we present a statistical perspective on several major neural architectures, including feedforward networks, Deep Sets, and Transformers, and examine how they naturally support amortized Bayesian inference. We explore how these models perform structured approximation and also probabilistic reasoning in ways that yield controlled generalization error throughout a wide range of deployment scenarios, and how these properties can be harnessed for Bayesian computation. Via simulation studies, we evaluate the accuracy, robustness, and uncertainty quantification of amortized inference across varying sample sizes, varying noise distributional families, varying sparsity levels, and multimodality, highlighting its strengths and limitations.