Mobile health leverages personalized and contextually tailored interventions optimized through bandit and reinforcement learning algorithms. In practice, however, challenges such as participant heterogeneity, nonstationarity, and nonlinear relationships hinder algorithm performance. We propose RoME, a **Ro**bust **M**ixed-**E**ffects contextual bandit algorithm that simultaneously addresses these challenges via (1) modeling the differential reward with user- and time-specific random effects, (2) network cohesion penalties, and (3) debiased machine learning for flexible estimation of baseline rewards. We establish a high-probability regret bound that depends solely on the dimension of the differential-reward model, enabling us to achieve robust regret bounds even when the baseline reward is highly complex. We demonstrate the superior performance of the RoME algorithm in a simulation and two off-policy evaluation studies.

Community detection is a fundamental task in network analysis. Learning underlying network structures has brought deep insights into the understanding of complex systems. While many methods have focused on clustering nodes into blocks, few accounts for the fact that interactions may exhibit edge-level clustering, which we call categories. Real network data often arise via a series of interactions. Interactions in complex systems can often be clustered into different categories and node-level community structures that depend on the category. In this paper, we introduce a category-and-block edge exchangeable model (CataBEEM) to study interaction networks with joint latent interaction-level category and node-level community structures. In particular, the proposed method models the network from the interaction process perspective and allows the incorporation of prior knowledge from auxiliary interaction-wise information. We derive an efficient variational inference algorithm that can be applied to networks consisting of millions of interactions and provide the theoretical bound of the misspecification rate. We demonstrate the effectiveness of our method in various simulation settings and apply the method to TalkLife data, a large-scale online peer-to-peer support network. We show CataBEEM detects more temporally consistent community structures and has better predictions than other methods.

Attention mechanisms take an expectation of a data representation with respect to probability weights. Recently, (Martins et al. 2020, 2021) proposed continuous attention mechanisms, focusing on unimodal attention densities from the exponential and deformed exponential families: the latter has sparse support. (Farinhas et al 2021) extended this to to multimodality via Gaussian mixture attention densities. In this paper, we extend this to kernel exponential families (Canu and Smola 2006) and our new sparse counterpart, kernel deformed exponential families. Theoretically, we show new existence results for both kernel exponential and deformed exponential families, and that the deformed case has similar approximation capabilities to kernel exponential families. Lacking closed form expressions for the context vector, we use numerical integration: we show exponential convergence for both kernel exponential and deformed exponential families. Experiments show that kernel continuous attention often outperforms unimodal continuous attention, and the sparse variant tends to highlight peaks of time series.

Panel count data describes aggregated counts of recurrent events observed at discrete time points. To understand dynamics of health behaviors and predict future negative events, the field of quantitative behavioral research has evolved to increasingly rely upon panel count data collected via multiple self reports, for example, about frequencies of smoking using in-the-moment surveys on mobile devices. However, missing reports are common and present a major barrier to downstream statistical learning. As a first step, under a missing completely at random assumption (MCAR), we propose a simple yet widely applicable functional EM algorithm to estimate the counting process mean function, which is of central interest to behavioral scientists. The proposed approach wraps several popular panel count inference methods, seamlessly deals with incomplete counts and is robust to misspecification of the Poisson process assumption. Theoretical analysis of the proposed algorithm provides finite-sample guarantees by extending parametric EM theory to the general non-parametric setting. We illustrate the utility of the proposed algorithm through numerical experiments and an analysis of smoking cessation data. We also discuss useful extensions to address deviations from the MCAR assumption and covariate effects.

An important mobile health (mHealth) task is the use of multimodal data, such as sensor streams and self-report, to construct interpretable time-to-event predictions of, for example, lapse to alcohol or illicit drug use. Interpretability of the prediction model is important for acceptance and adoption by domain scientists, enabling model outputs and parameters to inform theory and guide intervention design. Temporal latent state models are therefore attractive, and so we adopt the continuous time hidden Markov model (CT-HMM) due to its ability to describe irregular arrival times of event data. Standard CT-HMMs, however, are not specialized for predicting the time to a future event, the key variable for mHealth interventions. Also, standard emission models lack a sufficiently rich structure to describe multimodal data and incorporate domain knowledge. We present iSurvive, an extension of classical survival analysis to a CT-HMM. We present a parameter learning method for GLM emissions and survival model fitting, and present promising results on both synthetic data and an mHealth drug use dataset.