Structured Kernel Interpolation (SKI) scales Gaussian Processes (GPs) by approximating the kernel matrix via inducing point interpolation, achieving linear computational complexity. However, it lacks rigorous theoretical error analysis. This paper bridges this gap by proving error bounds for the SKI Gram matrix and examining their effect on hyperparameter estimation and posterior inference. We further provide a practical guide to selecting the number of inducing points under convolutional cubic interpolation: they should grow as $n^{d/3}$ for error control. Crucially, we identify two dimensionality regimes for the SKI Gram matrix spectral norm error vs. complexity trade-off. For $d<3$, any error tolerance can achieve linear time for sufficiently large sample size. For $d\geq 3$, the error must increase with sample size for our guarantees to hold. Our analysis provides key insights into SKI’s scalability-accuracy trade-offs, establishing precise conditions for achieving linear-time GP inference with controlled error.

The success of self-supervised contrastive learning hinges on identifying positive data pairs, such that when they are pushed together in embedding space, the space encodes useful information for subsequent downstream tasks. Constructing positive pairs is non-trivial as the pairing must be similar enough to reflect a shared semantic meaning, but different enough to capture within-class variation. Classical approaches in vision use augmentations to exploit well-established invariances to construct positive pairs, but invariances in the time-series domain are much less obvious. In our work, we propose a novel method of using a learned measure for identifying positive pairs. Our Retrieval-Based Reconstruction (REBAR) measure measures the similarity between two sequences as the reconstruction error that results from reconstructing one sequence with retrieved information from the other. Then, if the two sequences have high REBAR similarity, we label them as a positive pair. Through validation experiments, we show that the REBAR error is a predictor of mutual class membership. Once integrated into a contrastive learning framework, our REBAR method learns an embedding that achieves state-of-the-art performance on downstream tasks across various modalities.

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.

Second order stochastic optimizers allow parameter update step size and direction to adapt to loss curvature, but have traditionally required too much memory and compute for deep learning. Recently, Shampoo [Gupta et al., 2018] introduced a Kronecker factored preconditioner to reduce these requirements: it is used for large deep models [Anil et al., 2020] and in production [Anil et al., 2022]. However, it takes inverse matrix roots of ill-conditioned matrices. This requires 64-bit precision, imposing strong hardware constraints. In this paper, we propose a novel factorization, Kronecker Approximation-Domination (KrAD). Using KrAD, we update a matrix that directly approximates the inverse empirical Fisher matrix (like full matrix AdaGrad), avoiding inversion and hence 64-bit precision. We then propose KrADagrad , with similar computational costs to Shampoo and the same regret. Synthetic ill-conditioned experiments show improved performance over Shampoo for 32-bit precision, while for several real datasets we have comparable or better generalization.

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.

The promise of Mobile Health (mHealth) is the ability to use wearable sensors to monitor participant physiology at high frequencies during daily life to enable temporally-precise health interventions. However, a major challenge is frequent missing data. Despite a rich imputation literature, existing techniques are ineffective for the pulsative signals which comprise many mHealth applications, and a lack of available datasets has stymied progress. We address this gap with PulseImpute, the first large-scale pulsative signal imputation challenge which includes realistic mHealth missingness models, an extensive set of baselines, and clinically-relevant downstream tasks. Our baseline models include a novel transformer-based architecture designed to exploit the structure of pulsative signals. We hope that PulseImpute will enable the ML community to tackle this important and challenging task.

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.

Summary Analysts prototyping trading strategies often reuse previously computed values: both full problems and subproblems. Avoiding recomputing these would increase productivity. We built a memoization library that caches function computations to files to avoid recomputation. This should minimize the need for users to think about whether caching is appropriate while giving them control over speed, accuracy, and space usage. Guo and Engler built an automatic memoization library by modifying the Python interpreter, while jug and joblib are distributed computing libraries that do memoization. Our library attempts to maintain the ease of use of these libraries while offering a higher degree of control of how caching is carried out. It allows control of space usage for individual functions and all memoization, refreshing memoization for a specific function, and accuracy checking, and uses faster hashing and provides a divide and conquer approach to reuse previously computed subproblems. We show that for Markowitz optimization, Fama–French, and the singular value decomposition, memoization using our library greatly speeds up recomputation, often by over 99% versus no memoization and over 80% versus joblib. We also show how a divide‐and‐conquer memoization approach can give large speedups for sorting. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.