arXiv subjects

Emily C. Hector

Publications and source records attributed to Emily C. Hector.

24 records · Page 2Linked to original sources

arXiv2022

Statistical Inference for Streamed Longitudinal Data

Modern longitudinal data, for example from wearable devices, measures biological signals on a fixed set of participants at a diverging number of time points. Traditional statistical methods are not equipped to handle the computational burden of repeatedly analyzing the cumulatively growing dataset each time new data is collected. We propose a new estimation and inference framework for dynamic updating of point estimates and their standard errors across serially collected dependent datasets. The key technique is a decomposition of the extended score function of the quadratic inference function constructed over the cumulative longitudinal data into a sum of summary statistics over data batches. We show how this sum can be recursively updated without the need to access the whole dataset, resulting in a computationally efficient streaming procedure with minimal loss of statistical efficiency. We prove consistency and asymptotic normality of our streaming estimator as the number of data batches diverges, even as the number of independent participants remains fixed. Simulations highlight the advantages of our approach over traditional statistical methods that assume independence between data batches. Finally, we investigate the relationship between physical activity and several diseases through the analysis of accelerometry data from the National Health and Nutrition Examination Survey.

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arXiv2022

Distributed Inference for Spatial Extremes Modeling in High Dimensions

Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using max stable processes (MSPs). MSPs are computationally prohibitive to fit for as few as a dozen observations, with supposed computationally-efficient approaches like the composite likelihood remaining computationally burdensome with a few hundred observations. In this paper, we propose a spatial partitioning approach based on local modeling of subsets of the spatial domain that delivers computationally and statistically efficient inference. Marginal and dependence parameters of the MSP are estimated locally on subsets of observations using censored pairwise composite likelihood, and combined using a modified generalized method of moments procedure. The proposed distributed approach is extended to estimate spatially varying coefficient models to deliver computationally efficient modeling of spatial variation in marginal parameters. We demonstrate consistency and asymptotic normality of estimators, and show empirically that our approach leads to a surprising reduction in bias of parameter estimates over a full data approach. We illustrate the flexibility and practicability of our approach through simulations and the analysis of streamflow data from the U.S. Geological Survey.

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arXiv2021

Parallel-and-stream accelerator for computationally fast supervised learning

Two dominant distributed computing strategies have emerged to overcome the computational bottleneck of supervised learning with big data: parallel data processing in the MapReduce paradigm and serial data processing in the online streaming paradigm. Despite the two strategies' common divide-and-combine approach, they differ in how they aggregate information, leading to different trade-offs between statistical and computational performance. In this paper, we propose a new hybrid paradigm, termed a Parallel-and-Stream Accelerator (PASA), that uses the strengths of both strategies for computationally fast and statistically efficient supervised learning. PASA's architecture nests online streaming processing into each distributed and parallelized data process in a MapReduce framework. PASA leverages the advantages and mitigates the disadvantages of both the MapReduce and online streaming approaches to deliver a more flexible paradigm satisfying practical computing needs. We study the analytic properties and computational complexity of PASA, and detail its implementation for two key statistical learning tasks. We illustrate its performance through simulations and a large-scale data example building a prediction model for online purchases from advertising data.

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arXiv2020

Joint integrative analysis of multiple data sources with correlated vector outcomes

We propose a distributed quadratic inference function framework to jointly estimate regression parameters from multiple potentially heterogeneous data sources with correlated vector outcomes. The primary goal of this joint integrative analysis is to estimate covariate effects on all outcomes through a marginal regression model in a statistically and computationally efficient way. We develop a data integration procedure for statistical estimation and inference of regression parameters that is implemented in a fully distributed and parallelized computational scheme. To overcome computational and modeling challenges arising from the high-dimensional likelihood of the correlated vector outcomes, we propose to analyze each data source using Qu, Lindsay and Li (2000)'s quadratic inference functions, and then to jointly reestimate parameters from each data source by accounting for correlation between data sources using a combined meta-estimator in a similar spirit to Hansen (1982)'s generalised method of moments. We show both theoretically and numerically that the proposed method yields efficiency improvements and is computationally fast. We illustrate the proposed methodology with the joint integrative analysis of the association between smoking and metabolites in a large multi-cohort study and provide an R package for ease of implementation.

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arXiv2020

Doubly Distributed Supervised Learning and Inference with High-Dimensional Correlated Outcomes

This paper presents a unified framework for supervised learning and inference procedures using the divide-and-conquer approach for high-dimensional correlated outcomes. We propose a general class of estimators that can be implemented in a fully distributed and parallelized computational scheme. Modelling, computational and theoretical challenges related to high-dimensional correlated outcomes are overcome by dividing data at both outcome and subject levels, estimating the parameter of interest from blocks of data using a broad class of supervised learning procedures, and combining block estimators in a closed-form meta-estimator asymptotically equivalent to estimates obtained by Hansen (1982)'s generalized method of moments (GMM) that does not require the entire data to be reloaded on a common server. We provide rigorous theoretical justifications for the use of distributed estimators with correlated outcomes by studying the asymptotic behaviour of the combined estimator with fixed and diverging number of data divisions. Simulations illustrate the finite sample performance of the proposed method, and we provide an R package for ease of implementation.

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arXiv2020

A Distributed and Integrated Method of Moments for High-Dimensional Correlated Data Analysis

This paper is motivated by a regression analysis of electroencephalography (EEG) neuroimaging data with high-dimensional correlated responses with multi-level nested correlations. We develop a divide-and-conquer procedure implemented in a fully distributed and parallelized computational scheme for statistical estimation and inference of regression parameters. Despite significant efforts in the literature, the computational bottleneck associated with high-dimensional likelihoods prevents the scalability of existing methods. The proposed method addresses this challenge by dividing responses into subvectors to be analyzed separately and in parallel on a distributed platform using pairwise composite likelihood. Theoretical challenges related to combining results from dependent data are overcome in a statistically efficient way using a meta-estimator derived from Hansen's generalized method of moments. We provide a rigorous theoretical framework for efficient estimation, inference, and goodness-of-fit tests. We develop an R package for ease of implementation. We illustrate our method's performance with simulations and the analysis of the EEG data, and find that iron deficiency is significantly associated with two auditory recognition memory related potentials in the left parietal-occipital region of the brain.

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