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Multiple Imputation with Neural Network Gaussian Process for High-dimensional Incomplete Data

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arXiv 2022年

作者： Dai, Zongyu Bu, Zhiqi Long, Qi Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Division of Biostatistics University of Pennsylvania United States

Missing data are ubiquitous in real world applications and, if not adequately handled, may lead to the loss of information and biased findings in downstream analysis. Particularly, high-dimensional incomplete data with a moderate sample size, such as analysis of multi-omics data, present daunting challenges. Imputation is arguably the most popular method for handling missing data, though existing imputation methods have a number of limitations. Single imputation methods such as matrix completion methods do not adequately account for imputation uncertainty and hence would yield improper statistical inference. In contrast, multiple imputation (MI) methods allow for proper inference but existing methods do not perform well in high-dimensional settings. Our work aims to address these significant methodological gaps, leveraging recent advances in neural network Gaussian process (NNGP) from a Bayesian viewpoint. We propose two NNGP-based MI methods, namely MI-NNGP, that can apply multiple imputations for missing values from a joint (posterior predictive) distribution. The MI-NNGP methods are shown to significantly outperform existing state-of-the-art methods on synthetic and real datasets, in terms of imputation error, statistical inference, robustness to missing rates, and computation costs, under three missing data mechanisms, MCAR, MAR, and MNAR. Code is available in the GitHub repository https://***/bestadcarry/MI-NNGP. Copyright © 2022, The Authors. All rights reserved.

关键词： Gaussian noise (electronic)

A Differential Effect Approach to Partial Identification of Treatment Effects

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arXiv 2023年

作者： Chen, Kan Wang, Bingkai Small, Dylan S. Graduate Group of Applied Mathematics and Computational Science School of Arts and Sciences University of Pennsylvania PhiladelphiaPA United States Department of Statistics and Data Science The Wharton School University of Pennsylvania PhiladelphiaPA United States

We consider identification and inference for the average treatment effect and heterogeneous treatment effect conditional on observable covariates in the presence of unmeasured confounding. Since point identification of these treatment effects is not achievable without strong assumptions, we obtain bounds on these treatment effects by leveraging differential effects, a tool that allows for using a second treatment to learn the effect of the first treatment. The differential effect is the effect of using one treatment in lieu of the other. We provide conditions under which differential treatment effects can be used to point identify or partially identify treatment effects. Under these conditions, we develop a flexible and easy-to-implement semi-parametric framework to estimate bounds and leverage a two-stage approach to conduct statistical inference on effects of interest. The proposed method is examined through a simulation study and a case study that investigates the effect of smoking on the blood level of cadmium using the National Health and Nutrition Examination Survey. © 2023, CC BY.

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Optimal Complexity in Non-Convex Decentralized Learning over Time-Varying Networks

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arXiv 2022年

作者： Huang, Xinmeng Yuan, Kun Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Center for Machine Learning Research Peking University China

Decentralized optimization with time-varying networks is an emerging paradigm in machine learning. It saves remarkable communication overhead in large-scale deep training and is more robust in wireless scenarios especially when nodes are moving. Federated learning can also be regarded as decentralized optimization with time-varying communication patterns alternating between global averaging and local updates. While numerous studies exist to clarify its theoretical limits and develop efficient algorithms, it remains unclear what the optimal complexity is for non-convex decentralized stochastic optimization over time-varying networks. The main difficulties lie in how to gauge the effectiveness when transmitting messages between two nodes via time-varying communications, and how to establish the lower bound when the network size is fixed (which is a prerequisite in stochastic optimization). This paper resolves these challenges and establish the first lower bound complexity. We also develop a new decentralized algorithm to nearly attain the lower bound, showing the tightness of the lower bound and the optimality of our algorithm. Copyright © 2022, The Authors. All rights reserved.

关键词： Time varying networks

Learning operators with coupled attention

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2022年第1期23卷 9636-9698页

作者： Georgios Kissas Jacob H. Seidman Leonardo Ferreira Guilhoto Victor M. Preciado George J. Pappas Paris Perdikaris Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia PA Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia PA

Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data. We propose a novel operator learning method, LOCA (Learning Operators with Coupled Attention), motivated from the recent success of the attention mechanism. In our architecture, the input functions are mapped to a finite set of features which are then averaged with attention weights that depend on the output query locations. By coupling these attention weights together with an integral transform, LOCA is able to explicitly learn correlations in the target output functions, enabling us to approximate nonlinear operators even when the number of output function measurements in the training set is very small. Our formulation is accompanied by rigorous approximation theoretic guarantees on the universal expressiveness of the proposed model. Empirically, we evaluate the performance of LOCA on several operator learning scenarios involving systems governed by ordinary and partial differential equations, as well as a black-box climate prediction problem. Through these scenarios we demonstrate state of the art accuracy, robustness with respect to noisy input data, and a consistently small spread of errors over testing data sets, even for out-of-distribution prediction tasks.

关键词： deep learning reproducing kernel Hilbert spaces wavelet scattering networks functional data analysis universal approximation

Volumetric multi-contrast dynamics imaging for ex vivo liver microvasculature activity visualization using Jones matrix optical coherence tomography 25

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Volumetric multi-contrast dynamics imaging for ex vivo liver...

Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XXV 2021

作者： Mukherjee, P. Miyazawa, A. Shen, L.T.W. Fukuda, S. Yamashita, T. Oka, Y. Abd El-Sadek, I.G. Makita, S. Matsusaka, S. Oshika, T. Kano, H. Yasuno, Y. Computational Optics Group of University of Tsukuba Japan Faculty of Medicine of University of Tsukuba Japan Graduate School of Comprehensive Human Science of University of Tsukuba Japan Graduate School of Pure and Applied Sciences of University of Tsukuba Japan

ISBN: (数字)9781510640962

ISBN: (纸本)9781510640955

A three-dimensional multi-contrast tissue dynamics imaging method based on polarization-sensitive optical coherence tomography is presented to visualize microvascular tissue activity of mouse livers. Temporal variance of birefringence, temporal polarization uniformity and logarithmic OCT intensity variance are used to access the tissue dynamics. These methods are applied to time-course microvasculature activity visualization of dissected normal and inflammatory mouse liver. Multi-contrast projection images are generated to visualize vascular network of the liver. Cross-sectional and en face dynamics images show high activity around the periportal region of mouse liver at initial time point. Degradation of tissue activity is demonstrated by time-lapse imaging.

关键词： Liver Visualization Optical coherence tomography Tissues Birefringence Veins 3D image processing

Covariate-Balancing-Aware Interpretable Deep Learning Models for Treatment Effect Estimation

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arXiv 2022年

作者： Chen, Kan Yin, Qishuo Long, Qi Graduate Group of Applied Math and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Biostatistics Epidemiology and Informatics University of Pennsylvania PhiladelphiaPA19104 United States

Estimating treatment effects is of great importance for many biomedical applications with observational data. Particularly, interpretability of the treatment effects is preferable for many biomedical researchers. In this paper, we first provide a theoretical analysis and derive an upper bound for the bias of average treatment effect (ATE) estimation under the strong ignorability assumption. Derived by leveraging appealing properties of the Weighted Energy Distance, our upper bound is tighter than what has been reported in the literature. Motivated by the theoretical analysis, we propose a novel objective function for estimating the ATE that uses the energy distance balancing score and hence does not require correct specification of the propensity score model. We also leverage recently developed neural additive models to improve interpretability of deep learning models used for potential outcome prediction. We further enhance our proposed model with an energy distance balancing score weighted regularization. The superiority of our proposed model over current state-of-the-art methods is demonstrated in semi-synthetic experiments using two benchmark datasets, namely, IHDP and ACIC. © 2022, CC BY.

关键词： Medical applications

Entropy-Based Strategies for Multi-Bracket Pools

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arXiv 2023年

作者： Brill, Ryan S. Wyner, Abraham J. Barnett, Ian J. Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Department of Statistics and Data Science The Wharton School University of Pennsylvania United States Department of Biostatistics Perelman School University of Pennsylvania United States

Much work in the parimutuel betting literature has discussed estimating event outcome probabilities or developing optimal wagering strategies, particularly for horse race betting. Some betting pools, however, involve betting not just on a single event, but on a tuple of events. For example, pick six betting in horse racing, March Madness bracket challenges, and predicting a randomly drawn bitstring each involve making a series of individual forecasts. Although traditional optimal wagering strategies work well when the size of the tuple is very small (e.g., betting on the winner of a horse race), they are intractable for more general betting pools in higher dimensions (e.g., March Madness bracket challenges). Hence we pose the multi-brackets problem: supposing we wish to predict a tuple of events and that we know the true probabilities of each potential outcome of each event, what is the best way to tractably generate a set of n predicted tuples? The most general version of this problem is extremely difficult, so we begin with a simpler setting. In particular, we generate n independent predicted tuples according to a distribution having optimal entropy. This entropy-based approach is tractable, scalable, and performs well. Copyright © 2023, The Authors. All rights reserved.

关键词： Forecasting

Analytics, have some humility: a statistical view of fourth-down decision making

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arXiv 2023年

作者： Brill, Ryan S. Yurko, Ronald Wyner, Abraham J. Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Dept. of Statistics and Data Science Carnegie Mellon University United States Dept. of Statistics and Data Science The Wharton School University of Pennsylvania United States

The standard mathematical approach to fourth-down decision making in American football is to make the decision that maximizes estimated win probability. Win probability estimates arise from machine learning models fit from historical data. These models attempt to capture a nuanced relationship between a noisy binary outcome variable and game-state variables replete with interactions and non-linearities from a finite dataset of just a few thousand games. Thus, it is imperative to knit uncertainty quantification into the fourth-down decision procedure;we do so using bootstrapping. We find that uncertainty in the estimated optimal fourth-down decision is far greater than that currently expressed by sports analysts in popular sports media. Copyright © 2023, The Authors. All rights reserved.

关键词： Adversarial machine learning

Asymptotic Statistical Analysis of Sparse group LASSO via Approximate Message Passing Algorithm

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arXiv 2021年

作者： Chen, Kan Bu, Zhiqi Xu, Shiyun Graduate Group of Applied Mathematics and Computational Science University of Pennsylvania United States

Sparse group LASSO (SGL) is a regularized model for high-dimensional linear regression problems with grouped covariates. SGL applies l1 and l2 penalties on the individual predictors and group predictors, respectively, to guarantee sparse effects both on the inter-group and within-group levels. In this paper, we apply the approximate message passing (AMP) algorithm to efficiently solve the SGL problem under Gaussian random designs. We further use the recently developed state evolution analysis of AMP to derive an asymptotically exact characterization of SGL solution. This allows us to conduct multiple fine-grained statistical analyses of SGL, through which we investigate the effects of the group information and γ (proportion of `1 penalty). With the lens of various performance measures, we show that SGL with small γ benefits significantly from the group information and can outperform other SGL (including LASSO) or regularized models which does not exploit the group information, in terms of the recovery rate of signal, false discovery rate and mean squared error. Copyright © 2021, The Authors. All rights reserved.

关键词： Mean square error