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40th International Conference on Machine Learning, ICML 2023

作者： Lee, Donghwan Moniri, Behrad Huang, Xinmeng Dobriban, Edgar Hassani, Hamed Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PA United States Department of Electrical and Systems Engineering University of Pennsylvania PA United States Department of Statistics and Data Science University of Pennsylvania PA United States

Evaluating the performance of machine learning models under distribution shifts is challenging, especially when we only have unlabeled data from the shifted (target) domain, along with labeled data from the original (source) domain. Recent work suggests that the notion of disagreement, the degree to which two models trained with different randomness differ on the same input, is a key to tackling this problem. Experimentally, disagreement and prediction error have been shown to be strongly connected, which has been used to estimate model performance. Experiments have led to the discovery of the disagreement-on-the-line phenomenon, whereby the classification error under the target domain is often a linear function of the classification error under the source domain;and whenever this property holds, disagreement under the source and target domain follow the same linear relation. In this work, we develop a theoretical foundation for analyzing disagreement in high-dimensional random features regression;and study under what conditions the disagreement-on-the-line phenomenon occurs in our setting. Experiments on CIFAR-10-C, Tiny ImageNet-C, and Camelyon17 are consistent with our theory and support the universality of the theoretical findings. © 2023 Proceedings of Machine Learning Research. All rights reserved.

关键词： Errors

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The star geometry of critic-based regularizer learning 24

The star geometry of critic-based regularizer learning

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Proceedings of the 38th International Conference on Neural Information Processing Systems

作者： Oscar Leong Eliza O'Reilly Yong Sheng Soh Department of Statistics and Data Science University of California Los Angeles Department of Applied Mathematics and Statistics Johns Hopkins University Department of Mathematics National University of Singapore

ISBN: (纸本)9798331314385

Variational regularization is a classical technique to solve statistical inference tasks and inverse problems, with modern data-driven approaches parameterizing regularizes via deep neural networks showcasing impressive empirical performance. Recent works along these lines learn task-dependent regularizers. This is done by integrating information about the measurements and ground-truth data in an unsupervised, critic-based loss function, where the regularizer attributes low values to likely data and high values to unlikely data. However, there is little theory about the structure of regularizers learned via this process and how it relates to the two data distributions. To make progress on this challenge, we initiate a study of optimizing critic-based loss functions to learn regularizers over a particular family of regularizers: gauges (or Minkowski functionals) of star-shaped bodies. This family contains regularizers that are commonly employed in practice and shares properties with regularizers parameterized by deep neural networks. We specifically investigate critic-based losses derived from variational representations of statistical distances between probability measures. By leveraging tools from star geometry and dual Brunn-Minkowski theory, we illustrate how these losses can be interpreted as dual mixed volumes that depend on the data distribution. This allows us to derive exact expressions for the optimal regularizer in certain cases. Finally, we identify which neural network architectures give rise to such star body gauges and when such regularizers have favorable properties for optimization. More broadly, this work highlights how the tools of star geometry can aid in understanding the geometry of unsupervised regularizer learning.

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Missing data Analysis Using Statistical and Machine Learning Methods in Facility-Based Maternal Health Records

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SN Computer science 2022年第5期3卷 355页

作者： Memon, Shaheen M. Z. Wamala, Robert Kabano, Ignace H. Department of Statistical Methods and Actuarial Science Makerere University Kampala Uganda Department of Planning and Applied Statistics Makerere University Kampala Uganda Department of Applied Statistics School of Economics University of Rwanda Kigali Rwanda African Centre of Excellence in Data Science College of Business and Economics University of Rwanda Kigali Rwanda

Missing data are a rule rather than an exception in quantitative research. The questionable aspect however is the extent, pattern, mechanism, and treatment of missingness in facility-based paper maternal health records. We utilized data from maternal health records at Kawempe National Referral Hospital, Uganda. Only records of women who had given birth at the Hospital during January 2017 to January 2021 were considered. The analysis was done using R-Studio using frequency distributions, Pearson χ² Test. Treatment of missingness was done using Listwise deletion (LD), Mode Imputation, Multiple Imputation by chained equations (MICE), Imputation using K-Nearest Neighbors (KNN) and Random Forest (RF) Imputation. Performance of methods was investigated using prediction accuracy and the Kruskal–Wallis Test on Standard Errors (SEs) derived following a Logistic Regression. Overall, 5% of the data was missing. The proportion of missingness ranged from 1.4 to 20.7% in variables. Case-wise missingness was established where 2498 out of the 4626 cases (54%) had at-least one variable with missing value. The pattern of missingness was arbitrary. The data suggest either missing at random or missing completely at random. With the exception of LD, no difference in SEs following Logistic Regression was noted in the imputation methods for treatment of missingness (p > 0.05). Further, LD yielded the lowest prediction accuracy after Logistic Regression. No major variations were noted in the prediction accuracy following a Logistic Regression after imputation using MICE, mode imputation, KNN and RF. Missingness in facility-based health records should not be ignored. Researchers need to pay attention to both overall and case-wise missingness. © 2022, The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.

关键词： Facility-based records Imputation Maternal morbidity Missing data Missing mechanism Missing pattern

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A Permutation-Free Kernel Independence Test

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Journal of Machine Learning Research 2023年 24卷

作者： Shekhar, Shubhanshu Kim, Ilmun Ramdas, Aaditya Department of Statistics and Data Science Carnegie Mellon University PittsburghPA15213 United States Department of Statistics and Data Science Department of Applied Statistics Yonsei University Seodaemun-gu Seoul03722 Korea Republic of Department of Statistics and Data Science Machine Learning Department Carnegie Mellon University PittsburghPA15213 United States

In nonparametric independence testing, we observe i.i.d. data {(Xi,Yi)}in=1, where X ∈ X,Y ∈ Y lie in any general spaces, and we wish to test the null that X is independent of Y. Modern test statistics such as the kernel Hilbert–Schmidt Independence Criterion (HSIC) and Distance Covariance (dCov) have intractable null distributions due to the degeneracy of the underlying U-statistics. Hence, in practice, one often resorts to using permutation testing, which provides a nonasymptotic guarantee at the expense of recalculating the quadratic-time statistics (say) a few hundred times. In this paper, we provide a simple but nontrivial modification of HSIC and dCov (called xHSIC and xdCov, pronounced "cross" HSIC/dCov) so that they have a limiting Gaussian distribution under the null, and thus do not require permutations. We show that our new tests, like the originals, are consistent against fixed alternatives, and minimax rate optimal against smooth local alternatives. Numerical simulations demonstrate that compared to the permutation tests, our variants have the same power within a constant factor, giving practitioners a new option for large problems or data-analysis pipelines where computation, not sample size, could be the bottleneck. © 2023 Shubhanshu Shekhar, Ilmun Kim, and Aaditya Ramdas.

关键词： Gaussian distribution

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Nonstationary sparse spectral permanental process 24

Nonstationary sparse spectral permanental process

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Proceedings of the 38th International Conference on Neural Information Processing Systems

作者： Zicheng Sun Yixuan Zhang Zenan Ling Xuhui Fan Feng Zhou Center for Applied Statistics and School of Statistics Renmin University of China School of Statistics and Data Science Southeast University School of EIC Huazhong University of Science and Technology School of Computing Macquarie University Center for Applied Statistics and School of Statistics Renmin University of China and Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing

ISBN: (纸本)9798331314385

Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of non-stationary kernels. This technique relaxes the constraints on kernel types and stationarity, allowing for more flexible modeling while reducing computational complexity to the linear level. Additionally, we introduce a deep kernel variant by hierarchically stacking multiple spectral feature mappings, further enhancing the model's expressiveness to capture complex patterns in data. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of our approach, particularly in scenarios with pronounced data nonstationarity. Additionally, ablation studies are conducted to provide insights into the impact of various hyperparameters on model performance. Code is publicly available at https://***/SZC20/DNSSPP.

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Multimodal Adaptive Dynamic Graph Learning for Multivariate Time Series Forecasting

SSRN

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SSRN 2024年

作者： Lee, Seunghan Lee, Kibok Park, Taeyoung Department of Statistics and Data Science Yonsei University Seoul03722 Korea Republic of Department of Applied Statistics Yonsei University Seoul03722 Korea Republic of

Graph neural networks (GNNs) have been successfully applied to model both spatial and temporal relationships in multivariate time series (MTS) forecasting. However, recent advances in spatio-temporal GNNs are generally made under an assumption that the underlying relationships between MTS are known, which is often unrealistic in many real-world applications. While a few recent studies learn to predict the relationships, they are still limited in that they focus only on either global characteristics that are constant over time or local characteristics that are limited to a specific time period. In this article, we propose a novel graph learning algorithm for MTS forecasting by generating multimodal adaptive dynamic graphs capturing both global and local characteristics of MTS. Specifically, we propose to convert long-range temporal sequences to spatial images and generate global multimodal graphs using convolutional networks. Then, global multimodal graphs are dynamically used with time-varying attention weights to represent the local characteristics of input time series for a specific period of time. Experimental results show that the proposed method outperforms state-of-the-art graph learning methods across benchmarks in different domains. The source codes are available at: https://***/seunghan96/MAD-GL2. © 2024, The Authors. All rights reserved.

关键词： Graph neural networks

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Causally Disentangled Generative Variational AutoEncoder

arXiv

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arXiv 2023年

作者： SeungHwan, A.N. Song, Kyungwoo Jeon, Jong-June Department of Statistics University of Seoul Korea Republic of Department of Applied Statistics Department of Statistics and Data Science Yonsei University Korea Republic of

We present a new supervised learning technique for the Variational AutoEncoder (VAE) that allows it to learn a causally disentangled representation and generate causally disentangled outcomes simultaneously. We call this approach Causally Disentangled Generation (CDG). CDG is a generative model that accurately decodes an output based on a causally disentangled representation. Our research demonstrates that adding supervised regularization to the encoder alone is insufficient for achieving a generative model with CDG, even for a simple task. Therefore, we explore the necessary and sufficient conditions for achieving CDG within a specific model. Additionally, we introduce a universal metric for evaluating the causal disentanglement of a generative model. Empirical results from both image and tabular datasets support our findings. © 2023, CC BY-NC-SA.

关键词： Supervised learning

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Expressivity of deterministic quantum computation with one qubit

arXiv

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arXiv 2024年

作者： Kim, Yujin Park, Daniel K. Department of Statistics and Data Science Yonsei University Seoul03722 Korea Republic of Department of Applied Statistics Yonsei University Seoul03722 Korea Republic of

Deterministic quantum computation with one qubit (DQC1) is of significant theoretical and practical interest due to its computational advantages in certain problems, despite its subuniversality with limited quantum resources. In this work, we introduce parameterized DQC1 as a quantum machine learning model. We demonstrate that the gradient of the measurement outcome of a DQC1 circuit with respect to its gate parameters can be computed directly using the DQC1 protocol. This allows for gradient-based optimization of DQC1 circuits, positioning DQC1 as the sole quantum protocol for both training and inference. We then analyze the expressivity of the parameterized DQC1 circuits, characterizing the set of learnable functions, and show that DQC1-based machine learning (ML) is as powerful as quantum neural networks based on universal computation. Our findings highlight the potential of DQC1 as a practical and versatile platform for ML, capable of rivaling more complex quantum computing models while utilizing simpler quantum resources. Copyright © 2024, The Authors. All rights reserved.

关键词： Qubits

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Invertibility of Discrete-Time Linear Systems with Sparse Inputs 63

Invertibility of Discrete-Time Linear Systems with Sparse In...

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Poe, Kyle Mallada, Enrique Vidal, Rene University of Pennsylvania Applied Mathematics and Computational Science Group PA19104 United States Johns Hopkins University Mallada Is with the Department of Electrical and Computer Engineering MD21218 United States University of Pennsylvania Radiology Computer and Information Science Statistics and Data Science Departments of Electrical and Systems Engineering PA19104 United States

ISBN: (纸本)9798350316339

One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics, and spectral structure of a system have been used to characterize the well-posedness of this problem, without assumptions on the inputs. However, certain structural assumptions, such as input sparsity, have been shown to translate to practical gains in the performance of inversion algorithms, surpassing classical guarantees. Establishing necessary and sufficient conditions for left invertibility of systems with sparse inputs is therefore a crucial step toward understanding the performance limits of system inversion under structured input assumptions. In this work, we provide the first necessary and sufficient characterizations of left invertibility for linear systems with sparse inputs, echoing classic characterizations for standard linear systems. The key insight in deriving these results is in establishing the existence of two novel geometric invariants unique to the sparseinput setting, the weakly unobservable and strongly reachable subspace arrangements. By means of a concrete example, we demonstrate the utility of these characterizations. We conclude by discussing extensions and applications of this framework to several related problems in sparse control. © 2024 IEEE.

关键词： State space methods

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Exploring the difficulty of estimating win probability: a simulation study

arXiv

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arXiv 2024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

Estimating win probability is one of the classic modeling tasks of sports analytics. Many widely used win probability estimators use machine learning to fit the relationship between a binary win/loss outcome variable and certain game-state variables. To illustrate just how difficult it is to accurately fit such a model from noisy and highly correlated observational data, in this paper we conduct a simulation study. We create a simplified random walk version of football in which true win probability at each game-state is known, and we see how well a model recovers it. We find that the dependence structure of observational play-by-play data substantially inflates the bias and variance of estimators and lowers the effective sample size. This makes it essential to quantify uncertainty in win probability estimates, but typical bootstrapped confidence intervals are too narrow and don’t achieve nominal coverage. Hence, we introduce a novel method, the fractional bootstrap, to calibrate these intervals to achieve adequate coverage. Our findings are not unique to the particular application of estimating win probability;they are broadly applicable across sports analytics, as myriad other sports datasets are clustered into groups of observations that share the same outcome. © 2024, CC BY.

关键词： Sports

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