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COMPOSITE BAYESIAN OPTIMIZATION IN FUNCTION SPACES USING NEON - NEURAL EPISTEMIC OPERATOR NETWORKS

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arXiv 2024年

作者： Guilhoto, Leonardo Ferreira Perdikaris, Paris Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces. In this paper, we introduce NEON (Neural Epistemic Operator Networks), an architecture for generating predictions with uncertainty using a single operator network backbone, which presents orders of magnitude less trainable parameters than deep ensembles of comparable performance. We showcase the utility of this method for sequential decision-making by examining the problem of composite Bayesian Optimization (BO), where we aim to optimize a function f = g ◦ h, where h : X → C(Y, ds) is an unknown map which outputs elements of a function space, and g : C(Y, ds) → is a known and cheap-to-compute functional. By comparing our approach to other state-of-the-art methods on toy and real world scenarios, we demonstrate that NEON achieves state-of-the-art performance while requiring orders of magnitude less trainable *** Codes 68T37 © 2024, CC BY-NC-SA.

关键词： Toys

A subgroup-aware scoring approach to the study of effect modification in observational studies

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arXiv 2024年

作者： Fan, Yijun Small, Dylan S. Graduate Group of Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Statistics and Data Science University of Pennsylvania PhiladelphiaPA19104 United States

Effect modification means the size of a treatment effect varies with an observed covariate. Generally speaking, a larger treatment effect with more stable error terms is less sensitive to bias. Thus, we might be able to conclude that a study is less sensitive to unmeasured bias by using these subgroups experiencing larger treatment effects. Lee et al. (2018) proposed the submax method that leverages the joint distribution of test statistics from subgroups to draw a firmer conclusion if effect modification occurs. However, one version of the submax method uses M-statistics as the test statistics and is implemented in the R package submax (Rosenbaum, 2017). The scaling factor in the M-statistics is computed using all observations combined across subgroups. We show that this combining can confuse effect modification with outliers. We propose a novel group M-statistic that scores the matched pairs in each subgroup to tackle the issue. We examine our novel scoring strategy in extensive settings to show the superior performance. The proposed method is applied to an observational study of the effect of a malaria prevention treatment in West Africa. Copyright © 2024, The Authors. All rights reserved.

关键词： Malaria control

T-Cal: an optimal test for the calibration of predictive models

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2023年第1期24卷 15959-16030页

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

The prediction accuracy of machine learning methods is steadily increasing, but the calibration of their uncertainty predictions poses a significant challenge. Numerous works focus on obtaining well-calibrated predictive models, but less is known about reliably assessing model calibration. This limits our ability to know when algorithms for improving calibration have a real effect, and when their improvements are merely artifacts due to random noise in finite datasets. In this work, we consider detecting mis-calibration of predictive models using a finite validation dataset as a hypothesis testing problem. The null hypothesis is that the predictive model is calibrated, while the alternative hypothesis is that the deviation from calibration is sufficiently *** find that detecting mis-calibration is only possible when the conditional probabilities of the classes are sufficiently smooth functions of the predictions. When the conditional class probabilities are Hölder continuous, we propose T-Cal, a minimax optimal test for calibration based on a debiased plug-in estimator of the ℓ2-Expected Calibration Error (ECE). We further propose adaptive T-Cal, a version that is adaptive to unknown smoothness. We verify our theoretical findings with a broad range of experiments, including with several popular deep neural net architectures and several standard post-hoc calibration methods. T-Cal is a practical general-purpose tool, which--combined with classical tests for discrete-valued predictors--can be used to test the calibration of virtually any probabilistic classification method. T-Cal is available at https://***/dh7401/T-Cal.

关键词： uncertainty quantification calibration nonparametric statistics hypothesis testing minimax optimality

Anisotropic Oldroyd-type models for non-colloidal suspensions of viscoelastic particles in Newtonian and yield-stress fluids via homogenization

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science Talks 2022年 4卷

作者： Ponte Castañeda, Pedro Department of Mechanical Engineering and Applied Mechanics Graduate Group of Applied Math and Computational Science University of Pennsylvania Philadelphia United States

This talk presents new rheological models, derived by means of homogenization techniques, for non-colloidal suspensions of particles undergoing finite deformations and rotations under Stokes flow conditions. The particles can be nonlinear viscoelastic, or elasto-viscoplastic, while the suspending fluid can be Newtonian or viscoplastic. The microstructure is described by two microstructural ellipsoids, which are allowed to evolve with the flow, characterizing the shape and orientation of the inclusions and the angular dependence of their distribution in space. The models account for particle interactions through the two-point correlation function for the particle centers, in a way that reproduces exactly classical and more recent estimates for dilute suspensions. While special cases of the models have been considered in earlier publications, novel features of this work include the possibility of multiple inclusion families, physically motivated evolutions laws for the particle distributions and more general rheological behaviors for the matrix and inclusions. The resulting models can be viewed as anisotropic generalizations of Oldroyd's invariant models accounting for statistical measures of the microstructure and their evolution. © 2022 The Author

关键词： Multiphase and particle-laden flows Non-Newtonian flows Particle/fluid flow Rheology Suspensions Yield-stress fluids

Hiring under Congestion and Algorithmic Monoculture: Value of Strategic Behavior

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arXiv 2025年

作者： Baek, Jackie Bastani, Hamsa Chen, Shihan Stern School of Business New York University United States Wharton School University of Pennsylvania United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States

We study the impact of strategic behavior in a setting where firms compete to hire a shared pool of applicants, and firms use a common algorithm to evaluate the applicants. Each applicant is associated with a scalar score that is observed by all firms, provided by the algorithm. Firms simultaneously make interview decisions, where the number of interviews is capacity-constrained. Job offers are given to those who pass the interview, and an applicant who receives multiple offers accept one of them uniformly at random. We fully characterize the set of Nash equilibria under this model. Defining social welfare as the total number of applicants hired, we then compare the social welfare at a Nash equilibrium to a naive baseline where all firms interview applicants with the highest scores. We show that the Nash equilibrium greatly improves upon social welfare compared to the naive baseline, especially when the interview capacity is small and the number of firms is large. We also show that the price of anarchy is small, providing further appeal for the equilibrium solution. We then study how the firms may converge to a Nash equilibrium. We show that when firms make interview decisions sequentially and each firm takes the best response action assuming they are the last to act, this process converges to an equilibrium when interview capacities are small. However, we show that the task of computing the best response is difficult if firms have to use its own historical samples to estimate it, while this task becomes trivial if firms have information on the degree of competition for each applicant. Therefore, converging to an equilibrium can be greatly facilitated if firms have information on the level of competition for each applicant. Copyright © 2025, The Authors. All rights reserved.

关键词： Nash equilibrium

Tackling Copyright Issues in AI Image Generation Through Originality Estimation and Genericization

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arXiv 2024年

作者： Chiba-Okabe, Hiroaki Su, Weijie J. Department of Statistics and Data Science Wharton School University of Pennsylvania PhiladelphiaPA19104 United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States

The rapid progress of generative AI technology has sparked significant copyright concerns, leading to numerous lawsuits filed against AI developers. Notably, generative AI’s capacity for generating images of copyrighted characters has been well documented in the literature, and while various techniques for mitigating copyright issues have been studied, significant risks remain. Here, we propose a genericization method that modifies the outputs of a generative model to make them more generic and less likely to imitate distinctive features of copyrighted materials. To achieve this, we introduce a metric for quantifying the level of originality of data, estimated by drawing samples from a generative model, and applied in the genericization process. As a practical implementation, we introduce PREGen (Prompt Rewriting-Enhanced Genericization), which combines our genericization method with an existing mitigation technique. Compared to the existing method, PREGen reduces the likelihood of generating copyrighted characters by more than half when the names of copyrighted characters are used as the prompt. Additionally, while generative models can produce copyrighted characters even when their names are not directly mentioned in the prompt, PREGen almost entirely prevents the generation of such characters in these cases. Ultimately, this study advances computational approaches for quantifying and strengthening copyright protection, thereby providing practical methodologies to promote responsible generative AI development. © 2024, CC BY.

关键词： Generative adversarial networks

Wasserstein F-tests for Fréchet regression on Bures-Wasserstein manifolds

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arXiv 2024年

作者： Xu, Haoshu Li, Hongzhe Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Biostatistics Epidemiology and Informatics University of Pennsylvania PhiladelphiaPA19104 United States

This paper addresses the problem of regression analysis where the outcome is a random covariance matrix and the covariates are Euclidean. The study is situated within the framework of Fréchet regression on the Bures-Wasserstein manifold, which is pertinent to fields like single-cell genomics and neuroscience, where covariance matrices are observed across many samples. Fréchet regression on the Bures-Wasserstein manifold is formulated as estimating the conditional Fréchet mean given covariates x. A non-asymptotic √n-rate of convergence (up to log n factors) is obtained for our estimator, uniformly for x √log n, which is crucial for deriving the asymptotic null distribution and assessing the power of our proposed statistical test for the null hypothesis of no association. Additionally, a central limit theorem for the point estimate is derived, offering insights into testing covariate effects. The null distribution of the test statistic is shown to converge to a weighted sum of independent chi-square distributions. The test’s power is also demonstrated against a sequence of contiguous alternatives. Simulation results validate the accuracy of the asymptotic distributions. Finally, the proposed methods are applied to a single-cell gene expression dataset, illustrating changes in gene co-expression networks with age. © 2024, CC BY.

关键词： Regression analysis

Lower Bounds and Nearly Optimal Algorithms in Distributed Learning with Communication Compression

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arXiv 2022年

作者： Huang, Xinmeng Chen, Yiming Yin, Wotao Yuan, Kun Graduate Group in Applied Mathematics and Computational Science Univ. of Pennsylvania United States DAMO Academy Alibaba Group China

Recent advances in distributed optimization and learning have shown that communication compression is one of the most effective means of reducing communication. While there have been many results on convergence rates under communication compression, a theoretical lower bound is still missing. Analyses of algorithms with communication compression have attributed convergence to two abstract properties: the unbiased property or the contractive property. They can be applied with either unidirectional compression (only messages from workers to server are compressed) or bidirectional compression. In this paper, we consider distributed stochastic algorithms for minimizing smooth and non-convex objective functions under communication compression. We establish a convergence lower bound for algorithms whether using unbiased or contractive compressors in unidirection or bidirection. To close the gap between the lower bound and the existing upper bounds, we further propose an algorithm, NEOLITHIC, which almost reaches our lower bound (up to logarithm factors) under mild conditions. Our results also show that using contractive bidirectional compression can yield iterative methods that converge as fast as those using unbiased unidirectional compression. The experimental results validate our findings. Copyright © 2022, The Authors. All rights reserved.

关键词： Iterative methods

Exploring the difficulty of estimating win probability: a simulation study

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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