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Correcting for heterogeneity in real-time epidemiological indicators

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arXiv 2023年

作者： Rumack, Aaron Rosenfeld, Roni Townes, F. William Machine Learning Department Carnegie Mellon University PittsburghPA United States Department of Statistics & Data Science Carnegie Mellon University PittsburghPA United States

Auxiliary data sources have become increasingly important in epidemiological surveillance, as they are often available at a finer spatial and temporal resolution, larger coverage, and lower latency than traditional surveillance signals. We describe the problem of spatial and temporal heterogeneity in these signals derived from these data sources, where spatial and/or temporal biases are present. We present a method to use a "guiding" signal to correct for these biases and produce a more reliable signal that can be used for modeling and forecasting. The method assumes that the heterogeneity can be approximated by a low-rank matrix and that the temporal heterogeneity is smooth over time. We also present a hyperparameter selection algorithm to choose the parameters representing the matrix rank and degree of temporal smoothness of the corrections. In the absence of ground truth, we use maps and plots to argue that this method does indeed reduce heterogeneity. Reducing heterogeneity from auxiliary data sources greatly increases their utility in modeling and forecasting epidemics. © 2023, CC BY-NC-SA.

关键词： Matrix algebra

Post-selection inference for e-value based confidence intervals

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arXiv 2022年

作者： Xu, Ziyu Wang, Ruodu Ramdas, Aaditya Departments of Statistics Carnegie Mellon University United States Departments of Machine Learning Carnegie Mellon University United States Department of Statistics and Actuarial Science University of Waterloo Canada

Suppose that one can construct a valid (1 − δ)-confidence interval (CI) for each of K parameters of potential interest. If a data analyst uses an arbitrary data-dependent criterion to select some subset S of parameters, then the aforementioned CIs for the selected parameters are no longer valid due to selection bias. We design a new method to adjust the intervals in order to control the false coverage rate (FCR). The main established method is the "BY procedure" by Benjamini and Yekutieli (JASA, 2005). The BY guarantees require certain restrictions on the selection criterion and on the dependence between the CIs. We propose a new simple method which, in contrast, is valid under any dependence structure between the original CIs, and any (unknown) selection criterion, but which only applies to a special, yet broad, class of CIs that we call e-CIs. To elaborate, our procedure simply reports (1 − δ|S|/K)-CIs for the selected parameters, and we prove that it controls the FCR at δ for confidence intervals that implicitly invert e-values;examples include those constructed via supermartingale methods, via universal inference, or via Chernoff-style bounds, among others. The e-BY procedure is admissible, and recovers the BY procedure as a special case via a particular calibrator. Our work also has implications for post-selection inference in sequential settings, since it applies at stopping times, to continuously-monitored confidence sequences, and under bandit sampling. We demonstrate the efficacy of our procedure using numerical simulations and real A/B testing data from Twitter. Copyright © 2022, The Authors. All rights reserved.

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Optimal Ridge Regularization for Out-of-Distribution Prediction

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arXiv 2024年

作者： Patil, Pratik Du, Jin-Hong Tibshirani, Ryan J. Department of Statistics University of California BerkeleyCA94720 United States Department of Statistics and Data Science Carnegie Mellon University PittsburghPA15213 United States Machine Learning Department Carnegie Mellon University PittsburghPA15213 United States

We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-distribution prediction, where the test distribution deviates arbitrarily from the train distribution. We establish general conditions that determine the sign of the optimal regularization level under covariate and regression shifts. These conditions capture the alignment between the covariance and signal structures in the train and test data and reveal stark differences compared to the in-distribution setting. For example, a negative regularization level can be optimal under covariate shift or regression shift, even when the training features are isotropic or the design is underparameterized. Furthermore, we prove that the optimally tuned risk is monotonic in the data aspect ratio, even in the out-of-distribution setting and when optimizing over negative regularization levels. In general, our results do not make any modeling assumptions for the train or the test distributions, except for moment bounds, and allow for arbitrary shifts and the widest possible range of (negative) regularization levels. Copyright © 2024, The Authors. All rights reserved.

关键词： Aspect ratio

Implicit Regularization Paths of Weighted Neural Representations

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arXiv 2024年

作者： Du, Jin-Hong Patil, Pratik Department of Statistics and Data Science Carnegie Mellon University PittsburghPA15213 United States Machine Learning Department Carnegie Mellon University PittsburghPA15213 United States Department of Statistics University of California BerkeleyCA94720 United States

We study the implicit regularization effects induced by (observation) weighting of pretrained features. For weight and feature matrices of bounded operator norms that are infinitesimally free with respect to (normalized) trace functionals, we derive equivalence paths connecting different weighting matrices and ridge regularization levels. Specifically, we show that ridge estimators trained on weighted features along the same path are asymptotically equivalent when evaluated against test vectors of bounded norms. These paths can be interpreted as matching the effective degrees of freedom of ridge estimators fitted with weighted features. For the special case of subsampling without replacement, our results apply to independently sampled random features and kernel features and confirm recent conjectures (Conjectures 7 and 8) of the authors on the existence of such paths in [50]. We also present an additive risk decomposition for ensembles of weighted estimators and show that the risks are equivalent along the paths when the ensemble size goes to infinity. As a practical consequence of the path equivalences, we develop an efficient cross-validation method for tuning and apply it to subsampled pretrained representations across several models (e.g., ResNet-50) and datasets (e.g., CIFAR-100). Copyright © 2024, The Authors. All rights reserved.

关键词： Matrix algebra

Position: insights from survey methodology can improve training data 24

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Position: insights from survey methodology can improve train...

Proceedings of the 41st International Conference on machine learning

作者： Stephanie Eckman Barbara Plank Frauke Kreuter Social Data Science Center University of Maryland College Park MD Center for Information and Language Processing (CIS) LMU Munich Germany and Computer Science Department IT University of Copenhagen Denmark and Munich Center for Machine Learning (MCML) LMU Munich Germany Institute for Statistics and Munich Center for Machine Learning (MCML) LMU Munich Germany and Social Data Science Center and Joint Program in Survey Methodology University of Maryland College Park MD

Whether future AI models are fair, trustworthy, and aligned with the public's interests rests in part on our ability to collect accurate data about what we want the models to do. However, collecting high-quality data is difficult, and few AI/ML researchers are trained in data collection methods. Recent research in data-centric AI has show that higher quality training data leads to better performing models, making this the right moment to introduce AI/ML researchers to the field of survey methodology, the science of data collection. We summarize insights from the survey methodology literature and discuss how they can improve the quality of training and feedback data. We also suggest collaborative research ideas into how biases in data collection can be mitigated, making models more accurate and human-centric.

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Best Arm Identification under Additive Transfer Bandits 55

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Best Arm Identification under Additive Transfer Bandits

55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021

作者： Neopane, Ojash Ramdas, Aaditya Singh, Aarti Carnegie Mellon University Machine Learning Department PittsburghPA United States Carnegie Mellon University Department of Statistics and Data Science PittsburghPA United States

ISBN: (纸本)9781665458283

We consider a variant of the best arm identification (BAI) problem in multi-armed bandits (MAB) in which there are two sets of arms (source and target), and the objective is to determine the best target arm while only pulling source arms. In this paper, we study the setting when, despite the means being unknown, there is a known additive relationship between the source and target MAB instances. We show how our framework covers a range of previously studied pure exploration problems and additionally captures new problems. We propose and theoretically analyze an LUCB-style algorithm to identify an e-optimal target arm with high probability. Our theoretical analysis highlights aspects of this transfer learning problem that do not arise in the typical BAI setup, and yet recover the LUCB algorithm for single domain BAI as a special case. © 2021 IEEE.

关键词： Additives

A permutation-free kernel two-sample test

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arXiv 2022年

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

The kernel Maximum Mean Discrepancy (MMD) is a popular multivariate distance metric between distributions that has found utility in two-sample testing. The usual kernel-MMD test statistic is a degenerate U-statistic under the null, and thus it has an intractable limiting distribution. Hence, to design a level-α test, one usually selects the rejection threshold as the (1−α)-quantile of the permutation distribution. The resulting nonparametric test has finite-sample validity but suffers from large computational cost, since every permutation takes quadratic time. We propose the cross-MMD, a new quadratic-time MMD test statistic based on sample-splitting and studentization. We prove that under mild assumptions, the cross-MMD has a limiting standard Gaussian distribution under the null. Importantly, we also show that the resulting test is consistent against any fixed alternative, and when using the Gaussian kernel, it has minimax rate-optimal power against local alternatives. For large sample sizes, our new cross-MMD provides a significant speedup over the MMD, for only a slight loss in power. © 2022, CC BY.

关键词： Sampling

CENTRAL LIMIT THEOREMS FOR SMOOTH OPTIMAL TRANSPORT MAPS

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arXiv 2023年

作者： Manole, Tudor Balakrishnan, Sivaraman Niles-Weed, Jonathan Wasserman, Larry Statistics and Data Science Center Massachusetts Institute of Technology United States Department of Statistics and Data Science Carnegie Mellon University United States Machine Learning Department Carnegie Mellon University United States Center for Data Science New York University United States Courant Institute of Mathematical Sciences New York University United States

One of the central objects in the theory of optimal transport is the Brenier map: the unique monotone transformation which pushes forward an absolutely continuous probability law onto any other given law. A line of recent work has analyzed L2 convergence rates of plugin estimators of Brenier maps, which are defined as the Brenier map between density estimators of the underlying distributions. In this work, we show that such estimators satisfy a pointwise central limit theorem when the underlying laws are supported on the flat torus of dimension d ≥ 3. We also derive a negative result, showing that these estimators do not converge weakly in L2 when the dimension is sufficiently large. Our proofs hinge upon a quantitative linearization of the Monge-Ampère equation, which may be of independent interest. This result allows us to reduce our problem to that of deriving limit laws for the solution of a uniformly elliptic partial differential equation with a stochastic right-hand side, subject to periodic boundary conditions. Copyright © 2023, The Authors. All rights reserved.

关键词： Stochastic systems

Frequentist Inference for Semi-mechanistic Epidemic Models with Interventions

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arXiv 2023年

作者： Bong, Heejong Ventura, Valérie Wasserman, Larry Department of Statistics University of Michigan Ann ArborMI United States Department of Statistics & Data Science and Delphi Research Group Carnegie Mellon University PittsburghPA United States Department of Statistics & Data Science Machine Learning Department Delphi Research Group Carnegie Mellon University PittsburghPA United States

The effect of public health interventions on an epidemic are often estimated by adding the intervention to epidemic models. During the Covid-19 epidemic, numerous papers used such methods for making scenario predictions. The majority of these papers use Bayesian methods to estimate the parameters of the model. In this paper we show how to use frequentist methods for estimating these effects which avoids having to specify prior distributions. We also use model-free shrinkage methods to improve estimation when there are many different geographic regions. This allows us to borrow strength from different regions while still getting confidence intervals with correct coverage and without having to specify a hierarchical model. Throughout, we focus on a semi-mechanistic model which provides a simple, tractable alternative to compartmental methods. © 2023, CC BY.

关键词： COVID-19