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The extended Ville’s inequality for nonintegrable nonnegative supermartingale

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arXiv 2023年

作者： Wang, Hongjian Ramdas, Aaditya Department of Statistics and Data Science Carnegie Mellon University United States Machine Learning Department Carnegie Mellon University United States

Following the initial work by Robbins, we rigorously present an extended theory of nonnegative supermartingales, requiring neither integrability nor finiteness. In particular, we derive a key maximal inequality foreshadowed by Robbins, which we call the extended Ville’s inequality, that strengthens the classical Ville’s inequality (for integrable nonnegative supermartingales), and also applies to our nonintegrable setting. We derive an extension of the method of mixtures, which applies to σ-finite mixtures of our extended nonnegative supermartingales. We present some implications of our theory for sequential statistics, such as the use of improper mixtures (priors) in deriving nonparametric confidence sequences and (extended) e-processes. Copyright © 2023, The Authors. All rights reserved.

关键词： Statistics

Generalized equivalences between subsampling and ridge regularization 23

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Generalized equivalences between subsampling and ridge regul...

Proceedings of the 37th International Conference on Neural Information Processing Systems

作者： Pratik Patil Jin-Hong Du Department of Statistics University of California Berkeley CA Department of Statistics and Data Science & Machine Learning Department Carnegie Mellon University Pittsburgh PA

We establish precise structural and risk equivalences between subsampling and ridge regularization for ensemble ridge estimators. Specifically, we prove that linear and quadratic functionals of subsample ridge estimators, when fitted with different ridge regularization levels λ and subsample aspect ratios ψ, are asymptotically equivalent along specific paths in the (λ, ψ)-plane (where ψ is the ratio of the feature dimension to the subsample size). Our results only require bounded moment assumptions on feature and response distributions and allow for arbitrary joint distributions. Furthermore, we provide a data-dependent method to determine the equivalent paths of (λ, ψ). An indirect implication of our equivalences is that optimally tuned ridge regression exhibits a monotonic prediction risk in the data aspect ratio. This resolves a recent open problem raised by Nakkiran et al. [1] for general data distributions under proportional asymptotics, assuming a mild regularity condition that maintains regression hardness through linearized signal-to-noise ratios.

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Huber-Robust Confidence Sequences

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arXiv 2023年

作者： Wang, Hongjian Ramdas, Aaditya Machine Learning Department Carnegie Mellon University United States Department of Statistics and Data Science Carnegie Mellon University United States

Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known upper bound on the p-th central moment (p > 1), but allowing for (at most) Ε fraction of arbitrary distribution corruption, as in Huber’s contamination model. We do this by designing new robust exponential supermartingales, and show that the resulting confidence sequences attain the optimal width achieved in the nonsequential setting. Perhaps surprisingly, the constant margin between our sequential result and the lower bound is smaller than even fixed-time robust confidence intervals based on the trimmed mean, for example. Since confidence sequences are a common tool used within A/B/n testing and bandits, these results open the door to sequential experimentation that is robust to outliers and adversarial corruptions. Copyright © 2023, The Authors. All rights reserved.

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An Empirical Analysis on Spatial Reasoning Capabilities of Large Multimodal Models

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arXiv 2024年

作者： Shiri, Fatemeh Guo, Xiao-Yu Far, Mona Golestan Yu, Xin Haffari, Gholamreza Li, Yuan-Fang Department of Data Science & AI Monash University Australia Australian Institute for Machine Learning University of Adelaide Australia School of Electrical Engineering and Computer Science University of Queensland Australia

Large Multimodal Models (LMMs) have achieved strong performance across a range of vision and language tasks. However, their spatial reasoning capabilities are under-investigated. In this paper, we construct a novel VQA dataset, Spatial-MM, to comprehensively study LMMs’ spatial understanding and reasoning capabilities. Our analyses on object-relationship and multi-hop reasoning reveal several important findings. Firstly, bounding boxes and scene graphs, even synthetic ones, can significantly enhance LMMs’ spatial reasoning. Secondly, LMMs struggle more with questions posed from the human perspective than the camera perspective about the image. Thirdly, chain of thought (CoT) prompting does not improve model performance on complex multi-hop questions involving spatial relations. Lastly, our perturbation analysis on GQA-spatial reveals that LMMs are much stronger at basic object detection than complex spatial reasoning. We believe our benchmark dataset and in-depth analyses can spark further research on LMMs spatial reasoning. © 2024, CC BY.

关键词： Visual languages

Auditing Fairness by Betting

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arXiv 2023年

作者： Chugg, Ben Cortes-Gomez, Santiago Wilder, Bryan Ramdas, Aaditya Machine Learning Department Carnegie Mellon University United States Department of Statistics and Data Science Carnegie Mellon University United States

We provide practical, efficient, and nonparametric methods for auditing the fairness of deployed classification and regression models. Whereas previous work relies on a fixed-sample size, our methods are sequential and allow for the continuous monitoring of incoming data, making them highly amenable to tracking the fairness of real-world systems. We also allow the data to be collected by a probabilistic policy as opposed to sampled uniformly from the population. This enables auditing to be conducted on data gathered for another purpose. Moreover, this policy may change over time and different policies may be used on different subpopulations. Finally, our methods can handle distribution shift resulting from either changes to the model or changes in the underlying population. Our approach is based on recent progress in anytime-valid inference and game-theoretic statistics-the "testing by betting" framework in particular. These connections ensure that our methods are interpretable, fast, and easy to implement. We demonstrate the efficacy of our approach on three benchmark fairness datasets. © 2023, CC BY.

关键词： Population statistics

A Review of machine learning Algorithms in Diabetes Management 4

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A Review of Machine Learning Algorithms in Diabetes Manageme...

4th International Conference on Sentiment Analysis and Deep learning, ICSADL 2025

作者： Gayaki, Unnati Daronde, Subodh Tale, Abhay Barhate, Aditya Datta Meghe Institute of Higher Education and Research Faculty of Engineering and Technology Department of Computer Science and Engineering Maharashtra Wardha India Faculty of Engineering and Technology Department of Biomedical Engineering Maharashtra Wardha India Datta Meghe Institute of Higher Education and Research Faculty of Engineering and Technology Department of Artificial Intelligence and Data Science Maharashtra Wardha India Datta Meghe Institute of Higher Education and Research Faculty of Engineering and Technology Department of Artificial Intelligence and Machine Learning Maharashtra Wardha India

ISBN: (纸本)9798331523923

Diabetes is a prevalent and chronic disease affecting millions worldwide, posing significant challenges in its management and treatment. This review article aims to explore the current and potential future roles of machine learning (ML) in diabetes management, focusing on progress, applications, and challenges. It discusses various ML techniques, including support vector machines (SVM), logistic regression, decision trees, ensemble methods, and advanced deep learning approaches such as long short-term memory (LSTM) networks and convolutional neural networks (CNN). These methods have demonstrated benefits in analytics, patient monitoring, decision support systems, personalised treatment, and patient engagement. However, significant challenges persist, such as computational complexity, data quality, limited interoperability of systems, and ethical concerns regarding AI use in healthcare. The article addresses these challenges by fostering collaboration between AI implementers and health care professionals. This collaboration is essential to develop long-term, legally compliant, and solution-oriented frameworks that enhance patient care and diabetes management and pave the way for more efficient and ethical AI applications in healthcare. © 2025 IEEE.

关键词： Support vector machines

Reducing sequential change detection to sequential estimation

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arXiv 2023年

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

We consider the problem of sequential change detection, where the goal is to design a scheme for detecting any changes in a parameter or functional θ of the data stream distribution that has small detection delay, but guarantees control on the frequency of false alarms in the absence of changes. In this paper, we describe a simple reduction from sequential change detection to sequential estimation using confidence sequences: we begin a new (1 − α)-confidence sequence at each time step, and proclaim a change when the intersection of all active confidence sequences becomes empty. We prove that the average run length is at least 1/α, resulting in a change detection scheme with minimal structural assumptions (thus allowing for possibly dependent observations, and nonparametric distribution classes), but strong guarantees. We also describe an interesting parallel with Lorden's reduction from change detection to sequential testing and connections to the recent "e-detector" framework. © 2023, CC BY.

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Counterfactually Comparing Abstaining Classifiers

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arXiv 2023年

作者： Choe, Yo Joong Gangrade, Aditya Ramdas, Aaditya Data Science Institute University of Chicago United States Department of EECS University of Michigan United States Department of Statistics and Data Science Machine Learning Department Carnegie Mellon University United States

Abstaining classifiers have the option to abstain from making predictions on inputs that they are unsure about. These classifiers are becoming increasingly popular in high-stakes decision-making problems, as they can withhold uncertain predictions to improve their reliability and safety. When evaluating black-box abstaining classifier(s), however, we lack a principled approach that accounts for what the classifier would have predicted on its abstentions. These missing predictions matter when they can eventually be utilized, either directly or as a backup option in a failure mode. In this paper, we introduce a novel approach and perspective to the problem of evaluating and comparing abstaining classifiers by treating abstentions as missing data. Our evaluation approach is centered around defining the counterfactual score of an abstaining classifier, defined as the expected performance of the classifier had it not been allowed to abstain. We specify the conditions under which the counterfactual score is identifiable: if the abstentions are stochastic, and if the evaluation data is independent of the training data (ensuring that the predictions are missing at random), then the score is identifiable. Note that, if abstentions are deterministic, then the score is unidentifiable because the classifier can perform arbitrarily poorly on its abstentions. Leveraging tools from observational causal inference, we then develop nonparametric and doubly robust methods to efficiently estimate this quantity under identification. Our approach is examined in both simulated and real data experiments. © 2023, CC BY-SA.

关键词： Forecasting

Sequential Predictive Two-Sample and Independence Testing

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arXiv 2023年

作者： Podkopaev, Aleksandr Ramdas, Aaditya Department of Statistics & Data Science Carnegie Mellon University United States Machine Learning Department Carnegie Mellon University United States

We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data, while maintaining type I error control. We build upon the principle of (nonparametric) testing by betting, where a gambler places bets on future observations and their wealth measures evidence against the null hypothesis. While recently developed kernel-based betting strategies often work well on simple distributions, selecting a suitable kernel for high-dimensional or structured data, such as images, is often nontrivial. To address this drawback, we design prediction-based betting strategies that rely on the following fact: if a sequentially updated predictor starts to consistently determine (a) which distribution an instance is drawn from, or (b) whether an instance is drawn from the joint distribution or the product of the marginal distributions (the latter produced by external randomization), it provides evidence against the two-sample or independence nulls respectively. We empirically demonstrate the superiority of our tests over kernel-based approaches under structured settings. Our tests can be applied beyond the case of independent and identically distributed data, remaining valid and powerful even when the data distribution drifts over time. Copyright © 2023, The Authors. All rights reserved.

关键词： Product design