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无标签网络总体：图空间几何与广义测地主成分AI 解读

Abstract Statistical analysis for populations of networks is widely applicable, but challenging, as networks have strongly non-Euclidean behaviour. Graph space is an exhaustive framework for studying populations of unlabelled networks that are weighted or unweighted, uni- or multilayered, directed or undirected. Viewing graph space as the quotient of a Euclidean space with respect to a finite group action, we show that it is not a manifold, and that its curvature is…

面向有限总体的定制推断：条件有效性与跨分布迁移AI 解读

Summary Parameters of subpopulations can be more relevant than those of superpopulations. For example, a healthcare provider may be interested in the effect of a treatment plan for a specific subset of their patients; policymakers may be concerned with the impact of a policy in a particular state within a given population. In these cases, the focus is on a specific finite population, as opposed to an infinite superpopulation. Such a population can be characterized by fixing…

模型选择后兼具信息量与一致渐近有效性的混合置信区间AI 解读

Abstract I propose a new type of confidence interval for correct asymptotic inference after using data to select a model of interest without assuming any model is correctly specified. This hybrid confidence interval is constructed by combining techniques from the selective inference and post-selection inference literatures to yield a short confidence interval across a wide range of data realizations. I show that hybrid confidence intervals have correct asymptotic coverage,…

可扩展子抽样：计算、聚合与推断AI 解读

Abstract Subsampling has seen a resurgence in the big data era where the standard, full-resample size bootstrap can be infeasible to compute. Nevertheless, even choosing a single random subsample of size b can be computationally challenging with both b and the sample size n being very large. This paper shows how a set of appropriately chosen, nonrandom subsamples can be used to conduct effective, and computationally feasible, subsampling distribution estimation. Furthermore,…

暴露映射误设下的因果推断：分离定义与假设AI 解读

Summary Exposure mappings facilitate investigations of complex causal effects when units interact in experiments. Current methods require experimenters to use the same exposure mappings to define the effect of interest and to impose assumptions on the interference structure. However, the two roles rarely coincide in practice, and experimenters are forced to make the often questionable assumption that their exposures are correctly specified. This paper argues that the two…

用于评估自回归过程处理效应的动态合成控制法AI 解读

Abstract Motivated by evaluating the effects of air pollution alerts on air quality, we propose the dynamic synthetic control method for micro-level data with time-varying confounders and spatial dependence under an auto-regressive model setting. We employ the empirical likelihood to define the synthetic control weights, which ensures a unique solution and permits theoretical analysis. The dynamic matching increases the feasibility of matching and enables us to assess the…

重新审视免带宽推断：样本分割方法AI 解读

Abstract The bandwidth-free tests for a multi-dimensional parameter have attracted considerable attention in econometrics and statistics literature. These tests can be conveniently implemented due to their tuning-parameter free nature and possess more accurate size as compared to the traditional heteroskedasticity and autocorrelation consistent-based approaches. However, when sample size is small/medium, these bandwidth-free tests exhibit large size distortion when both the…

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Art Owen 对《通过投注估计有界随机变量均值》的讨论意见AI 解读

I congratulate the authors on some very interesting work making connections between likelihood, betting and martingales. What caught my eye was the connection to the empirical likelihood (EL) (Owen, 2001) and the dual likelihood (Mykland, 1995). The hindsight optimal λ solves 0=∑i=1t(xi−m)/(1+λT(xi−m))=0 corresponding to the observation weights wi∝1/(1+λT(xi−m)) used in EL. Two common alternatives use weights wi∝(1−λT(xi−m)) and wi∝exp(−λT(xi−m)) arising from L2 and entropy…

David Siegmund 对《通过下注估计有界随机变量均值》的讨论AI 解读

This contribution by Waudby-Smith and Ramdas provides a host of new insights combined with a concise, yet comprehensive, historical review of “any time valid inference”, which has blossomed in recent years after the hiatus that followed its beginnings in the mid-20th Century. Particularly, attractive is the authors’ systematic use of martingales of the form (29) to facilitate the betting interpretation and give unified derivations of a large diversity of inequalities. Given…

Thomas等对《通过下注估计有界随机变量均值》的讨论意见AI 解读

We enthusiastically agree about the importance of developing tighter confidence intervals and sequences for the mean—the topic of this paper. There are increasing concerns about the safety and fairness of machine learning systems, and we believe one powerful tool for ensuring that machine learning systems are safe, fair, and otherwise reliable is for them to provide guarantees in the form of their confidence that the models they produce will satisfy certain safety or…

Davison与Rodionov对《通过下注估计有界随机变量均值》的讨论AI 解读

We congratulate the authors on a wide-ranging contribution to a statistical hardy perennial. The restriction that the support be known and bounded appears highly restrictive, yet Proposition 3 suggests much wider potential for applications, one of which we briefly explore below. The Pickands–Balkema–de Haan theorem (Balkema & de Haan, 1974; Pickands, 1975) establishes that the distribution of a random variable X, conditioned on its exceeding a high threshold u can in rather…

Philip B. Stark 对《通过投注估计有界随机变量均值》的讨论AI 解读

This paper is a gem, and I predict it will have lasting impact on theoretical and applied statistics. Drawing on intellectual heritage spanning more than 80 years, illustrating and leveraging deep connections among results in probability, finance, information theory, computer science, and statistics, Waudby-Smith and Ramdas present mature, intuitive, flexible, computable, and powerful methods for two fundamental (indeed, canonical) nonparametric inference problems:…

Howard对《通过下注估计有界随机变量均值》的讨论AI 解读

I congratulate the authors on this creative and well-written contribution. It’s always a delight to see new insights into such a fundamental problem as inference for the mean of bounded observations, and certainly inspires excitement about the future of game-theoretic statistical inference. Besides the impressive technical contributions, I appreciate how the authors draw previously unappreciated connections between work in information theory, finance, and online learning,…

李佳怡、李远通与戴晓武对“通过下注估计有界随机变量均值”的讨论AI 解读

We congratulate Waudby-Smith and Ramdas for their interesting paper Waudby-Smith and Ramdas (2020b) in generating confidence intervals and time-uniform confidence sequences for mean estimation with bounded observations. Their methodology utilises composite non-negative martingales and establishes a connection to game-theoretic probability. Our comments will focus on numerical comparisons with alternative methods. The corresponding code is available at…

王若度对《通过下注估计有界随机变量均值》的讨论AI 解读

I congratulate Ian Waudby-Smith and Aaditya Ramdas for this excellent contribution to the theory of e-testing (or testing by betting). Over the past several years, this theory has been developed rapidly in multiple exciting directions. The contribution of Waudby-Smith and Ramdas is an important piece in this active stream of literature. I have a few comments on the approach in the current paper and its generalisations. The main approach taken in the paper (see its Theorem…

对Waudby-Smith与Ramdas的致谢动议附议及《以投注估计有界随机变量均值》的讨论AI 解读

The paper proposes an elegant new framework for deriving time-uniform confidence intervals for the mean of a sequence of random variables. The proposed technique is based on a game-theoretic view of statistical inference, rephrasing the problem of building confidence intervals as identifying a set of coin-betting games with a certain ‘plausibility’ property: if one can get ‘implausibly rich’ in a game by betting on the mean being lower (resp. higher) than a certain…

Angelopoulos 对《通过下注估计有界随机变量均值》的讨论AI 解读

I congratulate Waudby-Smith and Ramdas for their paper, which develops algorithms for confidence sequences motivated by betting. An impressive consequence of their work is the derivation of confidence intervals for a fixed sample size n, given by Theorem 3/Remark 3 and Theorem 4/Remark 4. These bounds, which my colleagues and I have referred to eponymously as the WSR bounds, prove quite useful for quantifying the uncertainty of artificial intelligence algorithms. I will give…

江荣与余克明对《通过下注估计有界随机变量均值》的讨论AI 解读

We want to congratulate the authors on estimating means of bounded random variables in both with- and without-replacement settings. The authors constructed confidence intervals and time-uniform confidence sequences for the mean of a bounded random variable using test supermartingale technique. It deepens our understanding of the confidence sequence. Confidence sequence is one particular tool in sequential design that facilitates anytime-valid inference. In particular,…

Ryan Martin对《通过下注估计有界随机变量均值》的讨论AI 解读

Congratulations to Waudby-Smith and Ramdas (WSR) for their excellent contribution to the rapidly growing literature on anytime-valid inference. Since some of my work involves imprecise probability, Professor Ramdas asked me privately what, if any, connections there are between e-values, etc. and imprecise probability. The answer to his question might be of general interest, so I’ll share it here. Following WSR, let (Xt:t≥1) be a [0,1]-valued process with distribution P∈Pμ…

GRASP：分类学习的拟合优度检验AI 解读

Abstract Performance of classifiers is often measured in terms of average accuracy on test data. Despite being a standard measure, average accuracy fails in characterising the fit of the model to the underlying conditional law of labels given the features vector (Y∣X), e.g. due to model misspecification, over fitting, and high-dimensionality. In this paper, we consider the fundamental problem of assessing the goodness-of-fit for a general binary classifier. Our framework…

估计函数的经验减偏调整AI 解读

Abstract We develop a novel, general framework for reduced-bias M-estimation from asymptotically unbiased estimating functions. The framework relies on an empirical approximation of the bias by a function of derivatives of estimating function contributions. Reduced-bias M-estimation operates either implicitly, solving empirically adjusted estimating equations, or explicitly, subtracting the estimated bias from the original M-estimates, and applies to partially or fully…

度修正及相关随机块模型的Monte Carlo拟合优度检验AI 解读

Abstract We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the latent block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal…

用于贝叶斯模型诊断的留出预测检验AI 解读

Abstract Bayesian modelling helps applied researchers to articulate assumptions about their data and develop models tailored for specific applications. Thanks to good methods for approximate posterior inference, researchers can now easily build, use, and revise complicated Bayesian models for large and rich data. These capabilities, however, bring into focus the problem of model criticism. Researchers need tools to diagnose the fitness of their models, to understand where…