论文检索

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…

Abstract We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form "empirical-Bernstein" CSs and CIs (converging exactly to the oracle Bernstein width) as well as non-closed-form "betting" CSs and CIs. Our method combines new composite nonnegative (super)martingales with Ville's maximal inequality, with…

鞅后验分布AI 解读

Abstract The prior distribution is the usual starting point for Bayesian uncertainty. In this paper, we present a different perspective that focuses on missing observations as the source of statistical uncertainty, with the parameter of interest being known precisely given the entire population. We argue that the foundation of Bayesian inference is to assign a distribution on missing observations conditional on what has been observed. In the i.i.d. setting with an observed…

Huk、Pacchiardi、Dutta 与 Steel 对《鞅后验分布》的讨论AI 解读

We congratulate the authors for this thought-provoking paper. The recursive definition of the predictive distributions through a bivariate copula (Section 4) depends on a hyperparameter ρ, which the authors tune by minimising the prequential log-score −∑i=1nlogpi−1(yi) (Section 4.5.2). The prequential framework nicely connects with the predictive resampling approach used later. However, other strictly proper scoring rules (Gneiting & Raftery, 2007) could be used in place of…

用于稀疏贝叶斯推断的快速异步 MCMC 采样器AI 解读

Abstract We propose a very fast approximate Markov chain Monte Carlo sampling framework that is applicable to a large class of sparse Bayesian inference problems. The computational cost per iteration in several regression models is of order O(n(s+J)), where n is the sample size, s is the underlying sparsity of the model, and J is the size of a randomly selected subset of regressors. This cost can be further reduced by data sub-sampling when stochastic gradient Langevin…

对《鞅后验分布》的致谢动议附议与讨论AI 解读

Let me first congratulate the authors for an interesting, thought provoking and inspiring article, with many fine examples. However, I wonder whether the specific setup has sufficient generality to cover interesting cases, and I should have liked to see the ideas in this paper confronted with some different situations. Firstly, let me remind everyone of the standard Bayesian setup, where we have observablesX,Y⁠, a parameter Θ of interest that in principle should be added to…

Kolyan Ray 与 Botond Szabo 对“鞅后验分布”的讨论AI 解读

We congratulate the authors for their thought-provoking article, which includes proposing a copula-based update for the predictive density and establishing its frequentist consistency under relatively mild assumptions. In this contribution, we further explore the frequentist properties of (Bayesian) predictive densities and illustrate through a simple example that, similarly to the posterior distribution, the predictive distribution can also be inconsistent. One therefore…

Wijayatunga对《鞅后验分布》的讨论意见AI 解读

Statistical uncertainty in (an estimate of) a parameter of a probability distribution is due to missing (unseen) observations (when it is estimated), as authors have noted. We can think that an estimate of the parameter has the maximal uncertainty when no observation is used for it, and no uncertainty when all possible observations are used for it. For example, in Bayesian sense, for a Bernoulli parameter, Beta distribution with parameter values α=1 and β=1 represents the…

布莱克·莫亚对《鞅后验分布》的讨论意见AI 解读

I would like to congratulate the authors on an expository and intuitive representation of statistical uncertainty. To assist in the further investigation of predictive resampling techniques, I have developed a software package for R (R Core Team, 2022) which implements some of the algorithms presented here as well as from subsequent work (Moya & Walker, 2023). The CopRe package (Moya, 2022), named for the copula resampling technique described in Section 4, can be installed…

贾琦顾与郭胜尹对《鞅后验分布》的讨论AI 解读

We congratulate the authors for their thought-provoking paper, especially in the three aspects as follows. Instead of imposing a prior π(θ) on the parameter θ of a likelihood function fθ(y)⁠, where both π and fθ are elicited subjectively, the authors proposed the framework of martingale posterior to directly model the predictive p(yn+1:∞∣y1:n) for which only the prior predictive p(y) needs to be specified. As a result, Bayesian inference can be conducted on any parameter (or…

Bertrand Clarke 对《鞅后验分布》的讨论AI 解读

To see the effect of the paper on statistical practice, consider the following hypothetical dialogue between a Quantitative Scientist (QS) and a Predictive Statistician (PS). QS: I’ve been thinking about the data generating mechanism and what we can safely assume pre-experimentally. PS: Actually, I’m more interested in what you think your n+1 data point would be. If you were going to predict your n+1 measurement, how would you do it? QS: I’d guess what the true model is and…

Ben Swallow对《鞅后验分布》的讨论意见AI 解读

Fong et al. (2023) present an interesting and novel approach to conducting Bayesian posterior estimation utilising a joint predictive distribution over missing potential observations and justify how this approach of generating one-step-ahead predictive distributions naturally aligns with the Bayesian likelihood-prior paradigm. The authors mention time series and hierarchical data as areas of potential future development. However, one of the major topics in Bayesian…

高维矩阵值时间序列的双向动态因子模型AI 解读

Abstract In this article, we introduce a two-way dynamic factor model (2w-DFM) for high-dimensional matrix-valued time series and study some of the basic theoretical properties in terms of identifiability and estimation accuracy. The proposed model aims to capture separable and low-dimensional effects of row and column attributes and their correlations across rows, columns, and time points. Complementary to other dynamic factor models for high-dimensional data, the 2w-DFM…

基于回归秩得分的异质分位数处理效应去偏推断AI 解读

Abstract Understanding treatment effect heterogeneity is vital to many scientific fields because the same treatment may affect different individuals differently. Quantile regression provides a natural framework for modelling such heterogeneity. We propose a new method for inference on heterogeneous quantile treatment effects (HQTE) in the presence of high-dimensional covariates. Our estimator combines an ℓ1-penalised regression adjustment with a quantile-specific bias…

基于 l₁ 球先验的贝叶斯推断：用精确零值求解组合问题AI 解读

Abstract The l1-regularisation is very popular in high-dimensional statistics—it changes a combinatorial problem of choosing which subset of the parameter is zero, into a simple continuous optimisation. Using a continuous prior concentrated near zero, the Bayesian counterparts are successful in quantifying the uncertainty in the variable selection problems; nevertheless, the lack of exact zeros makes it difficult for broader problems such as change-point detection and rank…

基于深度神经网络的图像响应回归AI 解读

Abstract Delineating associations between images and covariates is a central aim of imaging studies. To tackle this problem, we propose a novel non-parametric approach in the framework of spatially varying coefficient models, where the spatially varying functions are estimated through deep neural networks. Our method incorporates spatial smoothness, handles subject heterogeneity, and provides straightforward interpretations. It is also highly flexible and accurate, making it…

矩阵值数据的核心收缩协方差估计AI 解读

Abstract A separable covariance model can describe the among-row and among-column correlations of a random matrix and permits likelihood-based inference with a very small sample size. However, if the assumption of separability is not met, data analysis with a separable model may misrepresent important dependence patterns in the data. As a compromise between separable and unstructured covariance estimation, we decompose a covariance matrix into a separable component and a…