Nicolas Privault, Anthony Réveillac
Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes using their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
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Shrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon his discovery of the famous paradox involving the multivariate Gaussian. A large portion of the subsequent literature only considers the efficiency of shrinkage, and that of an associated procedure known as Stein's Unbiased Risk Estimate, or SURE, in the Gaussian setting of that original work. We investigate what extensions to the domain of validity of shrinkage and SURE can be made away from the Gaussian through the use of tools developed in the probabilistic area now known as Stein's method. We s…
Two-Step Mixed-Type Multivariate Bayesian Sparse Variable Selection with Shrinkage Priors
提出一种使用收缩先验的混合类型多元回归贝叶斯框架，通过新颖的两步变量选择方法，在 $p$ 相对 $n$ 呈指数增长时实现后验收缩，并具备确定筛选性质。
Bayesian shrinkage priors subject to linear constraints
针对含分类预测变量的贝叶斯回归模型中线性约束实现难题，提出满足任意线性约束且保留收缩先验局部自适应特性的多元正态先验族及高效算法，适用于多种收缩框架且表现优异。
We consider the problem of estimating a low-rank signal matrix from noisy measurements under the assumption that the distribution of the data matrix belongs to an exponential family. In this setting, we derive generalized Stein's unbiased risk estimation (SURE) formulas that hold for any spectral estimators which shrink or threshold the singular values of the data matrix. This leads to new data-driven spectral estimators, whose optimality is discussed using tools from random matrix theory and through numerical experiments. Under the spiked population model and in the asymptotic setting where t…
Although the block Gibbs sampler for the Bayesian graphical LASSO proposed by Wang (2012) has been widely applied and extended to various shrinkage priors in recent years, it has a less noticeable but possibly severe disadvantage that the positive definiteness of a precision matrix in the Gaussian graphical model is not guaranteed in each cycle of the Gibbs sampler. Specifically, if the dimension of the precision matrix exceeds the sample size, the positive definiteness of the precision matrix will be barely satisfied and the Gibbs sampler will almost surely fail. In this paper, we propose mod…
Shrinkage through multiple identifiability
本文提出一个经验贝叶斯框架，用于聚合来自同一因果参数的多个识别函数的估计值，通过后验均值合并渐近线性估计量，建立在精确可识别性和非嵌套 regime 中的稳健性，提供频率学置信区间和贝叶斯预测区间。
JojoSCL: Shrinkage Contrastive Learning for single-cell RNA sequence Clustering
针对scRNA-seq数据高维稀疏导致聚类困难的问题，提出自监督对比学习框架JojoSCL，通过引入基于分层贝叶斯估计和SURE优化的收缩估计器减少类内离散度，在十个数据集上显著优于现有方法。
We address the problem of signal denoising via transform-domain shrinkage based on a novel $\textit{risk}$ criterion called the minimum probability of error (MPE), which measures the probability that the estimated parameter lies outside an $ε$-neighborhood of the actual value. However, the MPE, similar to the mean-squared error (MSE), depends on the ground-truth parameter, and has to be estimated from the noisy observations. We consider linear shrinkage-based denoising functions, wherein the optimum shrinkage parameter is obtained by minimizing an estimate of the MPE. When the probability of e…
Shrinkage priors for Bayesian Substitute Confounders
针对多原因观察研究中替代混杂因子过度编码问题，提出贝叶斯因子分配框架，利用收缩先验学习稀疏替代混杂因子，保持粗粒度多原因依赖，并证明后验集中性和重叠保持几何性质，实现潜在结果的一致性估计。
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of attention in the problem of estimating sparse, high-dimensional linear models. This paper extends these ideas, and presents a Bayesian grouped model with continuous global-local shrinkage priors to handle complex group hierarchies that include overlapping and multilevel group structures. As the posterior mean is never a sparse estimate of the linear model coeffic…
Model estimates obtained from traditional subspace identification methods may be subject to significant variance. This elevated variance is aggravated in the cases of large models or of a limited sample size. Common solutions to reduce the effect of variance are regularized estimators, shrinkage estimators and Bayesian estimation. In the current work we investigate the latter two solutions, which have not yet been applied to subspace identification. Our experimental results show that our proposed estimators may reduce the estimation risk up to $40\%$ of that of traditional subspace methods.
This study proposes a novel hierarchical prior for inferring possibly low-rank matrices measured with noise. We consider three-component matrix factorization, as in singular value decomposition, and its fully Bayesian inference. The proposed prior is specified by a scale mixture of exponential distributions that has spike and slab components. The weights for the spike/slab parts are inferred using a special prior based on a cumulative shrinkage process. The proposed prior is designed to increasingly aggressively push less important, or essentially redundant, singular values toward zero, leadin…
Functional neuroimaging measures how the brain responds to complex stimuli. However, sample sizes are modest, noise is substantial, and stimuli are high dimensional. Hence, direct estimates are inherently imprecise and call for regularization. We compare a suite of approaches which regularize via shrinkage: ridge regression, the elastic net (a generalization of ridge regression and the lasso), and a hierarchical Bayesian model based on small area estimation (SAE). We contrast regularization with spatial smoothing and combinations of smoothing and shrinkage. All methods are tested on functional…
Smooth SCAD: A Raised Cosine SCAD Type Thresholding Rule for Wavelet Denoising
本文提出一种平滑SCAD阈值规则，用于小波去噪，结合低偏差、精确稀疏性和分析便利性，提供可操作的改进。
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal shrinkage intensities and estimate them consistently. The developed distribution-free estimators obey almost surely the smallest Frobenius loss over all linear shrinkage estimators for the covariance matrix. The case we consider includes the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that $p/n\rightarrow c\in (0, +\infty)$. …
Model-based Clustering for Network Data via a Latent Shrinkage Position Cluster Model
本文提出潜在收缩位置聚类模型（LSPCM），通过贝叶斯非参数收缩先验和稀疏有限高斯混合模型，同时推断网络数据潜在空间的有效维度与聚类数量，并通过模拟和真实Twitter数据验证了其性能。
Optimal Linear Shrinkage Estimator for Large Dimensional Precision Matrix
本文针对高维精度矩阵估计问题，基于随机矩阵理论构造了免分布的最优线性收缩估计量，直接估计精度矩阵而无需对协方差矩阵求逆，并证明其几乎必然达到最小 Frobenius 损失，模拟实验显示该方法在非正态数据下仍具有显著改进和稳健性。
Bayesian Univariate-Guided Sparse Regression for Ultra-High-Dimensional Data
本文提出BUGS框架，通过连续调节收缩实现边际关联信息的直接整合，提升信号噪声分离。BUGS-Active在超高维下实现高效计算，应用于DNA甲基化研究，展现准确预测与可解释稀疏选择。
We consider quasi-admissibility/inadmissibility of Stein-type shrinkage estimators of the mean of a multivariate normal distribution with covariance matrix an unknown multiple of the identity. Quasi-admissibility/inadmissibility is defined in terms of non-existence/existence of a solution to a differential inequality based on Stein's unbiased risk estimate (SURE). We find a sharp boundary between quasi-admissible and quasi-inadmissible estimators related to the optimal James-Stein estimator. We also find a class of priors related to the Strawderman class in the known variance case where the bo…
Mens: Nonlinear shrinkage estimation in nonparanormal models for financial applications
研究针对非正态模型开发非线性收缩协方差估计理论，提出无边际非线性收缩估计器MENS，给出其经验谱分布收敛律及渐近最优性，建立尖峰相变，通过模拟和回测验证其优势，兼具稳健性与效率，对高维配置决策有实用价值。
Driver Identification and PCA Augmented Selection Shrinkage Framework for Nordic System Price Forecasting
本文提出结合K-means、MSTD、SARIMA和PCA的系统框架识别北欧系统价格驱动因素，并通过多预测选择收缩算法优化组合预测，以较低计算成本超越TFT等先进方法。
From Cross-Validation to SURE: Asymptotic Risk of Tuned Regularized Estimators
本文推导了通过n折交叉验证调节的正则化经验风险最小化估计器的渐近风险函数，展示了其在正常均值模型中的预测性能。
This paper establishes the argmin of a random objective function to be unique almost surely. This paper first formulates a general result that proves almost sure uniqueness without convexity of the objective function. The general result is then applied to a variety of applications in statistics. Four applications are discussed, including uniqueness of M-estimators, both classical likelihood and penalized likelihood estimators, and two applications of the argmin theorem, threshold regression and weak identification.
Energetic Variational Gaussian Process Regression for Computer Experiments
本文提出基于能量变分推断的高斯过程回归方法，推导参数后验分布并引入收缩估计实现均值函数变量选择，通过三个基准示例验证其有效性。
In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well as to obtain an identified model. Our approach consists in specifying sparse hierarchical priors on the mixture weights and component means. In a deliberately overfitting mixture model the sparse prior on the weights empties superfluous components during MCMC. A straightforward estimator for the true number of components is given by the most frequent number…
In the framework of matrix valued observables with low rank means, Stein's unbiased risk estimate (SURE) can be useful for risk estimation and for tuning the amount of shrinkage towards low rank matrices. This was demonstrated by Candès et al. (2013) for singular value soft thresholding, which is a Lipschitz continuous estimator. SURE provides an unbiased risk estimate for an estimator whenever the differentiability requirements for Stein's lemma are satisfied. Lipschitz continuity of the estimator is sufficient, but it is emphasized that differentiability Lebesgue almost everywhere isn't. The…
Resolution-Adaptive Compact-Support Priors for Bayesian Wavelet Denoising
该研究提出分辨率自适应贝叶斯小波去噪方法，采用尖峰-板条先验，经模拟和地震数据验证，其高斯似然版本在多数场景下优于多种现有去噪方法。
Asymptotic Theory for Regularized System Identification Part I: Empirical Bayes Hyper-parameter Estimator
本文研究正则化有限脉冲响应模型估计中经验贝叶斯超参数估计器的渐近理论，通过分析其依分布收敛性和模型估计器的渐近分布，揭示了影响收敛性质的因素，并通过Monte Carlo仿真验证了理论结果。
Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like "time is randomly assigned" or "time is an instrument." Partial identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects. It is shown that the usual, linear, fixed-effects estimator is not a consistent estimator of the identified …
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