论文检索

Korobov 空间上分类的泛化分析AI 解读

In this paper, the classification algorithm arising from Tikhonov regularization is discussed. The main intention is to derive learning rates for the excess misclassification error according to the convex $η$-norm loss function $φ(v)=(1 - v)_{+}^η$, $η\geq1$. Following the argument, the estimation of error under Tsybakov noise conditions is studied. In addition, we propose the rate of $L_p$ approximation of functions from Korobov space $X^{2, p}([-1,1]^{d})$, $1\leq p \leq \infty$…

分层变分图融合Lasso：恢复空间成分数据中的相对速率AI 解读

The analysis of spatial data from biological imaging technology, such as imaging mass spectrometry (IMS) or imaging mass cytometry (IMC), is challenging because of a competitive sampling process which convolves signals from molecules in a single pixel. To address this, we develop a scalable Bayesian framework that leverages natural sparsity in spatial signal patterns to recover relative rates for each molecule across the entire image. Our method relies on the use of a…

重尾高频金融观测下的因子与特质 VAR 波动率矩阵模型AI 解读

This paper introduces a novel process for both factor and idiosyncratic volatility matrices whose eigenvalues follow the vector auto-regressive (VAR) model. We call it the factor and idiosyncratic VAR (FIVAR) model. The FIVAR model accounts for the dynamics of the factor and idiosyncratic volatilities and includes many parameters. In addition, many empirical studies have shown that high-frequency stock returns and volatilities often exhibit heavy tails. To handle these two…

含向量时间序列协变量的时空矩阵自回归模型AI 解读

We develop a new methodology for forecasting matrix-valued time series with historical matrix data and auxiliary vector time series data. We focus on a time series of matrices defined on a static 2-D spatial grid and an auxiliary time series of non-spatial vectors. The proposed model, Matrix AutoRegression with Auxiliary Covariates (MARAC), contains an autoregressive component for the historical matrix predictors and an additive component that maps the auxiliary vector…

稳健的高维时变系数估计AI 解读

In this paper, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of high-frequency observations as well as time variations of coefficient processes. Specifically, we employ the Huber loss and a truncation scheme to handle heavy-tailed observations, while $\ell_{1}$-regularization is adopted to overcome the curse of…

利用动态降维预测高维时间序列AI 解读

Many dimension reduction techniques have been developed for independent data, and most have also been extended to time series. However, these methods often fail to account for the dynamic dependencies both within and across series. In this work, we propose a general framework for forecasting high-dimensional time series that integrates dynamic dimension reduction with regularization techniques. The effectiveness of the proposed approach is illustrated through a simulated…

增强生存树AI 解读

We introduce a new survival tree method for censored failure time data that incorporates three key advancements over traditional approaches. First, we develop a more computationally efficient splitting procedure that effectively mitigates the end-cut preference problem, and we propose an intersected validation strategy to reduce the variable selection bias inherent in greedy searches. Second, we present a novel framework for determining tree structures through fused…

估计理论中的功效主导：第三条病态轴AI 解读

This paper introduces a novel framework for estimation theory by introducing a second-order diagnostic for estimator design. While classical analysis focuses on the bias-variance trade-off, we present a more foundational constraint. This result is model-agnostic, domain-agnostic, and is valid for both parametric and non-parametric problems, Bayesian and frequentist frameworks. We propose to classify the estimators into three primary power regimes. We theoretically establish…

稀疏非线性混合效应模型中的后验收缩率AI 解读

Recent works have shown an interest in investigating the frequentist asymptotic properties of Bayesian procedures for high-dimensional linear models under sparsity constraints. However, there exists a gap in the literature regarding analogous theoretical findings for non-linear models within the high-dimensional setting. The current study provides a novel contribution, focusing specifically on a non-linear mixed-effects model. In this model, the residual variance is assumed…

HP-ACCORD：临床多组学研究中的大规模偏相关网络学习AI 解读

Graphical model estimation from multi-omics data requires a balance between statistical estimation performance and computational scalability. We introduce a novel pseudolikelihood-based graphical model framework that reparameterizes the target precision matrix while preserving the sparsity pattern and estimates it by minimizing an $\ell_1$-penalized empirical risk based on a new loss function. The proposed estimator maintains estimation and selection consistency in various…

带预测特征输入的核岭回归及其在因子型非参数回归中的应用AI 解读

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive performance has received continuous attention for more than two decades. However, in many modern regression problems where the feature inputs used in KRR cannot be directly observed and must instead be inferred from other measurements,…

协变量分布偏移下的自动去偏机器学习AI 解读

We present machine learning estimators for causal and predictive parameters under covariate shift, where covariate distributions differ between training and target populations. One such parameter is the average effect of a policy that alters the covariate distribution, such as a treatment modifying surrogate covariates used to predict long-term outcomes. Another example is the average treatment effect for a population with a shifted covariate distribution, like the effect of…

概率性与非线性压缩感知AI 解读

We present a smooth probabilistic reformulation of $\ell_0$ regularized regression that does not require Monte Carlo sampling and allows for the computation of exact gradients, facilitating rapid convergence to local optima of the best subset selection problem. The method drastically improves convergence speed compared to similar Monte Carlo based approaches. Furthermore, we empirically demonstrate that it outperforms compressive sensing algorithms such as IHT and (Relaxed-)…

高维 Lasso 区间估计的替代似然近似AI 解读

Classical frequentist approaches to inference for the lasso emphasize exact coverage for each feature, which requires debiasing and severs the connection between confidence intervals and the original lasso estimates. To address this, in earlier work we introduced the idea of average coverage, allowing for biased intervals that align with the lasso point estimates, and proposed the Relaxed Lasso Posterior (RL-P) intervals, which leverage the Bayesian interpretation of the…

高维统计推断与充分降维关联下的变量选择AI 解读

Simultaneous variable selection and statistical inference is challenging in high-dimensional data analysis. Most existing post-selection inference methods require explicitly specified regression models, which are often linear, as well as sparsity in the regression model. The performance of such procedures can be poor under either misspecified nonlinear models or a violation of the sparsity assumption. In this paper, we propose a sufficient dimension association (SDA)…

非齐次隐半马尔可夫与惩罚向量自回归的环境风险评估AI 解读

Motivated by the study of pollution trends in the city of Bergen, we introduce a flexible statistical framework for modeling multivariate air pollution data via a nonhomogeneous Hidden Semi-Markov Vector Auto-Regression. The hidden process captures unobserved environmental conditions, while the vector autoregressive structure accounts for temporal autocorrelation and cross-pollutant dependencies. The model further allows time-varying environmental conditions to influence…

双重下降：理解不可识别参数的线性模型估计与过拟合模型AI 解读

We consider ordinary least squares estimation and variations on least squares estimation such as penalized (regularized) least squares and spectral shrinkage estimates for problems with p > n and associated problems with prediction of new observations. After the introduction of Section 1, Section 2 examines a number of commonly used estimators for p > n. Section 3 introduces prediction with p > n. Section 4 introduces notational changes to facilitate discussion of…

截断现象的传输方法AI 解读

Substantial progress has recently been made in the understanding of the cutoff phenomenon for Markov processes, using an information-theoretic statistics known as varentropy [Sal23; Sal24; Sal25a; PS25]. In the present paper, we propose an alternative approach which bypasses the use of varentropy and exploits instead a new W-TV transport inequality, combined with a classical parabolic regularization estimate [BGL01; OV01]. While currently restricted to non-negatively curved…

加性全局Fréchet回归的变量选择AI 解读

We present a novel framework for variable selection in Fréchet regression with responses in general metric spaces, a setting increasingly relevant for analyzing non-Euclidean data such as probability distributions and covariance matrices. Building on the concept of (weak) Fréchet conditional means, we develop an additive regression model that represents the metric-based discrepancy of the response as a sum of covariate-specific nonlinear functions in reproducing kernel…

基于样条从噪声数据中识别偏微分方程模型AI 解读

We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the cubic splines to estimate unobservable derivatives. The underlying PDE is based on a subset of these derivatives. This stage is computationally efficient: its computational complexity is a product of a constant with the sample size; this…

非凸梯度下降的长时间动力学与普适性AI 解读

This paper develops a general approach to characterize the long-time trajectory behavior of nonconvex gradient descent in generalized single-index models in the large aspect ratio regime. In this regime, we show that for each iteration the gradient descent iterate concentrates around a deterministic vector called the `Gaussian theoretical gradient descent', whose dynamics can be tracked by a state evolution system of two recursive equations for two scalars. Our concentration…

高维门槛回归模型中的一致推断AI 解读

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1 estimation errors for the Lasso estimator of the slope parameters and the threshold parameter, accommodating heteroskedastic non-subgaussian error terms and non-subgaussian covariates. Next, we derive the asymptotic distribution of tests…

基于KOO方法、带图结构的分组线性回归一致性聚类AI 解读

The kick-one-out (KOO) method is a variable selection method based on a model selection criterion. The method is very simple, and yet it has consistency in variable selection under a high-dimensional asymptotic framework with a specific model selection criterion. This paper proposes the join-twotogether (JTT) method, which is a clustering method based on the KOO method for group-wise linear regression with graph structure. The JTT method formulates the clustering problem as…

多元模型中正则化估计的贝叶斯框架：融合近似计算概念AI 解读

This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding (quantization), thereby connecting two distinct paradigms: Bayesian inference and approximate computing. Next, Bayesian estimation of the means from two independent multivariate normal samples is employed to justify shrinkage estimators, i.e.,…