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分布输入分类的统计学习理论AI 解读

In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the learning phase, but only samples thereof. This problem is particularly amenable to kernel-based learning methods, where the distributions or samples are first embedded into a Hilbert space, often using kernel mean embeddings (KMEs), and…

通过 RKHS 嵌入实现无需重抽样的时间序列推断AI 解读

In this article, we study nonparametric inference problems in the context of multivariate or functional time series, including testing for goodness-of-fit, the presence of a change point in the marginal distribution, and the independence of two time series, among others. Most methodologies available in the existing literature address these problems by employing a bandwidth-dependent bootstrap or subsampling approach, which can be computationally expensive and/or sensitive to…

基于双重／去偏机器学习的时变连续处理双重差分AI 解读

We propose a difference-in-differences (DiD) framework designed for time-varying continuous treatments across multiple periods. Specifically, we estimate the average treatment effect on the treated (ATET) by comparing distinct non-zero treatment intensities. Identification rests on a conditional parallel trends assumption that accounts for observed covariates and past treatment histories. Our approach allows for lagged treatment effects and, in repeated cross-sectional…

如何选择因果推断的协变量平衡方法：模拟研究的实践启示AI 解读

Background: Inverse probability of treatment weighting (IPTW) is used for confounding adjustment in observational studies. Newer weighting methods include energy balancing (EB), kernel optimal matching (KOM), and tailored-loss covariate balancing propensity scores (TLF), but practical guidance remains limited. We evaluate their performance when implemented according to published recommendations. Methods: We conducted Monte Carlo simulations across 36 scenarios varying sample…

熵正则最优传输的筛法 M 估计AI 解读

Entropically regularized optimal transport between probability measures supported on compact subsets of Euclidean space admits a representation as an information projection under moment inequality constraints. Exploiting this structure, I develop a sieve-based approximation of the Fenchel dual, yielding a sequence of finite-dimensional convex programs whose sample analogues provide tractable estimators of the regularized optimal value and associated dual optimizers. Under…

核流形：高斯过程模型选择的几何方法AI 解读

Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains one of the most challenging and computationally expensive steps in probabilistic modeling. We present a Bayesian optimization framework built on kernel-of-kernels geometry, using expected divergence-based distances between GP priors to…

密度比的非参数推断：一致有效且有功效的置换检验AI 解读

We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient Markov Chain Monte Carlo scheme to draw weighted permutations of the pooled data, yielding exchangeable samples and finite sample validity. For power, if the statistic is an integral probability metric, our procedure is consistent under mild…

融合自回归与共同因子的矩阵时间序列框架AI 解读

Matrix-valued time series are ubiquitous in modern economics and finance, yet modeling them requires navigating a trade-off between flexibility and parsimony. We propose the Matrix Autoregressive model with Common Factors (MARCF), a unified framework for high-dimensional matrix time series that bridges the structural gap between the Matrix Autoregression (MAR) and Matrix Factor Model (MFM). While MAR typically assumes distinct predictor and response subspaces and MFM…

贝叶斯平滑分位数回归AI 解读

The standard asymmetric Laplace framework for Bayesian quantile regression (BQR) suffers from a fundamental decision-theoretic misalignment, yielding biased finite-sample estimates, and precludes gradient-based computation due to non-smoothness. We propose Bayesian smoothed quantile regression (BSQR), a principled framework built on a kernel-smoothed, fully differentiable likelihood. Methodologically, the symmetrizing property of our objective reduces inferential bias and…

最小信息马尔可夫模型AI 解读

The analysis of high-dimensional time series data has become increasingly important across a wide range of fields. Recently, a method for constructing the minimum information Markov kernel on finite state spaces was established. In this study, we propose a statistical model based on a parametrization of its dependence function, which we call the \textit{Minimum Information Markov Model}. We show that its parametrization induces an orthogonal structure between the stationary…

观察研究中估计个体化治疗规则的降维结局加权学习AI 解读

Individualized treatment regimes (ITRs) aim to improve clinical outcomes by assigning treatment based on patient-specific characteristics. However, existing methods often struggle with high-dimensional covariates, limiting accuracy, interpretability, and real-world applicability. We propose a novel sufficient dimension reduction approach that directly targets the contrast between potential outcomes and identifies a low-dimensional subspace of the covariates capturing…

非参数二元选择模型的核化估计方法AI 解读

We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its computational scalability in the number of covariates. For instance, even when assuming a normal error distribution as in probit models, commonly used sieves for approximating an unknown function of covariates can lead to a large-dimensional…

时间序列分析中的条件柯西–施瓦茨散度：核估计及聚类与欺诈检测应用AI 解读

We study the conditional Cauchy-Schwarz divergence (C-CSD) as a symmetric and density-free measure for time series analysis. We derive a practical kernel based estimator using radial basis function kernels on both the condition and output spaces, together with numerical stabilizations including a symmetric logarithmic form with an epsilon ridge and a robust bandwidth selection rule based on the interquartile range. Median heuristic bandwidths are applied to window vectors,…

边界处局部多项式密度估计的核函数选择AI 解读

Local polynomial density (LPD) estimators are widely used for inference on boundary features of the density function. Contrary to conventional wisdom, we show that kernel choice substantially affects efficiency. Theory, simulations, and empirical evidence indicate that the popular triangular kernel delivers large mean squared error, wide confidence intervals, and limited power for detecting discontinuities. Moreover, small-sample variance can explode because the…

向量空间与乘积度量空间中的多元核回归AI 解读

This paper derives limit properties of nonparametric kernel regression estimators without requiring existence of density for regressors in $\mathbb{R}^{q}.$ In functional regression limit properties are established for multivariate functional regression. The rate and asymptotic normality for the Nadaraya-Watson (NW) estimator is established for distributions of regressors in $\mathbb{R}^{q}$ that allow for mass points, factor structure, multicollinearity and nonlinear…

In multiple domains, statistical tasks are performed in distributed settings, with data split among several end machines that are connected to a fusion center. In various applications, the end machines have limited bandwidth and power, and thus a tight communication budget. In this work we focus on distributed learning of a sparse linear regression model, under severe communication constraints. We propose several two round distributed schemes, whose communication per machine…

单指数奖励的非参数赌博机：最优性与自适应性AI 解读

Contextual bandits are a central framework for sequential decision-making, with applications ranging from recommendation systems to clinical trials. While nonparametric methods can flexibly model complex reward structures, they suffer from the curse of dimensionality. We address this challenge using a single-index model, which projects high-dimensional covariates onto a one-dimensional subspace while preserving nonparametric flexibility. We first develop a nonasymptotic…

通过指数模型在多污染物暴露与结局间共享信息AI 解读

An important goal of environmental health research is to assess the health risks posed by mixtures of multiple environmental exposures. In these mixtures analyses, flexible models like Bayesian kernel machine regression and multiple index models are appealing because they allow for arbitrary non-linear exposure-outcome relationships. However, this flexibility comes at the cost of low power, particularly when exposures are highly correlated and the health effects are weak, as…

基于周期缩放 Korobov 核与指数衰减条件的密度估计AI 解读

We propose the periodic scaled Korobov kernel (PSKK) method for nonparametric density estimation on $\mathbb{R}^d$. By first wrapping the target density into a periodic version through modulo operation and subsequently applying kernel ridge regression in scaled Korobov spaces, we extend the kernel approach proposed by Kazashi and Nobile (SIAM J. Numer. Anal., 2023) and eliminate its requirement for inherent periodicity of the density function. This key modification enables…

基于路径签名的选择检测：含重组的多位点时间种群遗传模型AI 解读

In population genetics, there is often interest in inferring selection coefficients. This task becomes more challenging if multiple linked selected loci are considered simultaneously. For such a situation, we propose a novel generalized Bayesian framework where we compute a scoring rule posterior for the selection coefficients in multi-locus temporal population genetics models. As we consider trajectories of allele frequencies over time as our data, we choose to use a…

条件独立性检验在实践中的困难AI 解读

Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed that, contrary to the unconditional case, no universally finite-sample valid test can ever achieve nontrivial power. While informative, this result (based on "hiding" dependence) does not seem to explain the frequent practical failures…

利用微分熵差异检验参数分布族假设AI 解读

We introduce a broadly applicable statistical procedure for testing which parametric distribution family generated a random sample of data. The method, termed the Difference in Differential Entropy (DDE) test, provides a unified framework applicable to a wide range of distributional families, with asymptotic validity grounded in established maximum likelihood, bootstrap, and kernel density estimation principles. The test is straightforward to implement, computationally…

点过程强度函数的孪生核估计：基于轨道正则性的自适应非参数方法AI 解读

We develop TwinKernel methods for nonparametric estimation of intensity functions of point processes. Building on the general TwinKernel framework and combining it with martingale techniques for counting processes, we construct estimators that adapt to orbital regularity of the intensity function. Given a point process $N$ with intensity $λ$ and a cyclic group $G = \langle\varphi\rangle$ acting on the time/space domain, we transport kernels along group orbits to create a…

群轨道上的核输运自适应非参数估计：Oracle不等式与极小极大速率AI 解读

We develop a unified framework for nonparametric functional estimation based on kernel transport along orbits of discrete group actions, which we term \emph{Twin Spaces}. Given a base kernel $K$ and a group $G = \langle\varphi\rangle$ acting isometrically on the input space $E$, we construct a hierarchy of transported kernels $\{K_j\}_{j\geq 0}$ and a penalized model selection scheme satisfying a Kraft inequality. Our main contributions are threefold: (i) we establish…