论文检索

LITE：高效估计高斯最大概率AI 解读

We consider the problem of computing the probability of maximality (PoM) of a Gaussian random vector, i.e., the probability for each dimension to be maximal. This is a key challenge in applications ranging from Bayesian optimization to reinforcement learning, where the PoM not only helps with finding an optimal action, but yields a fine-grained analysis of the action domain, crucial in tasks such as drug discovery. Existing techniques are costly, scaling polynomially in…

物理信息机器学习：数学框架及时间序列预测应用AI 解读

Physics-informed machine learning (PIML) is an emerging framework that integrates physical knowledge into machine learning models. This physical prior often takes the form of a partial differential equation (PDE) system that the regression function must satisfy. In the first part of this dissertation, we analyze the statistical properties of PIML methods. In particular, we study the properties of physics-informed neural networks (PINNs) in terms of approximation,…

DUST：基于对偶性的精确多变点检测剪枝方法AI 解读

We tackle the challenge of detecting multiple change points in large time series by optimising a penalised likelihood derived from exponential family models. Dynamic programming algorithms can solve this task exactly with at most quadratic time complexity. In recent years, the development of pruning strategies has drastically improved their computational efficiency. However, the two existing approaches have notable limitations: PELT struggles with pruning efficiency in…

大样本离散时间事件数据的加性预测变量同步估计与模型选择AI 解读

Discrete-time hazard models are widely used when event times are measured in intervals or are not precisely observed. While these models can be estimated using standard generalized linear model techniques, they rely on extensive data augmentation, making estimation computationally demanding in high-dimensional settings. In this paper, we demonstrate how the recently proposed Batchwise Backfitting algorithm, a general framework for scalable estimation and variable selection…

高维投资组合优化中样本外夏普比率的估计AI 解读

Portfolio optimization aims at constructing a realistic portfolio with significant out-of-sample performance, which is typically measured by the out-of-sample Sharpe ratio. However, due to in-sample optimism, it is inappropriate to use the in-sample estimated covariance to evaluate the out-of-sample Sharpe, especially in the high dimensional settings. In this paper, we propose a novel method to estimate the out-of-sample Sharpe ratio using only in-sample data, based on…

面向医院再入院预测的异质性感知回归：非参数估计与结构化选择AI 解读

Readmission prediction is a critical but challenging clinical task, as the inherent relationship between high-dimensional covariates and readmission is complex and heterogeneous. Despite this complexity, models should be interpretable to aid clinicians in understanding an individual's risk prediction. Readmissions are often heterogeneous, as individuals hospitalized for different reasons, particularly across distinct clinical diagnosis groups, exhibit materially different…

Dirichlet-Laplace 先验下的后验计算AI 解读

Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized optimization methods. Bayesian approaches provide a probabilistic framework to formally quantify uncertainty through shrinkage priors. Among these, the Dirichlet-Laplace prior has attained recognition for its theoretical guarantees and wide…

高维广义线性模型的稳健惩罚估计AI 解读

Robust estimators for generalized linear models (GLMs) are not easy to develop due to the nature of the distributions involved. Recently, there has been growing interest in robust estimation methods, particularly in contexts involving a potentially large number of explanatory variables. Transformed M-estimators (MT-estimators) provide a natural extension of M-estimation techniques to the GLM framework, offering robust methodologies. We propose a penalized variant of…

函数型非线性外生输入自回归模型的代理建模AI 解读

We propose a novel functional approach to surrogate modeling of dynamical systems with exogenous inputs. This approach, named Functional Nonlinear AutoRegressive with eXogenous inputs (F-NARX), approximates the system response based on temporal features of the exogenous inputs and the system response. This marks a major step away from the discrete-time-centric approach of classical NARX models, which determines the relationship between selected time steps of the input/output…

标准化方式对正则化回归中收缩效应的影响AI 解读

Regularized models are often sensitive to the scales of the features in the data and it has therefore become standard practice to normalize (center and scale) the features before fitting the model. But there are many different ways to normalize the features and the choice may have dramatic effects on the resulting model. In spite of this, there has so far been no research on this topic. In this paper, we begin to bridge this knowledge gap by studying normalization in the…

长上下文线性系统辨识AI 解读

This paper addresses the problem of long-context linear system identification, where the state $x_t$ of a dynamical system at time $t$ depends linearly on previous states $x_s$ over a fixed context window of length $p$. We establish a sample complexity bound that matches the i.i.d. parametric rate up to logarithmic factors for a broad class of systems, extending previous works that considered only first-order dependencies. Our findings reveal a learning-without-mixing…

高维空间面板网络的一致有效推断AI 解读

We propose employing a high-dimensional generalized method of moments (GMM) estimator, regularized for dimension reduction and subsequently debiased to correct for shrinkage bias (referred to as a debiased-regularized estimator), for inference on large-scale spatial panel networks. In particular, the network structure, which incorporates a flexible sparse deviation that can be regarded either as a latent component or as a misspecification of a predetermined adjacency matrix,…

Lasso 类正则化器的经验贝叶斯估计：自动相关性判定分析AI 解读

This paper focuses on linear regression models with non-conjugate sparsity-inducing regularizers such as lasso and group lasso. Although the empirical Bayes approach enables us to estimate the regularization parameter, little is known on the properties of the estimators. In particular, many aspects regarding the specific conditions under which the mechanism of automatic relevance determination (ARD) occurs remain unexplained. In this paper, we derive the empirical Bayes…

利用凸聚类拟合分类时间序列的稀疏马尔可夫模型AI 解读

Higher-order Markov chains are frequently used to model categorical time series. However, a major problem with fitting such models is the exponentially growing number of parameters in the model order. A popular approach to parsimonious modeling is to use a Variable Length Markov Chain (VLMC), which determines relevant contexts (recent pasts) of variable orders and forms a context tree. A more general parsimonious modeling approach is given by Sparse Markov Models (SMMs),…

针对多种相关处理的收缩回归AI 解读

When using observational causal models, practitioners often want to disentangle the effects of many related, partially-overlapping treatments. Examples include estimating treatment effects of different marketing touchpoints, ordering different types of products, or signing up for different services. Common approaches that estimate separate treatment coefficients are too noisy for practical decision-making. We propose a computationally light model that uses a customized ridge…

异方差与非线性下子集 Anderson–Rubin 检验的一致有效性AI 解读

We consider the Anderson-Rubin (AR) statistic for a general set of nonlinear moment restrictions. The statistic is based on the criterion function of the continuous updating estimator (CUE) for a subset of parameters not constrained under the Null. We treat the data distribution nonparametrically with parametric moment restrictions imposed under the Null. We show that subset tests and confidence intervals based on the AR statistic are uniformly valid over a wide range of…

高维数据中 Lasso 与自适应 Lasso 的比较：三阴性乳腺癌的遗传生存分析AI 解读

In high-dimensional survival analysis, effective variable selection is crucial for both model interpretation and predictive performance. This paper investigates Cox regression with lasso and adaptive lasso penalties in genomic datasets where covariates far outnumber observations. We propose and evaluate four weight calculation strategies for adaptive lasso specifically designed for high-dimensional settings: ridge regression, principal component analysis (PCA), univariate…

用于帕金森病生物标志物发现的稀疏因果结构学习：惩罚化 FCIAI 解读

Parkinson's disease (PD) is a progressive neurodegenerative disorder that lacks reliable early-stage biomarkers for diagnosis, prognosis, and therapeutic monitoring. While cerebrospinal fluid (CSF) biomarkers, such as alpha-synuclein seed amplification assays (alphaSyn-SAA), offer diagnostic potential, their clinical utility is limited by invasiveness and incomplete specificity. Plasma biomarkers provide a minimally invasive alternative, but their mechanistic role in PD…

多环境GLAMP：面向迁移学习的近似消息传递及其在Lasso估计中的应用AI 解读

Approximate Message Passing (AMP) algorithms enable precise characterization of certain classes of random objects in the high-dimensional limit, and have found widespread applications in fields such as signal processing, statistics, and communications. In this work, we introduce Multi-Environment Generalized Long AMP, a novel AMP framework that applies to transfer learning problems with multiple data sources and distribution shifts. We rigorously establish state evolution…

缺失数据与测量误差下高维回归的稳健变量选择AI 解读

In our paper, we focus on robust variable selection for missing data and measurement error. Missing data and measurement errors can lead to confusing data distribution. We propose an exponential loss function with a tuning parameter to apply to Missing and measurement errors data. By adjusting the parameter, the loss function can be better and more robust under various data distributions. We use inverse probability weighting and additive error models to address missing data…

异质性下网络荟萃分析中节点的贝叶斯非参数合并与拆分AI 解读

Network meta-analysis (NMA) synthesizes evidence for multiple treatments, but decisions on node formation can have important statistical implications including bias or inflated uncertainty. Existing data-driven methods often lack flexibility or fail to fully account for node uncertainty and adjust for between-trial heterogeneity simultaneously. We introduce a Bayesian non-parametric framework using a Dirichlet process prior with a regularized horseshoe base measure. This…

大稀疏网络中β模型的L2正则化最大似然估计AI 解读

The $β$-model is a powerful tool for modeling large and sparse networks driven by degree heterogeneity, where many network models become infeasible due to computational challenge and network sparsity. However, existing estimation algorithms for $β$-model do not scale up. Also, theoretical understandings remain limited to dense networks. This paper brings several significant improvements over existing results to address the urgent needs of practice. We propose a new $\ell_2$-p…

加密资产对系统性与特质风险的异质暴露：分而治之的方法AI 解读

This paper analyzes realized return behavior across a broad set of crypto assets by estimating heterogeneous exposures to idiosyncratic and systematic risk. A key challenge arises from the latent nature of broader economy-wide risk sources: macro-financial proxies are unavailable at high-frequencies, while the abundance of low-frequency candidates offers limited guidance on empirical relevance. To address this, we develop a two-stage ``divide-and-conquer'' approach. The…

凸与非凸矩阵感知的高维统计理论AI 解读

The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to this problem, establishing minimax error rates when the number of measurements is sufficiently large relative to the rank and dimension of the low-rank matrix, though a precise comparison of these procedures still remains unexplored. In…