论文检索

Trans-Glasso：精度矩阵估计的迁移学习方法AI 解读

Precision matrix estimation is essential in various fields, yet it is challenging when samples for the target study are limited. Transfer learning can enhance estimation accuracy by leveraging data from related source studies. We propose Trans-Glasso, a two-step transfer learning method for precision matrix estimation. First, we obtain initial estimators using a multi-task learning objective that captures both shared and unique features across studies. Then, we refine these…

Rasch 模型题目参数估计的随机配对极大似然方法AI 解读

The Rasch model, a classical model in the item response theory, is widely used in psychometrics to model the relationship between individuals’ latent traits and their binary responses to assessments or questionnaires. In this article, we introduce a new likelihood-based estimator—random pairing maximum likelihood estimator (RP‐MLE) and its bootstrapped variant multiple random pairing MLE (MRP‐MLE) which faithfully estimate the item parameters in the Rasch model. The new…

最优应对 RKHS 非参数回归中的协变量偏移AI 解读

We study the covariate shift problem in the context of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We focus on two natural families of covariate shift problems defined using the likelihood ratios between the source and target distributions. When the likelihood ratios are uniformly bounded, we prove that the kernel ridge regression (KRR) estimator with a carefully chosen regularization parameter is minimax rate-optimal (up to a log factor) for a…

连接稳健主成分分析中的凸与非凸优化：噪声、异常值及缺失数据AI 解读

This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers and (3) missing data. This problem, often dubbed as robust principal component analysis (robust PCA), finds applications in various domains. Despite the wide applicability of convex relaxation, the available statistical support (particularly the stability analysis in the presence of random noise)…

主体间依赖分析：部分高斯图模型方法AI 解读

Different from traditional intra-subject analysis, the goal of inter-subject analysis (ISA) is to explore the dependency structure between different subjects with the intra-subject dependency as nuisance. ISA has important applications in neuroscience to study the functional connectivity between brain regions under natural stimuli. We propose a modeling framework for ISA that is based on Gaussian graphical models, under which ISA can be converted to the problem of estimation…

谱方法与正则化极大似然均可实现最优前 K 项排序AI 解读

This paper is concerned with the problem of top-$K$ ranking from pairwise comparisons. Given a collection of $n$ items and a few pairwise comparisons across them, one wishes to identify the set of $K$ items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model—the Bradley–Terry–Luce model, where each item is assigned a latent preference score, and where the outcome of each pairwise comparison depends solely on the relative scores of…