论文检索

整合预训练语言模型知识的泊松过程主题模型AI 解读

Topic modeling is traditionally applied to word counts without accounting for the context in which words appear. Recent advances in large language models (LLMs) offer contextualized word embeddings that capture deeper semantic meaning and relationships. We aim to leverage such embeddings to improve topic modeling.We use a pre-trained LLM to convert each document into a sequence of word embeddings. This sequence is then modeled as a Poisson point process, with its intensity…

利用情感分析改进投资决策：概率排序框架AI 解读

We develop a probabilistic framework to extract sentiment information from text by training a model to predict and rank sentiments in newly encountered documents. Our approach imposes a joint semi-parametric model on text and ordinal response variables, addressing the challenges of sparse sentiment signals and complex response distributions. Through a word screening procedure and the use of normalized ranks, our approach achieves consistent sentiment ranking without…

块模型家族的网络拟合优度检验AI 解读

The block-model family has four popular network models (SBM, DCBM, MMSBM, and DCMM). A fundamental problem is, how well each of these models fits with real networks. We propose GoF-MSCORE as a new Goodness-of-Fit (GoF) metric for DCMM (the broadest one among the four), with two main ideas. The first is to use cycle count statistics as a general recipe for GoF. The second is a novel network fitting scheme. GoF-MSCORE is a flexible GoF approach, and we further extend it to…

网络两样本比较的最优检验AI 解读

We are interested in the problem of two-sample network hypothesis testing: given two networks with the same set of nodes, we wish to test whether the underlying Bernoulli probability matrices of the two networks are the same or not. We propose Interlacing Balance Measure (IBM) as a new two-sample testing approach. We consider the Degree-Corrected Mixed-Membership (DCMM) model for undirected networks, where we allow severe degree heterogeneity, mixed-memberships, flexible…

严重度异质性下的最优网络成员归属估计AI 解读

Real networks often have severe degree heterogeneity, with maximum, average, and minimum node degrees differing significantly. This paper examines the impact of degree heterogeneity on statistical limits of network data analysis. Introducing the empirical heterogeneity distribution (EHD) under a degree-corrected mixed membership model, we show that the optimal rate of mixed membership estimation is an explicit functional of the EHD. This result confirms that severe degree…

江一聪与柯征对《网络潜在增长过程的根节点与社群推断》的讨论AI 解读

We congratulate the authors on an excellent paper! Crane and Xu (2021) proposed novel methods for finding ‘root nodes’ from a single snapshot of a dynamic network process, with several interesting real-data examples. We now consider a new application for finding ‘root papers’ in a citation network. The MADStat dataset (Ji et al., 2022; Ke et al., 2023) consists of the bibtex and citation information of over 83 K papers, which we use to construct paper citation networks.…

社会网络的混合社群归属估计AI 解读

In economics and social science, network data are regularly observed, and a thorough understanding of the network community structure facilitates the comprehension of economic patterns and activities. Consider an undirected network with n nodes and K communities. We model the network using the Degree-Corrected Mixed-Membership (DCMM) model, where for each node i=1,2,…,n, there exists a membership vector πi=(πi(1),πi(2),…,πi(K))′, where πi(k) is the weight that node i puts on…

利用奇异值分解进行主题建模AI 解读

The probabilistic topic model imposes a low-rank structure on the expectation of the corpus matrix. Therefore, singular value decomposition (SVD) is a natural tool of dimension reduction. We propose an SVD-based method for estimating a topic model. Our method constructs an estimate of the topic matrix from only a few leading singular vectors of the data matrix, and has a great advantage in memory use and computational cost for large-scale corpora. The core ideas behind our…

网络社区数量的最优估计AI 解读

In network analysis, how to estimate the number of communities K is a fundamental problem. We consider a broad setting where we allow severe degree heterogeneity and a wide range of sparsity levels, and propose Stepwise Goodness of Fit (StGoF) as a new approach. This is a stepwise algorithm, where for m=1,2,…, we alternately use a community detection step and a goodness of fit (GoF) step. We adapt SCORE Jin for community detection, and propose a new GoF metric. We show that…

基于谱主体特征值匹配的协方差尖峰特征值数量估计AI 解读

The spiked covariance model has gained increasing popularity in high-dimensional data analysis. A fundamental problem is determination of the number of spiked eigenvalues, K. For estimation of K, most attention has focused on the use of top eigenvalues of sample covariance matrix, and there is little investigation into proper ways of using bulk eigenvalues to estimate K. We propose a principled approach to incorporating bulk eigenvalues in the estimation of K. Our method…

《统计学家的共同被引与共同署名网络》答辩回应AI 解读

We thank David Donoho for very encouraging comments. As always, his penetrating vision and deep thoughts are extremely stimulating. We are glad that he summarizes a major philosophical difference b...

网络检验中带符号多边形统计量的最优自适应性AI 解读

Given a symmetric social network, we are interested in testing whether it has only one community or multiple communities. The desired tests should (a) accommodate severe degree heterogeneity, (b) accommodate mixed memberships, (c) have a tractable null distribution and (d) adapt automatically to different levels of sparsity, and achieve the optimal phase diagram. How to find such a test is a challenging problem. We propose the Signed Polygon as a class of new tests. Fixing…

高维聚类及相关问题的相变AI 解读

Consider a two-class clustering problem where we observe $X_{i}=\ell_{i}\mu+Z_{i}$, $Z_{i}\stackrel{\mathit{i.i.d.}}{\sim}N(0,I_{p})$, $1\leq i\leq n$. The feature vector $\mu\in R^{p}$ is unknown but is presumably sparse. The class labels $\ell_{i}\in\{-1,1\}$ are also unknown and the main interest is to estimate them. We are interested in the statistical limits. In the two-dimensional phase space calibrating the rarity and strengths of useful features, we find the precise…

QUADRO：基于瑞利商优化的监督降维AI 解读

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method - named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization) - for analyzing high- dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent…

预印本版本摘要 · 查看来源

This paper explores the homogeneity of coefficients in high-dimensional regression, which extends the sparsity concept and is more general and suitable for many applications. Homogeneity arises when regression coefficients corresponding to neighboring geographical regions or a similar cluster of covariates are expected to be approximately the same. Sparsity corresponds to a special case of homogeneity with a large cluster of known atom zero. In this article, we propose a new…

Consider a linear model $Y=X\beta+z$, where $X=X_{n,p}$ and $z\sim N(0,I_{n})$. The vector $\beta$ is unknown but is sparse in the sense that most of its coordinates are $0$. The main interest is to separate its nonzero coordinates from the zero ones (i.e., variable selection). Motivated by examples in long-memory time series (Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer]) and the change-point problem (Bhattacharya [In Change-Point…