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高维局部依赖数据的广义隶属度估计AI 解读

This work focuses on the mixed membership models for multivariate categorical data widely used for analyzing survey responses and population genetics data. These grade of membership (GoM) models offer rich modeling power but present significant estimation challenges for high-dimensional polytomous data. Popular existing approaches, such as Bayesian MCMC inference, are not scalable and lack theoretical guarantees in high-dimensional settings. To address this, we first observe…

自适应迁移聚类：统一框架AI 解读

We propose a general transfer learning framework for clustering given a main dataset and an auxiliary one about the same subjects. The two datasets may reflect similar but different latent grouping structures of the subjects. We propose an adaptive transfer clustering (ATC) algorithm that automatically leverages the commonality in the presence of unknown discrepancy, by optimizing an estimated bias-variance decomposition. It applies to a broad class of statistical models…

深度离散编码器：具有离散潜在层的可识别深度生成模型AI 解读

In the era of generative AI, deep generative models (DGMs) with latent representations have gained tremendous popularity. Despite their impressive empirical performance, the statistical properties of these models remain underexplored. DGMs are often overparametrized, non-identifiable, and uninterpretable black boxes, raising serious concerns when deploying them in high-stakes applications. Motivated by this, we propose interpretable deep generative models for rich data types…

高维离散数据的程度异质性潜在类别分析AI 解读

The latent class model is a widely used mixture model for multivariate discrete data. Besides the existence of qualitatively heterogeneous latent classes, real data often exhibit additional quantitative heterogeneity nested within each latent class. The modern latent class analysis also faces extra challenges, including the high-dimensionality, sparsity, and heteroscedastic noise inherent in discrete data. Motivated by these phenomena, we introduce the Degree-heterogeneous…

何银秋、顾玉琪、应志良对《使用 Varimax 的经典因子分析可进行统计推断》的讨论AI 解读

We congratulate the authors on an impressive paper that demystifies the popular Varimax rotation. They showed that the Varimax rotation can identify true axes of latent factors under the leptokurtic condition in a low-rank semiparametric factor model Different from (1), the exploratory Item Factor Analysis (IFA), widely used in social and behavioural sciences, adopts a nonlinear transformation of the low-rank structure: where the binary data matrix R contains N individuals’…

贝叶斯金字塔：离散数据的可识别多层离散潜结构模型AI 解读

Abstract High-dimensional categorical data are routinely collected in biomedical and social sciences. It is of great importance to build interpretable parsimonious models that perform dimension reduction and uncover meaningful latent structures from such discrete data. Identifiability is a fundamental requirement for valid modeling and inference in such scenarios, yet is challenging to address when there are complex latent structures. In this article, we propose a class of…

大规模结构化潜在属性分析的联合最大似然方法AI 解读

Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent attributes explain the dependence of observed variables in a highly structured fashion. Usually, the maximum marginal likelihood estimation approach is adopted for SLAMs, treating the latent attributes as random effects. The increasing scope of…

受限潜在类别模型的部分可识别性AI 解读

Latent class models have wide applications in social and biological sciences. In many applications, prespecified restrictions are imposed on the parameter space of latent class models, through a design matrix, to reflect practitioners’ assumptions about how the observed responses depend on subjects’ latent traits. Though widely used in various fields, such restricted latent class models suffer from nonidentifiability due to their discreteness nature and complex structure of…