通过随机插值和充分表示进行半监督条件生成学习
Semi-Supervised Conditional Generative Learning through Stochastic Interpolation and Sufficient Representations
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中文总结 AI 辅助
针对半监督条件生成建模难题，提出结合条件随机插值与低维潜在表示的RepG框架，将生成分为两阶段，隔离监督学习到低维空间，理论推导其误差分解与收敛率，有效减轻维度诅咒。
中文摘要 AI 辅助
在半监督环境中，标记数据稀缺而未标记样本丰富，条件生成建模仍是一个具有挑战性的问题。为有效利用未标记数据集中嵌入的结构信息并补偿稀疏条件信号，我们提出了一个将条件随机插值与低维潜在表示相结合的半监督框架。RepG将生成分解为两个阶段：依赖标签的潜在采样和高维重建。这将条件依赖的监督学习隔离到低维空间，只需少量标签，同时纯粹利用丰富的未标记数据进行重建。理论上，我们建立了一个误差分解，表明RepG的Kullback-Leibler散度包括逐阶段估计误差和由条件互信息量化的结构偏差。对于深度神经网络估计器，我们推导了非渐近收敛率，证明RepG显著提高了样本复杂度。通过将监督估计负担限制在潜在表示的低固有维度，RepG实现了严格更快的收敛率。我们的理论结果表明，该方法有效减轻了直接环境空间生成建模中固有的维度诅咒。
英文摘要
Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant. To effectively leverage structural information embedded within the unlabeled dataset and compensate for sparse conditioning signals, we propose a semi-supervised framework combining conditional stochastic interpolation with low-dimensional latent representations. RepG decomposes generation into two stages: label-dependent latent sampling and high-dimensional reconstruction. This isolates the supervised learning of conditional dependencies to a low-dimensional space, requiring few labels while utilizing the abundant unlabeled data purely for reconstruction. Theoretically, we establish an error decomposition showing that the Kullback-Leibler divergence of RepG comprises stage-wise estimation errors and a structural bias quantified by conditional mutual information. For deep neural network estimators, we derive non-asymptotic convergence rates proving that RepG significantly improves sample complexity. By confining the supervised estimation burden to the low intrinsic dimension of the latent representation, RepG achieves a strictly faster convergence rate. Complemented by a minimax lower bound, our theoretical results demonstrate that this method effectively mitigates the curse of dimensionality inherent in direct ambient-space generative modeling.
发表机构
- Institute for Mathematics and Artificial Intelligence, Wuhan University, Wuhan, China（数学与人工智能研究院，武汉大学，武汉，中国）
- School of Artificial Intelligence, Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, China（人工智能学院，湖北省计算科学重点实验室，武汉大学，武汉，中国）
- Departments of Data Science and Artificial Intelligence, and Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China（数据科学与人工智能系，应用数学系，香港理工大学，香港，中国）
机构由 AI 辅助整理，请以论文原文为准。
