Deep Discrete Encoders: Identifiable Deep Generative Models for Rich Data with Discrete Latent Layers
提出深度离散编码器（DDE），一种具有多个二进制潜层的可解释深度生成模型，理论证明其可识别性，并开发高效估计算法，应用于分层主题建模、图像表示学习和教育测试中的反应时间建模。
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 with discrete latent layers, called Deep Discrete Encoders (DDEs). A DDE is a directed graphical model with multiple binary latent layers. Theoretically, we propose transparent identifiability conditions for DDEs, which imply progressively smaller sizes of the latent layers as they go deeper. Identifiability ensures consistent parameter estimation and inspires an interpretable design of the deep architecture. Computationally, we propose a scalable estimation pipeline of a layerwise nonlinear spectral initialization followed by a penalized stochastic approximation EM algorithm. This procedure can efficiently estimate models with exponentially many latent components. Extensive simulation studies for high-dimensional data and deep architectures validate our theoretical results and demonstrate the excellent performance of our algorithms. We apply DDEs to three diverse real datasets with different data types to perform hierarchical topic modeling, image representation learning, and response time modeling in educational testing.