Structured Nonparametric Variational Inference for Dependent Latent Modeling
Variational inference (VI) is a core engine of modern AI, enabling scalable approximate Bayesian learning and uncertainty-aware training of large probabilistic and generative models. In this paper, we propose Structured Nonparametric Variational Inference (SN-VI), a novel framework for modeling complex dependencies among latent variables in posterior approximation, leveraging multivariate spline techniques. Unlike traditional methods that rely on the mean-field assumption, SN-VI preserves intricate latent variable dependencies, providing a flexible and accurate approximation of posteriors with arbitrary shapes. We establish rigorous theoretical guarantees, including the derivation of the lower bound for the variational objective and proof of asymptotic consistency in posterior estimation. To facilitate practical implementation, we develop an algorithm that automatically identifies dependent latent variables and their underlying dependence structure, without requiring manual specification. Simulation studies validate the effectiveness of SN-VI in approximating posterior distributions with bounded support and complex dependencies. The proposed method has been successfully applied to high-dimensional structured data, including computer vision datasets and spatial transcriptomics. In these applications, SN-VI demonstrates improved generative model performance and effectively uncovers coupled biological signals through the learned dependency structure.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Beta Process Non-negative Matrix Factorization with Stochastic Structured Mean-Field Variational Inference
Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NM…
Variational InferenceTree-Structured Topic Modeling with Nonparametric Neural Variational Inference
Topic modeling has been widely used for discovering the latent semantic structure of documents, but most existing methods learn topics with a flat structure. Although probabilistic models can generate topic hierarchies b…
Variational InferenceNonparametric Variational Auto-encoders for Hierarchical Representation Learning
The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple…
ClusteringRepresentation LearningVariational InferenceCATVI: Conditional and Adaptively Truncated Variational Inference for Hierarchical Bayesian Nonparametric Models
Current variational inference methods for hierarchical Bayesian nonparametric models can neither characterize the correlation structure among latent variables due to the mean-field setting, nor infer the true posterior d…
ClusteringTopic ModelsVariational InferenceGamma Processes, Stick-Breaking, and Variational Inference
While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own r…
Variational Inference