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Poster
Bi-level Score Matching for Learning Energy-based Latent Variable Models
Fan Bao · Chongxuan LI · Kun Xu · Hang Su · Jun Zhu · Bo Zhang

Thu Dec 10 09:00 PM -- 11:00 PM (PST) @ Poster Session 6 #1790

Score matching (SM) provides a compelling approach to learn energy-based models (EBMs) by avoiding the calculation of partition function. However, it remains largely open to learn energy-based latent variable models (EBLVMs), except some special cases. This paper presents a bi-level score matching (BiSM) method to learn EBLVMs with general structures by reformulating SM as a bi-level optimization problem. The higher level introduces a variational posterior of the latent variables and optimizes a modified SM objective, and the lower level optimizes the variational posterior to fit the true posterior. To solve BiSM efficiently, we develop a stochastic optimization algorithm with gradient unrolling. Theoretically, we analyze the consistency of BiSM and the convergence of the stochastic algorithm. Empirically, we show the promise of BiSM in Gaussian restricted Boltzmann machines and highly nonstructural EBLVMs parameterized by deep convolutional neural networks. BiSM is comparable to the widely adopted contrastive divergence and SM methods when they are applicable; and can learn complex EBLVMs with intractable posteriors to generate natural images.

Author Information

Fan Bao (Tsinghua University)
Chongxuan LI (Tsinghua University)
Kun Xu (Tsinghua University)
Hang Su (Tsinghua Univiersity)
Jun Zhu (Tsinghua University)
Bo Zhang (Tsinghua University)

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