The authors replace discontinuous precedence and frontier constraints in a partial-order model with smooth surrogates, producing a continuous posterior that supports gradient MCMC and variational inference while recovering the hard model in the limit.
Partial order models for episcopal social status in 12th century England.IWSM 2011, page 437, 2011
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A Differentiable Bayesian Relaxation for Latent Partial-Order Inference
The authors replace discontinuous precedence and frontier constraints in a partial-order model with smooth surrogates, producing a continuous posterior that supports gradient MCMC and variational inference while recovering the hard model in the limit.