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.
Smooth minimization of non-smooth functions.Mathematical Programming, 103(1):127–152, 2005
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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.