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.
The complexity of the partial order dimension problem.SIAM Journal on Algebraic Discrete Methods, 3(3):351–358, 1982
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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.