Abstract | Experiments show that these approximation strategies produce results comparable to a state-of-the-art integer linear programming formulation for the same joint inference task along with a significant improvement in runtime. |
Conclusion | Experiments show that one of these approximation strategies produces results comparable to a state-of-the-art integer linear program for the same joint inference task with a 60% reduction in average inference time. |
Introduction | Joint methods have also been proposed that invoke integer linear programming (ILP) formulations to simultaneously consider multiple structural inference problems—both over n-grams and input dependencies (Martins and Smith, 2009) or n-grams and all possible dependencies (Thadani and McKeown, 2013). |
Introduction | We therefore consider methods to recover approximate solutions for the subproblem of finding the maximum weighted subtree in a graph, common among which is the use of a linear programming relaxation. |
Introduction | This linear program (LP) appears empirically tight for compression problems and our experiments indicate that simply using the non-integral solutions of this LP in Lagrangian relaxation can empirically lead to reasonable compressions. |
Background | Formally, from equation 3, the most probable interpretation, is the one that minimizes 27.61% Ar(d(7“))p. In case of p = 1, and given that all d (7“) are linear equations, then minimizing the sum requires solving a linear program , which, compared to inference in other probabilistic logics such as MLNs, can be done relatively efficiently using well-established techniques. |
Introduction | On the other hand, inference in PSL reduces to a linear programming problem, which is theoretically and practically much more efficient. |
PSL for STS | PSL’s inference is actually an iterative process where in each iteration a grounding phase is followed by an optimization phase (solving the linear program ). |
Adding Back Constraints | In general, it can be shown that Lagrangian relaxation is only guaranteed to solve a linear programming relaxation of the underlying combinatorial problem. |
Related Work | General linear programming approaches have also been applied to word alignment problems. |
Related Work | (2006) formulate the word alignment problem as quadratic assignment problem and solve it using an integer linear programming solver. |