An Integer Linear Programming Framework for Mining Constraints from Data

by   Tao Meng, et al.

Various structured output prediction problems (e.g., sequential tagging) involve constraints over the output space. By identifying these constraints, we can filter out infeasible solutions and build an accountable model. To this end, we present a general integer linear programming (ILP) framework for mining constraints from data. We model the inference of structured output prediction as an ILP problem. Then, given the coefficients of the objective function and the corresponding solution, we mine the underlying constraints by estimating the outer and inner polytopes of the feasible set. We verify the proposed constraint mining algorithm in various synthetic and real-world applications and demonstrate that the proposed approach successfully identifies the feasible set at scale. In particular, we show that our approach can learn to solve 9x9 Sudoku puzzles and minimal spanning tree problems from examples without providing the underlying rules. We also demonstrate results on hierarchical multi-label classification and conduct a theoretical analysis on how close the mined constraints are from the ground truth.



There are no comments yet.


page 1

page 2

page 3

page 4


A Mixed Integer Linear Programming Model for Multi-Satellite Scheduling

We address the multi-satellite scheduling problem with limited observati...

Speeding up Linear Programming using Randomized Linear Algebra

Linear programming (LP) is an extremely useful tool and has been success...

Visualizing Multidimensional Linear Programming Problems

The article proposes an n-dimensional mathematical model of the visual r...

An ILP Solver for Multi-label MRFS with Connectivity Constraints

Integer Linear Programming (ILP) formulations of Markov random fields (M...

Locally Feasibly Projected Sequential Quadratic Programming for Nonlinear Programming on Arbitrary Smooth Constraint Manifolds

High-dimensional nonlinear optimization problems subject to nonlinear co...

Robust Planning and Control For Polygonal Environments via Linear Programming

In this paper, we are concerned with the design of a set of controllers,...

Automating Personnel Rostering by Learning Constraints Using Tensors

Many problems in operations research require that constraints be specifi...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.