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Communication Dans Un Congrès Année : 2018

Efficient Algorithms for Non-convex Isotonic Regression through Submodular Optimization

Francis Bach

Résumé

We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints corresponding to first-order stochastic dominance. We propose new discretization schemes that lead to simple and efficient algorithms based on zero-th, first, or higher order oracles; these algorithms also lead to improvements without isotonic constraints. Finally, our experiments show that non-convex loss functions can be much more robust to outliers for isotonic regression, while still leading to an efficient optimization problem.
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Dates et versions

hal-01569934 , version 1 (27-07-2017)

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Francis Bach. Efficient Algorithms for Non-convex Isotonic Regression through Submodular Optimization. NIPS 2018 : Thirty-second Annual Conference on Neural Information Processing Systems, Dec 2018, Montreal, Canada. ⟨hal-01569934⟩
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