Robustness and generalization for metric learning
By Aurélien Bellet, Amaury Habrard. 2012
104 citations recorded by the source corpus.
Abstract Metric learning has attracted a lot of interest over the last decade, but the generalization ability of such methods has not been thoroughly studied. In this paper, we introduce an adaptation of the notion of algorithmic robustness (previously introduced by Xu and Mannor) that can be used to derive generalization bounds for metric learning. We further show that a weak notion of robustness is in fact a necessary and sufficient condition for a metric learning algorithm to generalize. To illustrate the applicability of the proposed framework, we derive generalization results for a large family of existing metric learning algorithms, including some sparse formulations that are not covered by the previous results.
Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Electrical and Electronic Engineering
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- Michaël Perrot
- Qiang Qiu
- Cynthia Rudin
- Harsh Parikh
- Alexander Volfovsky
- Amaury Habrard
- Robert Calderbank
- Guillermo Sapiro
In Computer Vision and Pattern Recognition
- Luc Van Gool
- Alan L. Yuille
- Trevor Darrell
- Dacheng Tao
- Ming-Hsuan Yang
- Andrea Vedaldi
- Bernt Schiele
- Jitendra Malik
In Electrical and Electronic Engineering
- Michaël Perrot
- Harsh Parikh
- Cynthia Rudin
- Alexander Volfovsky
- Amaury Habrard
- Robert Calderbank
- Guillermo Sapiro
- Qiang Qiu
Citations in the corpus
- Adversarially Robust Generalization Requires More Data (2018, positive): “Bellet and Habrard [5] gives similar results for metric learning.”
- A Survey on Metric Learning for Feature Vectors and Structured Data (2013, background): “Bellet and Habrard (2012) demonstrate how to adapt the more flexible notion of algorithmic robustness (Xu and Mannor, 2012) to the metric learning setting to derive (loose) generalization bounds for any matrix norm (including sparsity-inducing ones) as regularizer.”
- MALTS: Matching After Learning to Stretch (2018, methodology): “The following definitions and results closely align with the theoretical guarantees of distance metric learning algorithms in Bellet and Habrard (2015) and Xu and Mannor (2012). Our work extends these results to learn a distance metric for causal inference.”
- Revisiting Training Strategies and Generalization Performance in Deep Metric Learning (2020, background): “Existing works on generalization in metric learning focus on robustness of linear or kernel-based distance metrics (Bellet & Habrard, 2015; Bellet, 2013) and examine bounds on the generalization error (Huai et al., 2019).”
- A Theoretical Analysis of Metric Hypothesis Transfer Learning (2015, methodology): “Other ways to derive generalization guarantees are to use the Rademacher complexity as in (Cao et al., 2012; Guo & Ying, 2014) or to use the notion of algorithmic robustness (Bellet & Habrard, 2015).”
- Discriminative Robust Transformation Learning (2015, methodology): “We work with the following definition of (K, )-robustness [1].”