Timezone: »

 
Poster
Nonparametric Regression with Comparisons: Escaping the Curse of Dimensionality with Ordinal Information
Yichong Xu · Hariank Muthakana · Sivaraman Balakrishnan · Aarti Singh · Artur Dubrawski

Wed Jul 11 09:15 AM -- 12:00 PM (PDT) @ Hall B #142
in Posters Wed »

In supervised learning, we leverage a labeled dataset to design methods for function estimation. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is to understand the usefulness of, and to design algorithms to exploit, this alternative feedback. We focus on a semi-supervised setting where we obtain additional ordinal (or comparison) information for potentially unlabeled samples. We consider ordinal feedback of varying qualities where we have either a perfect ordering of the samples, a noisy ordering of the samples or noisy pairwise comparisons between the samples. We provide a precise quantification of the usefulness of these types of ordinal feedback in non-parametric regression, showing that in many cases it is possible to accurately estimate an underlying function with a very small labeled set, effectively escaping the curse of dimensionality. We develop an algorithm called Ranking-Regression (RR) and analyze its accuracy as a function of size of the labeled and unlabeled datasets and various noise parameters. We also present lower bounds, that establish fundamental limits for the task and show that RR is optimal in a variety of settings. Finally, we present experiments that show the efficacy of RR and investigate its robustness to various sources of noise and model-misspecification.

[ PDF] 

Author Information

Yichong Xu (Carnegie Mellon University)
Hariank Muthakana (Carnegie Mellon University)
Sivaraman Balakrishnan (Carnegie Mellon University)
Aarti Singh (Carnegie Mellon University)
Artur Dubrawski (CMU)

Related Events (a corresponding poster, oral, or spotlight)

More from the Same Authors