Rémi Flamary

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SVM with uncertain labels


SVM are efficient discriminative classifiers but they cannot be applied when the learning set consists of both certain labels {-1,1} and uncertain labels represented by a posterior probability estimate (0,1).

We address this problem in our SSP 2011 paper entitled :

E. Niaf, R. Flamary, C. Lartizien, S. Canu, Handling uncertainties in SVM classification, IEEE Workshop on Statistical Signal Processing , 2011.
Abstract: This paper addresses the pattern classification problem arising when available target data include some uncertainty information. Target data considered here is either qualitative (a class label) or quantitative (an estimation of the posterior probability). Our main contribution is a SVM inspired formulation of this problem allowing to take into account class label through a hinge loss as well as probability estimates using epsilon-insensitive cost function together with a minimum norm (maximum margin) objective. This formulation shows a dual form leading to a quadratic problem and allows the use of a representer theorem and associated kernel. The solution provided can be used for both decision and posterior probability estimation. Based on empirical evidence our method outperforms regular SVM in terms of probability predictions and classification performances.
author = { Niaf, E. and Flamary, R. and Lartizien, C. and Canu, S.},
title = {Handling uncertainties in SVM classification},
booktitle = { IEEE Workshop on Statistical Signal Processing },
editor = {},
year = {2011}

Basically we learn a unique classifier satisfying both classification performances on the certain labels and performs a probabilistic regression on the uncertain labels. Our approach proved efficient in terms of classification performances and probabilistic output compared to a classical Platt estimation.

Note that it has been drawn to our attention that, in our work, we address the problem 7.11 that can be seen page 223 in the very good book Learning with kernels from B. Scholkopf and A. Smola. We believe that we provide a new way to handle the uncertain case that leads to a better probabilistic prediction.


Current version: 0.2

Download : svm_uncertain_labels.zip


This toolbox requires the SVM and Kernel Methods Matlab Toolbox. A simple way to make everything work is to download the toolbox here and to unzip it in a subfolder of our code.

  • Download the zip files (both svm_uncertain_labels.zip and SVM-KM).
  • Extract the zip files (SVM-KM should be in a subfolder of our toolbox)
  • Try one of the example files in Matlab (test*.m).


This package contains our paper, a matlab function that learn from uncertain labels instead of certain ones (usvmclass.m), and 3 test scripts corresponding to the numerical experiments in the paper (test*.m). The code is Open Source and may be redistributed freely. Feel free to send us any improvement you make.

This is a joint work with Emilie Niaf, Carole Lartizien and Stéphane Canu.