# Estimating a Kernel Fisher Discriminant in the Presence of Label Noise

Neil D. Lawrence, University of Sheffield
Bernhard Schölkopf, Max Planck Institute, Tübingen

in Proceedings of the International Conference in Machine Learning 18

#### Abstract

Data noise is present in many machine learning problems domains, some of these are well studied but others have received less attention. In this paper we propose an algorithm for constructing a kernel Fisher discriminant (KFD) from training examples with noisy labels. The approach allows to associate with each example a probability of the label being flipped. We utilise an expectation maximization (EM) algorithm for updating the probabilities. The E-step uses class conditional probabilities estimated as a by-product of the KFD algorithm. The M-step updates the flip probabilities and determines the parameters of the discriminant. We have applied the approach to two real-world data-sets. The results show the feasibility of the approach.

  @InProceedings{lawrence-noisy01, title = {Estimating a Kernel Fisher Discriminant in the Presence of Label Noise}, author = {Neil D. Lawrence and Bernhard Schölkopf}, booktitle = {Proceedings of the International Conference in Machine Learning}, year = {2001}, editor = {Carla Brodley and Andrea P. Danyluk}, volume = {18}, address = {San Francisco, CA}, month = {00}, publisher = {Morgan Kauffman}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2001-01-01-lawrence-noisy01.md}, url = {http://inverseprobability.com/publications/lawrence-noisy01.html}, abstract = {Data noise is present in many machine learning problems domains, some of these are well studied but others have received less attention. In this paper we propose an algorithm for constructing a kernel Fisher discriminant (KFD) from training examples with *noisy labels*. The approach allows to associate with each example a probability of the label being flipped. We utilise an expectation maximization (EM) algorithm for updating the probabilities. The E-step uses class conditional probabilities estimated as a by-product of the KFD algorithm. The M-step updates the flip probabilities and determines the parameters of the discriminant. We have applied the approach to two real-world data-sets. The results show the feasibility of the approach.}, crossref = {Brodley:icml01}, key = {Lawrence:noisy01}, linkpsgz = {ftp://ftp.dcs.shef.ac.uk/home/neil/noisyfisher.ps.gz}, linksoftware = {http://inverseprobability.com/nkfd/}, group = {shefml} }
 %T Estimating a Kernel Fisher Discriminant in the Presence of Label Noise %A Neil D. Lawrence and Bernhard Schölkopf %B %C Proceedings of the International Conference in Machine Learning %D %E Carla Brodley and Andrea P. Danyluk %F lawrence-noisy01 %I Morgan Kauffman %P -- %R %U http://inverseprobability.com/publications/lawrence-noisy01.html %V 18 %X Data noise is present in many machine learning problems domains, some of these are well studied but others have received less attention. In this paper we propose an algorithm for constructing a kernel Fisher discriminant (KFD) from training examples with *noisy labels*. The approach allows to associate with each example a probability of the label being flipped. We utilise an expectation maximization (EM) algorithm for updating the probabilities. The E-step uses class conditional probabilities estimated as a by-product of the KFD algorithm. The M-step updates the flip probabilities and determines the parameters of the discriminant. We have applied the approach to two real-world data-sets. The results show the feasibility of the approach. 
 TY - CPAPER TI - Estimating a Kernel Fisher Discriminant in the Presence of Label Noise AU - Neil D. Lawrence AU - Bernhard Schölkopf BT - Proceedings of the International Conference in Machine Learning PY - 2001/01/01 DA - 2001/01/01 ED - Carla Brodley ED - Andrea P. Danyluk ID - lawrence-noisy01 PB - Morgan Kauffman SP - EP - UR - http://inverseprobability.com/publications/lawrence-noisy01.html AB - Data noise is present in many machine learning problems domains, some of these are well studied but others have received less attention. In this paper we propose an algorithm for constructing a kernel Fisher discriminant (KFD) from training examples with *noisy labels*. The approach allows to associate with each example a probability of the label being flipped. We utilise an expectation maximization (EM) algorithm for updating the probabilities. The E-step uses class conditional probabilities estimated as a by-product of the KFD algorithm. The M-step updates the flip probabilities and determines the parameters of the discriminant. We have applied the approach to two real-world data-sets. The results show the feasibility of the approach. ER - 
 Lawrence, N.D. & Schölkopf, B.. (2001). Estimating a Kernel Fisher Discriminant in the Presence of Label Noise. Proceedings of the International Conference in Machine Learning 18:-