Abstract
We consider the problem of assigning an input vector to one of m classes by predicting P(c|x) for c=1,...,m. For a two-class problem, the probability of class one given x is estimated by s(y(x)), where s(y)=1/(1+e-y). A Gaussian process prior is placed on y(x), and is combined with the training data to obtain predictions for new x points. We provide a Bayesian treatment, integrating over uncertainty in y and in the parameters that control the Gaussian process prior the necessary integration over y is carried out using Laplace's approximation. The method is generalized to multiclass problems (m>2) using the softmax function. We demonstrate the effectiveness of the method on a number of datasets.
| Original language | English |
|---|---|
| Pages (from-to) | 1342 -1351 |
| Number of pages | 10 |
| Journal | IEEE Transactions on Pattern Analysis and Machine Intelligence |
| Volume | 20 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 12 Dec 1998 |
Bibliographical note
©1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.Keywords
- assigning
- input vector
- probability
- Gaussian process
- training data
- predictions
- Bayesian treatment prior
- uncertainty
- Laplace
- approximation
- multi-class problems
- softmax function