1. Learning piecewise linear classifiers via Dirichlet Process
Ya Xue and Xuejun Liao
22 April 2005

2. Piecewise linear classifier
A piecewise linear classifier is a classifier that generates a piecewise linear decision boundary.
Consider the binary problem where the labeled data
We assume that each Dj contains at least one positive sample and one negative sample.
Associated with each Dj there is a linear classifier parameterized by wj
Assume Dj is primitive and the samples in it are always linearly separable

3. Piecewise linear classifier (cont’d)
It turns out that many of wj will become identical to each other, yielding a small number of distinct representative w’s.
Each distinct w represents a linear boundary that separate a subset of the samples in D and the ensemble of w gives us the piecewise linear boundary.
We use Dirichlet Process to learn wij , and automatically discover the piecewise linear boundary from wij

4. Gibbs Sampling of the Posterior Dirichlet Process

5. Results I
1000 burn-ins and 1000 samples.

9. Results II

13. Results M-Logit-DP 200 primary data and 200 auxiliary data.
5 labeled primary data.
MCMC: 3000 burn-ins and 1000 samples.