Multi-class Importance Weighted Kernel Logistic Regression (IWKLR)

Introduction

It solves the multi-class classification problems under semi-supervised learning condition using the weighted version of kernel logistic regression (KLR):

widetilde{{cal P}}_{delta}^{log}({mathrm V}; {cal Z}^{tr}) = -sum_{i = 1}^{n_{tr}} w({mathrm X}_i) log P(y_i | {mathrm X}_i, {mathrm V}) + frac{delta}{2} textnormal{trace} ({mathrm V} {mathrm K} {mathrm V}^{top}).

Especially, we aim to solve the semi-supervised classification problem under covariate shift, where the input distributions are different in the training and test phases but the conditional distribution of labels remains unchanged.

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Features

  • Can solve semi-supervised multi-class classification problems under covariate shift.

  • Can use designed kernels by users.

  • Can output class-posterior probabilities.

  • Written in mex function with BLAS.

Usage

  • Download & compile the source code.

  • Download the density ratio estimation scripts here (Software)

  • Run the script.

Examples (Toy data)

IWKLR 

Examples (Real data)

License

Copyright (c) 2010 Makoto Yamada

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Acknowledgement

I am grateful to Prof. Tomoko Matsui, Prof. Masashi Sugiyama, Mr. Christoph Sawade, and Mr. Arvid Terzibaschian for their support in developing this software.

Contact

I am happy to have any kind of feedbacks. E-mail: yamada AT sg DOT cs DOT titech DOT ac DOT jp

Reference

Yamada, M., Sugiyama, M., & Matsui, T.
Semi-supervised speaker identification under covariate shift.
Signal Processing, vol.90, no.8, pp.2353-2361, 2010.
[paper]