Adapting Component Analysis

A main problem in machine learning is to predict the response variables of a test set given the training data and its corresponding response variables. A predictive model can perform satisfactorily only if the training data is an appropriate representative of the test data. This is usually reflected in the assumption that the training data and the test data are drawn from the same underlying probability distribution. However, the assumption may not be correct in many applications for various reasons. We propose a method based on kernel distribution embedding and Hilbert-Schmidt Independence Criterion (HSIC) to address this problem. The proposed method explores a new representation of the data in a new feature space with two properties: (i) the distributions of the training and the test data sets are as close as possible in the new feature space, and (ii) the important structural information of the data is preserved. The algorithm can reduce the dimensionality of the data while it preserves the aforementioned properties and therefore it can be seen as a dimensionality reduction method as well. Our method has a closed-form solution and the experimental results show that it works well in practice.