Generative Local Metric Learning for Kernel Regression
This paper shows how metric learning can be used with Nadaraya-Watson (NW) kernel regression. Compared with standard approaches, such as bandwidth selection, we show how metric learning can significantly reduce the mean square error (MSE) in kernel regression, particularly for high-dimensional data. We propose a method for efficiently learning a good metric function based upon analyzing the performance of the NW estimator for Gaussian-distributed data. A key feature of our approach is that the NW estimator with a learned metric uses information from both the global and local structure of the training data. Theoretical and empirical results confirm that the learned metric can considerably reduce the bias and MSE for kernel regression even when the data are not confined to Gaussian.
Metric learning is one of the fundamental problems in person re-identification. This paper presents a metric learning method using Nadaraya-Watson (NW) kernel regression. The key feature of the work is that the NW estimator with a learned metric uses information from both the global and local structure of the training data. Theoretical and empirical 9 results confirm that the learned metric can considerably reduce the bias and MSE for kernel regression even when the data are not confined to Gaussian.
The main contribution lies in the following aspects: 
1.	Provided a formation on how metric learning can be embedded in a kernel regression method.
2.	Proposed and proved a theorem that guarantees the existence of a good metric that can eliminate the leading order bias at any point regardless of assumption of Gaussian distribution of the data.
3.	Under Gaussian model assumption, provided an efficient algorithm that can guarantee to achieve an optimal metric solution for reducing regression error. 
Overall, this paper’s reasoning is rigorous. Description is clear. The experiments sufficiently demonstrate the author’s claims for the proposed method.
However, it needs major revision before it is accepted. My comments are as follows:
1. The structure of the paper is confused. I suggest the authors add contributions of the papers in the introduction section. The usage and importance of this paper needs to be further clarified.
2.  I also find some grammar problems in this paper. Author needs to carefully check these mistakes, which is very important for readers. 
3. The limitations of the proposed method are scarcely discussed.
4. The works also cannot describe the latest developments since there are too few references after 2016.
5. The authors only show very few experiments results in section 5, I think it is not enough. Except MSE, the authors also should provide other comparisons, such as Root mean squared error of classication accuracy(RMSE) or MSE, etc. In this way, the results of the paper will be more reasonable.