# Carousel Greedy Algorithms for Feature Selection in Linear Regression
## 5 Conclusions and Future Work  
In this paper, we propose an application of CG to the feature selection problem. The approach is straightforward and does not require any commercial optimization software. It is also easy to understand. It provides a compromise solution between the best subset selection and stepwise regression. The running time of CG is usually much shorter than that of the best subset selection and a few times longer than that of stepwise regression. The RSS of CG is always at least as good as for stepwise regression, but is typically not as good as for best subset. Therefore, CG is a very practical method for obtaining (typically) near-optimal solutions to the best subset selection problem.  
With respect to the practical implications of our work, we point to the pervasiveness of greedy algorithms in the data science literature. Several well-known applications of the greedy algorithm include constructing a minimum spanning tree, implementing a Huffman encoding, and solving graph optimization problems (again, see [1]). In addition, numerous greedy algorithms have been proposed in the machine learning literature over the last 20 years for a wide variety of problems (e.g., see [34; 35; 36; 37; 38]). CG may not be directly applicable in every case, but we expect that it can be successfully applied in many of these cases.  
We also show that the result of our CG can produce a so-called FSI(1) minimum. Finally, we provide some generalizations to more complicated feature selection problems in Section 4.  
The implementation of CG still has some room for improvement. We leave this for future work, but here are some ideas. The computational experiments in this paper are based mainly on Algorithm 3, which includes a set of default parameter values. However, if we work from Algorithm 2, there may be a better set of parameter values, in general, or there may be better values for specific applications. Extensive computational experiments would have to focus on running time and accuracy in order to address this question. Furthermore, we think there are some more advanced results from numerical linear algebra that can be applied to improve the running time of the sequence of OLS problems that must be solved within CG. In addition, we think our approach can be applied to other problems in combinatorial optimization and data science. For example, we are beginning to look into the integration of neural networks and CG. The key idea is to replace the greedy selection function with a specifically trained neural network. CG could be employed to enhance the decisions recommended by the neural network. Again, we hope to explore this in future work.  
**Author Contributions:** Conceptualization, B.G.; methodology, J.W., B.G. and C.C.; software, J.W.; validation, J.W., B.G. and C.C.; formal analysis, J.W.; investigation, J.W.; resources, B.G. and C.C.; data curation, J.W.; writing--original draft preparation, J.W.; writing--review and editing, B.G.; visualization, J.W.; supervision, B.G. and C.C.; project administration, B.G. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Data Availability Statement:** The datasets presented in this study are available in UCI ML Repository at [[https://archive.ics.uci.edu/](https://archive.ics.uci.edu/)]([https://archive.ics.uci.edu/](https://archive.ics.uci.edu/)) ( accessed on 11 April 2023).  
**Conflicts of Interest:** The authors declare no conflict of interest.