Advertisement

Dynamic Mutation Based Pareto Optimization for Subset Selection

  • Mengxi Wu
  • Chao Qian
  • Ke Tang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10956)

Abstract

Subset selection that selects the best k variables from n variables is a fundamental problem in many areas. Pareto optimization for subset selection (called POSS) is a recently proposed approach for subset selection based on Pareto optimization and has shown good approximation performances. In the reproduction of POSS, it uses a fixed mutation rate, which may make POSS get trapped in local optimum. In this paper, we propose a new version of POSS by using a dynamic mutation rate, briefly called DM-POSS. We prove that DM-POSS can achieve the best known approximation guarantee for the application of sparse regression in polynomial time and show that DM-POSS can also empirically perform well.

Keywords

Subset selection Pareto optimization Sparse regression Dynamic mutation 

References

  1. 1.
    Das, A., Kempe, D.: Submodular meets spectral: Greedy algorithms for subset selection, sparse approximation and dictionary selection. In: 28th International Conference on Machine Learning, Bellevue, WA, pp. 1057–1064 (2011)Google Scholar
  2. 2.
    Davis, G., Mallat, S., Avellaneda, M.: Adaptive Greedy approximations. Constr. Approx. 13(1), 57–98 (1997)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Doerr, B., Le, H.P., Makhmara, R., Nguyen, T.D.: Fast genetic algorithms. In: 19th ACM Genetic and Evolutionary Computation Conference, Berlin, Germany, pp. 777–784 (2017)Google Scholar
  4. 4.
    Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoret. Comput. Sci. 276(1–2), 51–58 (2002)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Fischer, S., Wegener, I.: The one-dimensional Ising model: mutation versus recombination. Theoret. Comput. Sci. 344(2–3), 208–225 (2005)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Giel, O., Wegener, I.: Evolutionary algorithms and the maximum matching problem. In: 20th Annual Symposium on Theoretical Aspects of Computer Science, London, UK, pp. 415–426 (2003)Google Scholar
  7. 7.
    Gilbert, A.C., Muthukrishnan, S., Strauss, M.J.: Approximation of functions over redundant dictionaries using coherence. In: 14th Annual ACM-SIAM symposium on Discrete Algorithms, Baltimore, MA, pp. 243–252 (2003)Google Scholar
  8. 8.
    Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, D.C., pp. 137–146 (2003)Google Scholar
  9. 9.
    Miller, A.: Subset Selection in Regression. CRC Press, Boca Raton (2002)CrossRefGoogle Scholar
  10. 10.
    Qian, C., Yu, Y., Zhou, Z.H.: Subset selection by Pareto optimization. In: Advances in Neural Information Processing Systems 28, Montreal, Canada, pp. 1774–1782 (2015)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Anhui Province Key Lab of Big Data Analysis and ApplicationUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Shenzhen Key Lab of Computational IntelligenceSouthern University of Science and TechnologyShenzhenChina

Personalised recommendations