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DROP Spaces

DROP Spaces implements R1 and Rd Vector/Tensor Spaces (Validated and/or Normed), and Function Classes off of them.

Component Packages

  • Big DROP Spaces Big Package contains Big-data In-place Manipulation Utilities.

  • Cover DROP Spaces Cover Package implements the Vector Spaces Covering Number Estimator.

  • Function Class DROP Spaces Function Class Package implements the Normed Finite Spaces Function Class.

  • Instance DROP Spaces Instance Package implements Validated Continuous/Combinatorial Metric Spaces.

  • Iterator DROP Spaces Iterator Package implements the Iterative/Exhaustive Vector Space Scanners.

  • Metric DROP Spaces Metric Package contains the Hilbert/Banach Normed Metric Spaces.

  • RxToR1 DROP Spaces RxToR1 Package contains the Rx -> R1 Normed Function Spaces.

  • RxToRd DROP Spaces RxToRd Package contains the Rx -> Rd Normed Function Spaces.

  • Tensor DROP Spaces Tensor Package contains the Rx Continuous/Combinatorial Tensor Spaces.

References

  • Alon, N., S. Ben-David, N. Cesa-Bianchi, and D. Haussler (1993): Scale-sensitive Dimensions, Uniform-Convergence, and Learnability Proceedings of the ACM Symposium on the Foundations of Computer Science

  • Bartlett, P. L., S. R. Kulkarni, and S. E. Posner (1997): Covering Numbers for Real-valued Function Classes IEEE Transactions on Information Theory 43 (5) 1721-1724

  • Birge, L. (1987): Estimating a Density Under Order Restrictions: Non-asymptotic Minimax Risk Annals of Statistics 15 995-1012

  • Carl, B. (1985): Inequalities of the Bernstein-Jackson type and the Degree of Compactness of Operators in Banach Spaces Annals of the Fourier Institute 35 (3) 79-118

  • Carl, B., and I. Stephani (1990): Entropy, Compactness, and the Approximation of Operators Cambridge University Press Cambridge UK

  • Guo, Y., P. L. Bartlett, J. Shawe-Taylor, and R. C. Williamson (1999): Covering Numbers for Support Vector Machines, in: Proceedings of the 12th Annual Conference of Computational Learning Theory ACM New York 267-277

  • Knuth, D. (1973): The Art of Computer Programming Addison-Wesley

  • Oracle (2018): LinkedList (Java Platform SE 7) https://docs.oracle.com/javase/7/docs/api/java/util/LinkedList.html

  • Pollard, D. (1984): Convergence of Stochastic Processes Springer New York

  • Williamson, R. C., A. J. Smola, and B. Scholkopf (2000): Entropy Numbers of Linear Function Classes, in: Proceedings of the 13th Annual Conference on Computational Learning Theory ACM New York

DROP Specifications