Machine Learning Estimators: Implementation and Comparison in Python
-
Fabian Merle
Abstract
We compare different machine learning estimators and present details about their implementation in Python. The computational studies are conducted for classification as well as regression problems. Moreover, as one of the founding problems of machine learning, we present the specific classification task of handwritten digit recognition. In this connection, we discuss the mathematical formulation and of course the implementation details of this problem. All corresponding Python code is fully provided on request and can be downloaded from the author’s GitHub page https://github.com/Fab1Fatal.
References
[1] L. Devroye, L. Györfi and G. Lugosi, A Probabilistic Theory of Pattern Recognition, Appl. Math. (New York) 31, Springer, New York, 1996. 10.1007/978-1-4612-0711-5Search in Google Scholar
[2] T. Dunst and A. Prohl, The forward-backward stochastic heat equation: Numerical analysis and simulation, SIAM J. Sci. Comput. 38 (2016), 10.1137/15M1022951. 10.1137/15M1022951Search in Google Scholar
[3] L. Györfi, M. Kohler, A. Krzyzak and H. Walk, A Distribution-Free Theory of Nonparametric Regression, Springer Ser. Statist., Springer, New York, 2002. 10.1007/b97848Search in Google Scholar
[4] C. F. Higham and D. J. Higham, Deep learning: An Introduction for applied mathematicians, SIAM Rev. 61 (2019), 10.1137/18M1165748. 10.1137/18M1165748Search in Google Scholar
[5] I. Steinwart and A. Christmann, Support Vector Machines, Inform. Sci. Statist., Springer, New York, 2008. Search in Google Scholar
[6] https://en.wikipedia.org/wiki/Normalization_(image_processing). Search in Google Scholar
[7] https://en.wikipedia.org/wiki/Spatial_anti-aliasing. Search in Google Scholar
[8] https://github.com/Fab1Fatal. Search in Google Scholar
[9] https://scikit-learn.org/stable/. Search in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Convergence of an Operator Splitting Scheme for Fractional Conservation Laws with Lévy Noise
- The Partition of Unity Finite Element Method for the Schrödinger Equation
- Analysis and Numerical Simulation of Time-Fractional Derivative Contact Problem with Friction in Thermo-Viscoelasticity
- A Numerical Study of a Stabilized Hyperbolic Equation Inspired by Models for Bio-Polymerization
- Discontinuous Galerkin Methods for the Vlasov–Stokes System
- HDG Method for Nonlinear Parabolic Integro-Differential Equations
- Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem
- Machine Learning Estimators: Implementation and Comparison in Python
- Quasi-Optimality of an AFEM for General Second Order Elliptic PDE
- Quadratic Discontinuous Galerkin Finite Element Methods for the Unilateral Contact Problem
- A Novel Fully Decoupled Scheme for the MHD System with Variable Density
- A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control
Articles in the same Issue
- Frontmatter
- Convergence of an Operator Splitting Scheme for Fractional Conservation Laws with Lévy Noise
- The Partition of Unity Finite Element Method for the Schrödinger Equation
- Analysis and Numerical Simulation of Time-Fractional Derivative Contact Problem with Friction in Thermo-Viscoelasticity
- A Numerical Study of a Stabilized Hyperbolic Equation Inspired by Models for Bio-Polymerization
- Discontinuous Galerkin Methods for the Vlasov–Stokes System
- HDG Method for Nonlinear Parabolic Integro-Differential Equations
- Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem
- Machine Learning Estimators: Implementation and Comparison in Python
- Quasi-Optimality of an AFEM for General Second Order Elliptic PDE
- Quadratic Discontinuous Galerkin Finite Element Methods for the Unilateral Contact Problem
- A Novel Fully Decoupled Scheme for the MHD System with Variable Density
- A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control
