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Mathematical Background of Machine Learning

Abstract

This chapter classifies the different machine learning algorithms into domains and provides a formal definition of machine learning. In addition, the chapter describes briefly a common set of the classic machine learning techniques. These sets span from time series forecasting to different clustering methods including trees and Bayesian networks. The special domain of deep learning is addressed in the following chapter (Liermann, Li, & Schaudinnus, Deep learning—An introduction, 2019b).

Keywords

  • Machine learning
  • Supervised learning
  • Unsupervised learning
  • Reinforcement learning
  • Linear regression
  • Clustering
  • Connectivity-based models
  • K-fold cross-validation model validation
  • Bayesian network
  • Fraud detection

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Notes

  1. 1.

    Typically, in semi-supervised learning, a small amount of labeled data with a large amount of unlabeled data.

  2. 2.

    Unweighted pair group method with arithmetic mean or UPGMA SeeSeeUnweighted pair group method with arithmetic mean .

  3. 3.

    Ordering points to identify the clustering structure (see Ankerst, Breunig, Kriegel, & Sander, 1999).

  4. 4.

    Density-based spacial clustering of applications with noise (see Ester, Kriegel, Sander, & Xu, 1996).

  5. 5.

    Density-link clustering (see Achtert, Böhm, & Kröger, 2006).

  6. 6.

    Access method for multi-dimensional data, made to structure indexed records (see Guttman, 1984).

  7. 7.

    Tsamardinos, Aliferis, and Statnikov (2003), Yaramakala and Margaritis (2005).

  8. 8.

    Hard or crisp clustering involves strict and excluding placement of a data point in relation to a particular cluster, meaning that an observation cannot belong to two or more clusters at the same time. This would be possible under using fuzzy or soft partitioning and one point would belong to clusters to differing extents.

  9. 9.

    The list of CVIs is taken from Sarda-Espinosa (2019).

  10. 10.

    C stands for criterion.

  11. 11.

    In case of interest, one can refer to Desgraupes (2019).

  12. 12.

    The importance of the deep learning models described in Liermann et al., Deep learning—An introduction (2019b) could possible increase more dynamically.

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Liermann, V., Li, S., Dobryashkina, V. (2019). Mathematical Background of Machine Learning. In: Liermann, V., Stegmann, C. (eds) The Impact of Digital Transformation and FinTech on the Finance Professional. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-23719-6_16

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  • DOI: https://doi.org/10.1007/978-3-030-23719-6_16

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