Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Notation
- 1 Orientation
- 2 Supervised Learning Warm-Up
- 3 Unsupervised Learning Warm-Up
- 4 Interlude: Probability, Likelihood and Bayes
- 5 Probabilistic Modelling
- 6 Frequentist and Bayesian Uncertainty
- 7 Frequentist Linear Regression
- 8 Directed Graphical Models
- 9 Bayesian Linear Regression, Priors, and Regularisation
- 10 Bayesian Methods
- 11 Classification
- 12 Unsupervised Learning: A Deeper Dive
- 13 Neural Networks and Deep Learning
- 14 Expanding the Toolkit
- Appendix A Probability Theory
- Appendix B Linear Algebra
- Appendix C Jensen’s and Gibbs’ Inequalities
- References
- Index
3 - Unsupervised Learning Warm-Up
Published online by Cambridge University Press: aN Invalid Date NaN
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Notation
- 1 Orientation
- 2 Supervised Learning Warm-Up
- 3 Unsupervised Learning Warm-Up
- 4 Interlude: Probability, Likelihood and Bayes
- 5 Probabilistic Modelling
- 6 Frequentist and Bayesian Uncertainty
- 7 Frequentist Linear Regression
- 8 Directed Graphical Models
- 9 Bayesian Linear Regression, Priors, and Regularisation
- 10 Bayesian Methods
- 11 Classification
- 12 Unsupervised Learning: A Deeper Dive
- 13 Neural Networks and Deep Learning
- 14 Expanding the Toolkit
- Appendix A Probability Theory
- Appendix B Linear Algebra
- Appendix C Jensen’s and Gibbs’ Inequalities
- References
- Index
Summary
In this chapter, we explore an unsupervised learning problem: estimating a distribution function from two-dimensional data. Although there is no response variable, the workflow mirrors that of supervised learning. We select the best-fitting function within a family by maximising the sum of the log of the distribution's values at the observed data points. As in supervised learning, excessive flexibility leads to overfitting, while insufficient flexibility leads to underfitting. We use cross-validation to identify a function family that achieves a happy medium.
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- Inference in Statistical Modelling and Machine LearningA Concise Introduction, pp. 24 - 35Publisher: Cambridge University PressPrint publication year: 2026
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