Dictionary of Applied Machine Learning

model

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In machine learning (ML), the word model is used in different ways. Formally, a model is a hypothesis space $\hypospace$: the set of candidate hypothesis maps from which an ML method picks (or learns) one. In applied ML literature and in software libraries, the word model also refers to the trained predictor, i.e., to the learned hypothesis returned by an ML algorithm; the EU AI Act uses this sense in the compound term general-purpose AI model (GPAI model). A different type of mathematical model is a probabilistic model, which specifies a family of probability distributions that characterize a data generation process.

Definition

Consider the problem of predicting tomorrow's maximum daytime temperature from today's morning temperature. Machine learning (ML) methods learn a hypothesis map $\learnthypothesis$ that reads in today's morning temperature and delivers an accurate prediction of tomorrow's maximum temperature. This learned hypothesis is chosen from a (typically large) set of candidate hypothesis maps, i.e., a hypothesis space $\hypospace$.

The hypothesis space underlying an ML application is often referred to as the model of the method (Goodfellow et al., 2016, Sect. 5.1). For example, linear regression and logistic regression use the linear model as hypothesis space. A decision tree method uses a hypothesis space that consists of hypothesis maps generated by a flow chart. Large language model (LLM) systems use a hypothesis space consisting of non-linear maps represented by an artificial neural network (ANN).

Model training refers to the process of finding a hypothesis in the hypothesis space that yields accurate predictions. Strictly speaking, a trained (or fitted) model represents a learned hypothesis $\learnthypothesis$. In applied ML literature and in software libraries, the word model typically refers to a trained model, i.e., to a specific hypothesis map $\learnthypothesis$ (Goodfellow et al., 2016, Sect. 5.1; Murphy, 2012, Sect. 3.5.2; Prince, 2023). The EU AI Act uses the word model in the same sense (i.e., a learned hypothesis) in the compound term general-purpose AI model (GPAI model) (Parliament and Union, 2024, Art. 3(63)).

A different type of mathematical model is a probabilistic model, which specifies a family of probability distributions. Each such probability distribution defines a data generator: data points are realizations of independent and identically distributed (i.i.d.) random variables (RVs) with the given probability distribution.

Fig. 1 illustrates these three uses of the word model: the hypothesis space, the trained model, and the probabilistic model.

Figure 1 of the entry model
Figure 1: Three uses of the word model in ML practice. (a) Hypothesis space consisting of three linear maps. (b) Trained model: the learned hypothesis $\learnthypothesis = \algomap(\trainset)$ selected from the hypothesis space in (a) by an ML map $\algomap$ acting on a training set $\trainset$ of data points (blue circles). (c) Probabilistic model consisting of two probability distributions for the generation of data points with feature $\feature$ and label $\truelabel$
Synonyms: hypothesis space, hypothesis class, model class.

See also: hypothesis space, hypothesis, model parameter, parametric model, training, empirical risk minimization, probabilistic model, probability distribution, decision tree, neuron, artificial neural network, transformer, large language model, general-purpose AI model, artificial intelligence system.

References

  1. Goodfellow et al. (2016). Deep Learning. MIT Press.
  2. Murphy (2012). Machine Learning: A Probabilistic Perspective. MIT Press.
  3. Prince (2023). Understanding Deep Learning. MIT Press.
  4. Parliament and Union (2024). Regulation (EU) 2024/1689 of the European Parliament and of the Council of 13 June 2024 laying down harmonised rules on artificial intelligence and amending Regulations (EC) No 300/2008, (EU) No 167/2013, (EU) No 168/2013, (EU) 2018/858, (EU) 2018/1139 and (EU) 2019/2144 and Directives 2014/90/EU, (EU) 2016/797 and (EU) 2020/1828 (Artificial Intelligence Act) (Text with EEA relevance).

Cite this entry

@misc{dictml_model,
  author = {Jung, Alexander},
  title = {model},
  howpublished = {Dictionary of Applied Machine Learning (course edition)},
  year = {2026},
  doi = {10.5281/zenodo.21569296},
  note = {ISBN 978-952-64-3013-3, CC BY 4.0, retrieved 2026-08-06},
  url = {https://dictionaryofml.org/terms/model.html}
}