The Learning Problem

The learning problem posed by Vapnik:1

  • Given a sample: $\{z_i\}$ in the probability space $Z$;
  • Assuming a probability measure on the probability space $Z$;
  • Assuming a set of functions $Q(z, \alpha)$ (e.g. loss functions), where $\alpha$ is a set of parameters;
  • A risk functional to be minimized by tunning “the handles” $\alpha$, $R(\alpha)$.

The risk functional is

$$ R(\alpha) = \int Q(z, \alpha) \,\mathrm d F(z). $$

A learning problem is the minimization of this risk.


  1. Vapnik2000 Vladimir N. Vapnik. The Nature of Statistical Learning Theory. 2000. doi:10.1007/978-1-4757-3264-1  ↩︎

Planted: by ;

L Ma (2021). 'The Learning Problem', Datumorphism, 05 April. Available at: https://datumorphism.leima.is/cards/machine-learning/learning-theories/learning-problem/.