# 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.

Planted:
by L Ma;

References:

Dynamic Backlinks to

`cards/machine-learning/learning-theories/learning-problem`

:`cards/machine-learning/learning-theories/learning-problem`

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