An “induction principle”

Question

In section 4 Empirical Risk Minimzation of the paper Principles of Risk Minimization for Learning Theory by V. Vapnik, the author says the following:

In order to solve this problem, the following induction principle is proposed: the
risk functional $R(w)$ is replaced by the empirical risk functional
$$E(w) = \dfrac{1}{\mathscr{l}} \sum_{i = 1}^\mathscr{l} L(y_i, f(x_i, w)) \tag{3}$$
constructed on the basis of the training set (1). The induction principle of empirical risk minimization (ERM) assumes that the function $f(x, w^*_\mathscr{l})$, which minimizes $E(w)$ over the set $w \in W$, results in a risk $R(w^*_\mathscr{l})$ which is close to its minimum.

I am familiar with mathematical induction, such as in proofs, but what is an "induction principle", in general?

EDIT: It seems to me like the author's using "induction principle" here to refer to any principle (such as a mathematical expression) that allows one to induce some value? In this case, using the empirical risk functional $E(w)$ to find the risk $R(w^*_\mathscr{l})$ which is close to its minimum

Answer 1

The word comes from the way human think inductively from empirical experiment in contrast to deduction reasoning.

As stated in Statistical Induction Principle:

Inductive statistics is way for scientists to make evidence-based decisions based on empirical/experimental results.

Methods of inductive statistics (so called statistical induction) can under given assumptions to make general conclusions and to objectively enumerate their degree of confidence. The main aim of inductive statistics is to elaborate procedures how to create general conclusions from empirical data that can substitute subjective inductive thinking by objective inductive thinking based on concepts of probability theory.