Futility of Bias-Free Learning
- A learner that makes no a priori assumptions regarding
the identity of the target concept has no rational basis for
classifying any unseen instances.
- So, what is the inductive bias?
- Given an algorithm $L$ and a set of training instances
$D_c = \{\langle x,c(x) \rangle\}$, let $L(x_i,D_c)$ be the
classification given to $x_i$ by $L$ after training on
$D_c$. The inductive bias of $L$ is any minimal set
of assertions $B$ for any target concept $c$ and examples $D$
s.t.
\[\forall_{x_i \in X} B \wedge D_c \wedge x_i \entails L(x_i, D_c) \]
- For example, the inductive bias of the
Candidate-Elimination algorithm (with voting) is the
assumption that the target concept is contained in the
hypothesis space.
- That is, if we make that assumption then the
classification follows logically (by
deduction).
José M. Vidal
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