Abstract
It has been observed that a particular form of analogical inference, based on analogical proportions,
yields competitive results in classification tasks.
Using the algebraic normal form of Boolean functions, it has been shown that analogical prediction
is always exact iff the labeling function is affine.
We point out that affine functions are also meaningful when using another view of analogy. We address the accuracy of analogical inference for arbitrary Boolean functions and show that if a function
is epsilon-close to an affine function, then the probability
of making a wrong prediction is upper bounded by
4 epsilon. This result is confirmed by an empirical study
showing that the upper bound is tight. It highlights
the specificity of analogical inference,
also characterized in terms of the Hamming distance.
Keywords
- Machine Learning: Classification
- Knowledge Representation and Reasoning: Qualitative Reasoning
