Calibrated Associative Classification

Abstract

Given an input $x_i$ and an arbitrary output $c_j,$ a classification algorithm usually works by estimating the probability of $x_i$ being related to $c_j$ (i.e., class membership probability). Well calibrated classification algorithms are those able to produce functions that provide accurate estimates of class membership probabilities, that is, the estimated probability $\hat{p}(c_j|x_i)$ is close to $p(c_j|\hat{p}(c_j|x_i)),$ which is the true, (unknown) empirical probability of $x_i$ being related to output $c_j$ given that the probability estimated by the classification algorithm is $\hat{p}(c_j|x_i).$ Calibration is not a necessary property for producing an accurate approximation of the target function, and, thus, most of the research has focused on direct accuracy maximization strategies rather than on calibration. However, non-calibrated functions are problematic in applications where the reliability associated with a prediction must be taken into account (i.e., cost-sensitive classification , cautious classifications etc.). In these applications, a sensible use of the classification algorithm must be based on the reliability of its predictions (Veloso et al. Calibrated lazy associative classification, Inform Sci, 2009), and thus, the algorithm must produce well calibrated functions. In this chapter we introduce calibrated associative classification algorithms .