Response of Loss Functions to Label Noise (draft)
August 13, 2019 · Xingyu Li · Noise and Generalization · math information theory
Distortion on dataset distribution by nosie labels Let $t$ and $t^*$ be the correct target label and the noisy label, respectively. Presently, we focus on binary classification and assume the label noise only depends on the correct label, i.e. the error rates are: $$e _- = P(t^* = +1 | t= -1) \quad \text{and} \quad e _+ = P(t^*=-1|t=+1).$$ The noisy dataset defines the joint distribution $P(x, t^*)$, which relates to the clean distribution $P(x, t)$ through
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