Amplification

Let [construct space] 𝑌 ′ and [prediction space] 𝑌ˆ be categorical. Then, a model exhibits disparity amplification if 𝑑tv (𝑌ˆ |𝑍=0,𝑌ˆ |𝑍=1) 𝑑tv (𝑌 ′ |𝑍=0,𝑌 ′ |𝑍=1). dtv is the total variation distance defined as follows. Let 𝑌0 and 𝑌1 be categorical random variables with finite supports Y0 and Y1. Then, the total variation distance between 𝑌0 and 𝑌1 is 𝑑tv (𝑌0,𝑌1) = 12 Σ︁ 𝑦∈Y0∪Y1 Pr[𝑌0=𝑦] − Pr[𝑌1=𝑦] . In the special case where 𝑌0,𝑌1 ∈ {0, 1}, the total variation distance can also be expressed as | Pr[𝑌0=1] − Pr[𝑌1=1] |.