Consider gender debiasing regularization for word embeddings. The following are the word embeddings. Wg $(.)$ and Wa $(.)$ are the gender related and gender neutral parts.

$($i$)$ Calculate the gendered word regulating component J D$.$

$($ii$)$ Calculate the gender neutral word regulating component J E$.$

Word male seed word female seed word wg$(1)$ wg$(2)$ wg$(3)$ wa$(1)$ wa$(2)$

father yes $0\mathrm{.}80\mathrm{.}70\mathrm{.}40\mathrm{.}70\mathrm{.}6$

son yes $0\mathrm{.}750\mathrm{.}60\mathrm{.}30\mathrm{.}60\mathrm{.}5$

mother yes $0\mathrm{.}40\mathrm{.}40\mathrm{.}50\mathrm{.}40\mathrm{.}7$

daughter yes $0\mathrm{.}30\mathrm{.}50\mathrm{.}60\mathrm{.}30\mathrm{.}6$

teacher $0\mathrm{.}40\mathrm{.}30\mathrm{.}80\mathrm{.}80\mathrm{.}1$

doctor $0\mathrm{.}20\mathrm{.}10\mathrm{.}80\mathrm{.}40\mathrm{.}3$