Question: What are the three measures of bias which are reduced in experiments?
Evidence: Geometric bias mitigation uses the cosine distances between words to both measure and remove gender bias BIBREF0. This method implicitly defines bias as a geometric asymmetry between words when projected onto a subspace, such as the gender subspace constructed from a set of gender pairs such as $\mathcal {P} = \lbrace (he,she),(man,woman),(king,queen)...\rbrace $. The projection of a vector $v$ onto $B$ (the subspace) is defined by $v_B = \sum _{j=1}^{k} (v \cdot b_j) b_j$ where a subspace $B$ is defined by k orthogonal unit vectors $B = {b_1,...,b_k}$.
The WEAT statistic BIBREF1 demonstrates the presence of biases in word embeddings with an effect size defined as the mean test statistic across the two word sets:
Where $s$, the test statistic, is defined as: $s(w,A,B) = mean_{a \in A} cos(w,a) - mean_{b \in B} cos(w,a)$, and $X$,$Y$,$A$, and $B$ are groups of words for which the association is measured. Possible values range from $-2$ to 2 depending on the association of the words groups, and a value of zero indicates $X$ and $Y$ are equally associated with $A$ and $B$. See BIBREF4 for further details on WEAT.
The RIPA (relational inner product association) metric was developed as an alternative to WEAT, with the critique that WEAT is likely to overestimate the bias of a target attribute BIBREF4. The RIPA metric formalizes the measure of bias used in geometric bias mitigation as the inner product association of a word vector $v$ with respect to a relation vector $b$. The relation vector is constructed from the first principal component of the differences between gender word pairs. We report the absolute value of the RIPA metric as the value can be positive or negative according to the direction of the bias. A value of zero indicates a lack of bias, and the value is bound by $[-||w||,||w||]$.
The neighborhood bias metric proposed by BIBREF5 quantifies bias as the proportion of male socially-biased words among the $k$ nearest socially-biased male and female neighboring words, whereby biased words are obtained by projecting neutral words onto a gender relation vector. As we only examine the target word among the 1000 most socially-biased words in the vocabulary (500 male and 500 female), a word’s bias is measured as the ratio of its neighborhood of socially-biased male and socially-biased female words, so that a value of 0.5 in this metric would indicate a perfectly unbiased word, and values closer to 0 and 1 indicate stronger bias.
FLOAT SELECTED: Table 1: Remaining Bias (as measured by RIPA and Neighborhood metrics) in fastText embeddings for baseline (top two rows) and our (bottom three) methods. Figure 2: Remaining Bias (WEAT score)
Geometric bias mitigation uses the cosine distances between words to both measure and remove gender bias BIBREF0.
The WEAT statistic BIBREF1 demonstrates the presence of biases in word embeddings with an effect size defined as the mean test statistic across the two word sets:

Where $s$, the test statistic, is defined as: $s(w,A,B) = mean_{a \in A} cos(w,a) - mean_{b \in B} cos(w,a)$, and $X$,$Y$,$A$, and $B$ are groups of words for which the association is measured.
The RIPA (relational inner product association) metric was developed as an alternative to WEAT, with the critique that WEAT is likely to overestimate the bias of a target attribute BIBREF4. 
The neighborhood bias metric proposed by BIBREF5 quantifies bias as the proportion of male socially-biased words among the $k$ nearest socially-biased male and female neighboring words, whereby biased words are obtained by projecting neutral words onto a gender relation vector.
FLOAT SELECTED: Table 1: Remaining Bias (as measured by RIPA and Neighborhood metrics) in fastText embeddings for baseline (top two rows) and our (bottom three) methods. Figure 2: Remaining Bias (WEAT score)
Answer: RIPA, Neighborhood Metric, WEAT