What is a seed lexicon? It's an organization of words into sets to measure bias. So if I wanted to measure the bias in word embeddings between Male and Female names, first I would collect a sets of these names.

How to test for bias in word embeddings:

1. Use Word Embedding Association Test (WEAT). Given two sets \(\mathcal{X}\) and \(\mathcal{Y}\) from a seed lexicon, e.g. Male and Female names, and two other sets \(A\) and \(B\), e.g. professional work words and domestic work words, I might want to measure if the \(\mathcal{X}\) names are associated with one set in a way that the \(\mathcal{Y}\) names are not. So, I take:

\[ s(\mathcal{X}, \mathcal{Y}, A, B) = \sum_{x\in\mathcal{X}}s(x, A, B) - \sum_{y\in\mathcal{Y}}s(y, A, B) \] where \[ s(w,A,B) = \frac{1}{|A|}\sum_{a\in A} \text{sim}(w, a) - \frac{1}{|B|}\sum_{b\in B} \text{sim}(w, b) \] and \(\text{sim}\) is cosine-similarity. Intuition: \(s(w, A, B)\) measures how much more similar \(w\) is to the set of words \(A\) and \(B\). \(s(\mathcal{X}, \mathcal{Y}, A, B)\) measures that effect in aggregate.

1. Given two sets from a seed lexicon, do PCA on all the embeddings. Measure how much variance is explained by the first component of the resulting vectors. Assuming that the first component separates based on bias, i.e. encoded cultural biases, then we will see a lot of explained separation along this axis.

Who even comes up with seed-lexicons? How sensitive are bias tests, e.g. WEAT and PCA, to swapping out different lexicons? Answer: they're somewhat sensitive. So, you should examine where you get your seed lexicons.

Bibliography

• [Antoniak2021] Antoniak & Mimno, Bad Seeds : Evaluating Lexical Methods for Bias Measurement, , (2021).