In recent years, word embeddings have been widely used to measure biases in texts. Even if they have proven to be effective in detecting a wide variety of biases, metrics based on word embeddings lack transparency and interpretability. We analyze an alternative PMI-based metric to quantify biases in texts. It can be expressed as a function of conditional probabilities, which provides a simple interpretation in terms of word co-occurrences. We also prove that it can be approximated by an odds ratio, which allows estimating confidence intervals and statistical significance of textual biases. This approach produces similar results to metrics based on word embeddings when capturing gender gaps of the real world embedded in large corpora.

Recent research has shown that static word embeddings can encode words’ frequencies. However, little has been studied about this behavior. In the present work, we study how frequency and semantic similarity relate to one another in static word embeddings, and we assess the impact of this relationship on embedding-based bias metrics. We find that Skip-gram, GloVe and FastText embeddings tend to produce higher similarity between high-frequency words than between other frequency combinations. We show that the association between frequency and similarity also appears when words are randomly shuffled, and holds for different hyperparameter settings. This proves that the patterns we find are neither due to real semantic associations nor to specific parameters choices, and are an artifact produced by the word embeddings. To illustrate how frequencies can affect the measurement of biases related to gender, ethnicity, and affluence, we carry out a controlled experiment that shows that biases can even change sign or reverse their order when word frequencies change.

Numerous works use word embedding-based metrics to quantify societal biases and stereotypes in texts. Recent studies have found that word embeddings can capture semantic similarity but may be affected by word frequency. In this work we study the effect of frequency when measuring female vs. male gender bias with word embedding-based bias quantification methods. We find that Skip-gram with negative sampling and GloVe tend to detect male bias in high frequency words, while GloVe tends to return female bias in low frequency words. We show these behaviors still exist when words are randomly shuffled. This proves that the frequency-based effect observed in unshuffled corpora stems from properties of the metric rather than from word associations. The effect is spurious and problematic since bias metrics should depend exclusively on word co-occurrences and not individual word frequencies. Finally, we compare these results with the ones obtained with an alternative metric based on Pointwise Mutual Information. We find that this metric does not show a clear dependence on frequency, even though it is slightly skewed towards male bias across all frequencies.