Evaluating Metrics for Bias in Word Embeddings

TL;DR

A bias definition is formalized based on the ideas from previous works and derive conditions for bias metrics and a new metric is proposed, SAME, to address the shortcomings of existing metrics and mathematically prove that SAME behaves appropriately.

Abstract

Over the last years, word and sentence embeddings have established as text preprocessing for all kinds of NLP tasks and improved the performances significantly. Unfortunately, it has also been shown that these embeddings inherit various kinds of biases from the training data and thereby pass on biases present in society to NLP solutions. Many papers attempted to quantify bias in word or sentence embeddings to evaluate debiasing methods or compare different embedding models, usually with cosine-based metrics. However, lately some works have raised doubts about these metrics showing that even though such metrics report low biases, other tests still show biases. In fact, there is a great variety of bias metrics or tests proposed in the literature without any consensus on the optimal solutions. Yet we lack works that evaluate bias metrics on a theoretical level or elaborate the advantages and disadvantages of different bias metrics. In this work, we will explore different cosine based bias metrics. We formalize a bias definition based on the ideas from previous works and derive conditions for bias metrics. Furthermore, we thoroughly investigate the existing cosine-based metrics and their limitations to show why these metrics can fail to report biases in some cases. Finally, we propose a new metric, SAME, to address the shortcomings of existing metrics and mathematically prove that SAME behaves appropriately.

Figures (9)

• Figure 1: Simplified (2D) visualization of gender stereotypes in occupation embedding vectors. The occupation vectors in dotted lines show a less biased representation of the occupations. Ideally, all gender neutral terms should be represented on the neutral axis, thus being equidistant to $\bm{he}$ and $\bm{she}$. The red dotted line indicates the bias direction $\bm{g} = \pm (\bm{she}-\bm{he})$
• Figure 2: Bias of stereotypical male and female jobs as indicated by WEAT's $s(\bm{w},A,B)$ calculated on BERT embeddings. Differences along the y-axis are arbitrary shift for better visibility.
• Figure 3: Simplified visualization of gender stereotypes in embeddings. The occupation vectors are biased if $0 < \alpha < \frac{\theta}{2}$ or $0 < \beta < \frac{\theta}{2}$.
• Figure 4: This illustrates a case, where WEAT would report no bias since secretary and engineer have the same relative similarity towards he and she.
• Figure 5: Example for correlation of word-wise biases measured with the different bias scores compared to training biases (probability for male pronoun) $p$. Since MAC and the Direct Bias do not measure the direction of bias, we display $0.5-p$ on the x-axis.

Theorems & Definitions (32)

• Definition 1: word bias
• Definition 2: set bias
• Definition 3: skew
• Definition 4: stereotype
• Definition 5: magnitude-comparable
• Definition 6: unbiased-trustworthy
• Definition 7: skew-sensitive
• Definition 8: stereotype-sensitive
• Theorem 1
• proof