Relating Word Embedding Gender Biases to Gender Gaps: A Cross-Cultural Analysis

In plain words

Word embeddings are lists of numbers that stand for words, learned from large amounts of text. Because they learn from text written by people, they can pick up gender stereotypes. This paper turns that effect around: if the stereotypes in a community's text track real gaps between men and women, then measuring the stereotypes could say something about those gaps.

The authors trained a separate set of word vectors for each U.S. region and each country, using English tweets from 2018. In each set they measured how closely groups of neutral words lean toward "female" or "male", then checked how those scores line up with published statistics on pay, education, politics and health. Some word groups, such as threat words, track gaps closely; random word groups do not. The authors say these are correlations, not causes.

TL;DR

• Gender bias in embeddings from a region's tweets is measured as a signed projection of neutral words onto a male-female axis eq. 1.
• Those scores are correlated (by R²) with 18 international and 5 U.S. gender gap statistics, with feature selection on subsets of countries §4.1.
• Correlations are selective: themed word sets correlate with related gaps, random sets do not §4.1 §5.
• The authors report the correlations as evidence of association, not causation §5.
• No code or data are released, so the reported numbers cannot be reproduced from this card alone.

Problem

Gender gaps in pay, education, politics and health are measured by surveys and official statistics, and differ between regions and countries. The paper asks whether the gender associations in a culture's language, measured with standard word embedding bias methods, relate to those gaps §1. Prior work relates embedding bias to survey data or to historical trends, but not to a broad set of gaps across many cultures §1.

The method assumes that each culture can be represented by text it produces online (here, English tweets, which the authors acknowledge cover only some people) and that the gaps are measured at the same region or country level §3 §5.

Method

Data §3.

1. Collect public tweets from U.S. and international users over 100 days in 2018: the first ten days of each of the first ten months §3.
2. Assign each tweet to a region or country using the user's location property, keeping English tweets only §3.
3. Drop tweets with fewer than three words §3.
4. Replace URLs, user names, hashtags, images and emojis with placeholder tokens §3.
5. For each culture, sample up to 10 million tweets; the smallest culture has about 98K tweets and the largest about 122M (U.K.) §3.

Embeddings §2 §3 §4.3.

1. Train Word2Vec on each culture's corpus, with window size 10, a minimum count of 5 and 200-dimensional vectors §2.
2. The main experiments use Word2Vec; the variant (skip-gram or CBOW) is not stated there §3. Section 4.3 compares four algorithms: GloVe, Word2Vec skip-gram, Word2Vec CBOW and FastText skip-gram §2 §4.3.

Word sets §4.1.

1. Female and male word sets contain female and male pronouns and nouns, taken from the same lists for international and U.S. analyses §4.1.
2. The paper computes one vector for each gender by averaging the vectors of its words, following Garg et al. (2018) §4.1.
3. Neutral thematic word sets are built from survey-based sets (Williams and Best 1990) and from Garg et al. (2018), plus hand-built sets such as government, threat, communal, criminal, childcare and excellent §4.1. Only some words of each set are listed in the text §4.1.
4. Four random word sets from the vocabulary serve as a control fig. 1 fig. 3.

Bias score §4.1 eq. 1. For each culture, the bias of a neutral word set W is the mean of the projections of its words onto the unit male-female axis. The axis is the normalised difference between the female and male vectors.

# Average axis projection of a neutral word set  [§4.1] [eq. 1]
# Input:  embeddings E (word -> vector, dim 200), female words F,
#         male words M, neutral word set W
# Output: scalar bias score for one culture

def axis_projection_bias(E, F, M, W):
    # Average the vectors of each gender's words  [§4.1]
    female = mean([E[w] for w in F])                 # (200,)
    male = mean([E[w] for w in M])                   # (200,)
    # Unit vector from male towards female  [eq. 1]
    axis = (female - male) / norm(female - male)     # (200,)
    # Mean projection of the neutral words onto that axis  [eq. 1]
    return mean([dot(E[w], axis) for w in W])

Out-of-vocabulary handling for W, F and M is not stated §4.1.

Correlation with gaps §4.1 fig. 1 fig. 3. For each pair of word set and gap statistic, the paper reports R² across cultures. The description in the text is:

# Score one themed word set against one gap statistic  [§4.1]
# Input:  bias[c, w] for culture c and word w; gap[c] for each culture
# Output: mean R^2 over five repetitions

def score_word_set(bias, gap, repeats=5):
    scores = []
    for rep in range(repeats):
        # Draw 20% of the cultures for feature selection  [§4.1]
        # (a new draw per repetition is implied, not stated)
        subset = sample_fraction(num_cultures, 0.2)
        # Optionally remove words from the set; the rule is not stated  [§4.1]
        words = select_words(bias[subset], gap[subset])
        # R^2 of the gap against the selected words, over all cultures  [§4.1]
        # (regression form not stated)
        scores.append(r_squared(bias[:, words], gap))
    return mean(scores)

The text says feature selection "monotonically increases" R² and that using 20% of countries "helps prevent over-fitting" §4.1. See Pitfalls.

U.S. analysis §4.2 fig. 3 fig. 4. The same procedure is applied to 51 U.S. regions (50 states and Washington, D.C.), with U.S. gap statistics §4.2. The U.S. analysis performs feature selection using all states, not a subset fig. 5 caption.

Metric and algorithm comparison §4.3 fig. 5. Three bias metrics are compared on Word2Vec: the axis projection above, the relative L2 norm difference and the relative L2 norm ratio (both from Garg et al., 2018). The two norm-based metrics compute, for each neutral word, the L2 distance to the male and to the female vector, then subtract or divide the two distances and average over the word set §4.3. Axis projection with Word2Vec gives the highest R² in all three set-statistic pairs tested, and is used for all other experiments §4.3.

Adjective analysis §4.4 fig. 6 fig. 7. All adjectives in the embeddings are identified with WordNet, and each one's R² with each U.S. gap is computed. Adjectives with R² > 0.1 are kept §4.4. Valence and dominance of each kept adjective are taken from Warriner et al. (2013) norms, and the high-gap and low-gap groups are compared with a t-test §4.4.

Hyperparameters

Results

Author-reported. Setup: 2018 English tweets; 99 countries and 51 U.S. regions; Word2Vec with axis projection §3 §4.3. There is no external baseline with published numbers. Comparisons are internal: algorithms and metrics in §4.3, and random word sets as a control §4.1.

Paper vs code

No official code. The paper gives no code, data or repository link. The arXiv record, the LaTeX source (main.tex and included files) and the footnotes (WEF, SWE and Represent Women websites) name no repository §1 §3. GitHub searches for the title words, "gender gap word embedding", and the SIFT affiliation returned no repositories from the authors. The search results that did appear were unrelated third-party projects, which were not used.

Pitfalls

• Feature selection can inflate R². Words are selected on 20% of the cultures, and R² is then computed over all cultures, which include those 20%. The text says selection "monotonically increases" R² §4.1. The reported R² values are therefore not held-out estimates, so compare them with the random-word control in fig. 1 and fig. 3, not with absolute thresholds.
• Selection rule and model form are not stated. The paper does not say how words are dropped, whether the regression is univariate, whether it has an intercept, or how a word set becomes one or several features §4.1. An implementer must choose these, and results will change with the choice.
• Sign convention. R² is non-negative. The figures add a minus sign to show inverse correlation fig. 1 fig. 3. The sign is therefore a separate quantity, not part of R².
• Word2Vec variant is ambiguous. The main experiments say "Word2Vec" without naming skip-gram or CBOW §3. Section 4.3 lists both as separate algorithms §4.3. Choose one and state it.
• Word lists are incomplete. Thematic and random sets are given with "..." §4.1. Female and male lists are described, not enumerated §4.1. Full reproduction needs the lists, which the paper does not provide.
• Vector averaging. Female and male vectors are averages of their word vectors §4.1. The text does not say how out-of-vocabulary words are handled §4.1.
• Unequal corpus size. Cultures differ from 98K to 122M tweets, with a cap at 10M §3. The paper does not test whether embedding quality or bias scores depend on corpus size, but it argues that small corpora are still plausible sources §4.1.
• Collection and language detection. Tweet collection method, language identification and location resolution (beyond the user location property) are not described §3.
• Metric definitions. The norm-based metrics are described in words, not as equations §4.3. Implement them as stated in §4.3 and check against Garg et al. (2018).
• Multiple testing. The valence and dominance tests run across several statistics; the paper does not state a correction §4.4. WordNet version and adjective counts are not stated §4.4.
• Causality. The authors say correlations do not imply causation and have limited interpretive power §5. Do not use the scores as causal evidence.
• Single-word claims. The word "pretty" is named as the strongest single determinant §4.1. Treat it as a single observation.

Lineage

• Builds on: Garg et al. (2018), Word embeddings quantify 100 years of gender and ethnic stereotypes (word sets, averaged gender vectors, relative norm metrics). Bolukbasi et al. (2016), Man is to computer programmer as woman is to homemaker? (male-female axis) §1 §4.1.
• Compared against: GloVe, Word2Vec (skip-gram and CBOW), FastText §2 §4.3; relative L2 norm difference and ratio §4.3.
• Related gender-gap data: Global Gender Gap Index, WEF 2018 §2.
• Superseded by: not stated in the paper.