Gender Bias in Meta-Embeddings (2022)

Abstract: Different methods have been proposed to develop meta-embeddings from a given set of source embeddings. However, the source embeddings can contain unfair gender-related biases, and how these influence the meta-embeddings has not been studied yet.We study the gender bias in meta-embeddings created under three different settings:(1) meta-embedding multiple sources without performing any debiasing (Multi-Source No-Debiasing),(2) meta-embedding multiple sources debiased by a single method (Multi-Source Single-Debiasing), and(3) meta-embedding a single source debiased by different methods (Single-Source Multi-Debiasing).Our experimental results show that meta-embedding amplifies the gender biases compared to input source embeddings.We find that debiasing not only the sources but also their meta-embedding is needed to mitigate those biases.Moreover, we propose a novel debiasing method based on meta-embedding learning where we use multiple debiasing methods on a single source embedding and then create a single unbiased meta-embedding.

## introduction various pre-trained word embeddings have been successfully used as features for representing input texts in many nlp tasks @xcite @xcite @xcite . combining multiple word embeddings leads to more accurate and exhaustive meta-embeddings in terms of vocabulary, learned expressions etc @xcite . for example, there are meta-embedding methods that use the average of multiple embeddings @xcite , concatenate multiple embeddings @xcite , use locally-linear @xcite or global @xcite projections, or use autoencoders @xcite . however, the source embeddings can contain unfair gender-related biases @xcite @xcite . to address these drawbacks, various debiasing methods have been proposed in the literature. for example, many projection-based methods have been proposed to eliminate biases in static word embeddings @xcite @xcite . @xcite proposed a hard-debiasing (hard) method that projects gender-neutral words into a subspace, which is orthogonal to the gender dimension defined by a list of gender-definitional words. @xcite proposed iterative null-space projection (inlp) debiasing. they found that iteratively projecting word embeddings to the null space of the gender direction improves the debiasing performance. @xcite proposed dict-debiasing (dict) -a method for removing biases from pre-trained word embeddings using dictionaries, without requiring access to the original training resources or any knowledge regarding the word embedding algorithms used. on the other hand, to the best of our knowledge, the effect on gender bias due to meta-embedding that uses multiple sources has not been investigated. even if we had perfectly debiased the individual source embeddings, some meta-embedding methods such as averaging do not guarantee debiased meta-embeddings as we prove in §4. in this study, we classify meta-embeddings into the following three types from the viewpoint of debiasing and analyze them: (1) multi-source no-debiasing: meta-embeddings created from multiple source embeddings without any debiasing; (2) multi-source single-debiasing: meta-embeddings created from multiple source embeddings debiased by a single debiasing method; (3) single-source multi-debiasing: meta-embedding from the same source embedding, debiased using different debiasing methods. 1 multi-source single-debiasings were examined by debiasing: each source embeddings (pre), the learned meta-embeddings (post), and both source embeddings and meta-embeddings (both). figure 1 shows how a meta-embedding is learned for those methods. these methods are agnostic to types of metaembedding learning algorithms and demonstrate different aspects of debiasing effects. we use multi-source no-debiasings to investigate bias in meta-embeddings learned using existing approaches. the purpose of multi-source single-debiasing is to investigate how to effectively debias existing meta-embeddings. in single-source multi-debiasing, we combine the same embeddings debiased by different methods to investigate whether debiasing methods can complement each other's strengths and weaknesses to obtain more effective debiased embeddings. to the best of our knowledge, no studies have been proposed that combine multiple debiasing methods. we use three debiasing methods and five metaembeddings in our study. we focus on gender bias, since there are several methods @xcite @xcite that can be used to combine debiasing meth-ods and datasets @xcite @xcite that can be examined in different ways. experimental results show that the gender bias is amplified by meta-embedding methods without any treatment for debiasing. moreover, the gender bias increases with the number of source embeddings used in the meta-embedding. interestingly, we can successfully debias metaembeddings without losing their superiority of the performance improvements in two out of three word embedding benchmarks. the multi-source single-debiasing results indicate that debiasing both source embeddings and meta-embeddings is the best practice in two out of three bias evaluation benchmarks. we also demonstrate that single-source multi-debiasing performs better than using only one debiasing method in all three bias evaluation benchmarks. it can be seen as a debiasing method that uses an ensemble of existing debiasing methods via a meta-embedding framework to create more reliable unbiased embeddings than if we had used a single debiasing method. this is an important result given that there exists a broad range of debiasing methods proposed in the nlp community based on different principles and complementary strengths, yet no single best method exist @xcite . ## meta-embedding learning methods depending on whether debiasing methods are applied on source embeddings or their metaembedding, three variants can be identified: multi-source no-debiasing, multi-source single-debiasing and single-source multi-debiasing. to explain these settings further, let us consider a set of n source word embeddings s 1 , s 2 , . . . , s n re-spectively covering vocabularies (i.e. sets of words) v 1 , v 2 , . . . , v n . the embedding of a word w in s j is denoted by s j (w) ∈ r d j , where d j is the dimensionality of s j . in multi-source no-debiasing, meta-embedding m msnd (w) for word w is computed from s 1 (w), s 2 (w), . . . , s n (w) using some meta-embedding learning method, where msnd represents multi-source no-debiasing. multi-source single-debiasing and single-source multi-debiasing are obtained by applying debiasing methods described in § 3. let us denote debiasing for word embedding s j (w) as d(s j (w)). in multi-source single-debiasing, there are three types of debiasing possibilities: pre, post, and both. in pre, the debiased source embeddings d(s 1 (w)), d(s 2 (w)), . . . , d(s n (w)) are used to computed m mssdpre (w), where mssd represents multi-source single-debiasing. in post, debiasing is performed on the learned meta-embeddings as in m mssdpost (w) = d(m msnd (w)). in both, debiasing is performed for both pre and post, as in m mssdboth (w) = d(m mssdpre (w)). in single-source multi-debiasing, we use different debiasing methods for the same source embedding as here, m is the number of debiasing methods and ssmd represents single-source multi-debiasing. the source word embeddings, in general, do not have to cover the same set of words. much prior work in meta-embedding learning assume a common vocabulary over all source embeddings for simplicity. if a particular word is not covered by a source embedding, it can be assigned a zero vector, a randomly initialised vector or we could learn a regression model to predict the missing source embeddings @xcite . without loss of generality, we will assume that all words for evaluation are covered by a meta-embedding vocabulary v, which is composed by each source embedding's vocabulary v j , after applying any one of the above-mentioned methods. here j represents the j-th source embedding's vocabulary. each word w is assumed to be included in at least one of the vocabularies v j , and zero embeddings are assigned for w / ∈ v j . we consider five previously proposed metaembedding learning methods for static word embeddings in this study to learn m(w) for multi-source no-debiasing, multi-source single-debiasing and single-source multi-debiasing as follows: concatenation (conc @xcite , averaging (avg coates and bollegala, 2018), globally-linear meta-embedding (gle yin and schütze, 2016), locally-linear metaembedding @xcite , and averaged autoencoded meta-embeddings (aeme @xcite . according to @xcite , these are the most widely-used meta-embedding learning methods. they methods are described in detail in appendix §1. 3 debiasing methods for static word embeddings different methods have been proposed in prior work for debiasing static word embeddings. we consider the following three popular debiasing methods in this study: (1) hard-debiasing (hard bolukbasi et al., 2016), (2) iterative null space projection (inlp ravfogel et al., 2020), and (3) dictionary-based debiasing (dict kaneko and bollegala, 2021b). due to space constraints, we describe those methods in detail in appendix §2. by adapting these debiasing methods to the metaembeddings described in §2, we investigate multi-source single-debiasing and single-source multi-debiasing. ## avg does not protect hard debiasing in general, it is difficult to mathematically analyze the gender bias in debiased source embeddings when they are meta-embedded using a particular meta-embedding learning method. however, such an analysis is possible in the special case of the hard debiasing for conc and avg, and shows that even if all source embeddings are debiased their meta-embedding might not always remain debiased. let us consider applying hard to debias two sources s 1 , s 2 independently and create their metaembeddings separately using conc and avg. to simplify the discussion, let us assume that both s 1 and s 2 to be k-dimensional and having bias vector sets respectively {b here, w 1,b and w 2,b denote the projected source embeddings of w onto the gender subspaces in each source embedding spaces s 1 and s 2 . let us denote the concatenated meta-embedding of d 1 (w) and d 2 (w) by m conc (w). consider the bias vector b each term in (3) are separately zero because the debiased embeddings are orthogonal to the bias vectors by construction in each source. therefore, concatenated meta-embedding preserves the debiasing result under hard debiasing. however, this is not true for other metaembedding methods such as averaging. to see this, consider ⟨d 1 (w) + d 2 (w), b (1) j + b note that the first two terms in (4) are zero because they are in the same vector space and the innerproducts are taken w.r.t. to the corresponding bias vectors. however, the last two terms in (4) are not generally zero. therefore, avg does not generally preserve the hard debiasing result. ## experiments our goal in this paper is to evaluate whether gender bias is amplified and to what degree by the different meta-embedding learning methods. however, this bias amplification must be considered relative to the accuracy of the semantic representations produced by those meta-embedding learning methods. for example, a meta-embedding learning method can produce perfectly unbiased representations by mapping all words to a constant vector, which is useless for any downstream task requiring semantic representations of words. for this reason, we conduct our evaluations using two types of datasets to evaluate gender biases in the debiased embeddings, while preserving useful semantic information necessary for downstream tasks: (a) bias evaluation datasets covering different types of gender biases (described in §5.1) and (b) word embedding benchmarks related to semantic similarity prediction and pos tagging tasks (described in §5.2). ## conclusion we studied the gender bias due to meta-embedding under three settings: (1) multi-source no-debiasing, (2) multi-source single-debiasing (3) single-source multi-debiasing created from static word embeddings as sources. our experimental results show that although meta-embedding of multi-source no-debiasing improves performance over the input source embeddings, at the same time, it amplifies the unfair gender bias encoded in the source embeddings. furthermore, the level of gender bias encoded in a meta-embedding increases with the number of source embeddings used. we found that multi-source single-debiasing using previously proposed debiasing methods for static word embeddings can be effectively used to debiase meta-embeddings as well. furthermore, we proposed single-source multi-debiasing that com-bines the outputs from multiple debiasing methods and then create a single embedding via a metaembedding learning method.