Statistical Uncertainty in Word Embeddings: GloVe-V (2406.12165v1)

Abstract: Static word embeddings are ubiquitous in computational social science applications and contribute to practical decision-making in a variety of fields including law and healthcare. However, assessing the statistical uncertainty in downstream conclusions drawn from word embedding statistics has remained challenging. When using only point estimates for embeddings, researchers have no streamlined way of assessing the degree to which their model selection criteria or scientific conclusions are subject to noise due to sparsity in the underlying data used to generate the embeddings. We introduce a method to obtain approximate, easy-to-use, and scalable reconstruction error variance estimates for GloVe (Pennington et al., 2014), one of the most widely used word embedding models, using an analytical approximation to a multivariate normal model. To demonstrate the value of embeddings with variance (GloVe-V), we illustrate how our approach enables principled hypothesis testing in core word embedding tasks, such as comparing the similarity between different word pairs in vector space, assessing the performance of different models, and analyzing the relative degree of ethnic or gender bias in a corpus using different word lists.

• The paper establishes a probabilistic framework to derive reconstruction error variances for GloVe embeddings, enhancing statistical hypothesis testing in NLP.
• It offers a computationally efficient alternative to document bootstrap by providing sensitive variance estimates, especially for low-frequency words.
• Empirical evaluations on the COHA corpus demonstrate robust bias measurement and improved model performance through uncertainty quantification.

Statistical Uncertainty in Word Embeddings: GloVe-V

The paper "Statistical Uncertainty in Word Embeddings: GloVe-V," authored by Vallebueno et al., addresses a critical yet underexplored aspect of word embeddings: the statistical uncertainty inherent in the embeddings. This issue is particularly pertinent in applications within computational social science, where conclusions drawn from word embeddings can influence decisions in fields like law and healthcare. The authors introduce GloVe-V, a method to estimate reconstruction error variances for the popular GloVe model, thereby furnishing a principled approach to hypothesis testing and model evaluation in NLP.

Core Contributions

The contributions of this paper are threefold:

1. Statistical Foundations for GloVe Embedding Variances: The paper establishes the theoretical groundwork by recasting the GloVe optimization problem in a probabilistic framework. This facilitates the derivation of variances for GloVe embeddings, taking into account the statistical uncertainty due to data sparsity.
2. Impact on Conclusions Derived from Embeddings: The authors demonstrate how incorporating uncertainty can influence conclusions about word similarity, model selection, and textual bias.
3. Empirical Demonstration with Pre-computed Variances for COHA: Data releases including pre-computed embeddings and variances for frequently occurring words in the Corpus of Historical American English (COHA) and plans for releasing similar datasets for larger corpora make the approach readily accessible to other researchers.

Methodology

Reformulation of GloVe Optimization

Central to GloVe-V is the reformulation of the standard GloVe optimization problem. The GloVe objective minimizes the weighted least squares error between the logged co-occurrence matrix and the dot product of word and context vectors, adjusted by bias terms. By holding context vectors and bias terms fixed at their optimal values, the optimization problem is expressed as finding the weighted least squares projections for each word vector.

Probabilistic Interpretation

Leveraging this reformulation, a probabilistic model is constructed where the log-transformed co-occurrence counts follow a multivariate normal distribution. The variance of the word embeddings is thus derived from the covariance matrix of this multivariate normal model. This probabilistic foundation enables the derivation of asymptotic variances for differentiable test statistics using the delta method or simulation-based approaches for non-differentiable statistics.

Practical Estimation

The paper also addresses practical aspects of estimation, including numerical challenges when the number of context word co-occurrences is close to the embedding dimensionality. This is tackled by computing the Moore-Penrose pseudo-inverse for poorly conditioned Hessians, ensuring reliable variance estimates even in high-dimensional settings.

Empirical Results

The empirical validation uses the COHA corpus (1900-1999) to showcase the practical utility of GloVe-V variances. Several key observations are highlighted:

1. Uncertainty in Embedding Locations: Visualizations depict the uncertainty ellipses around 2D projections of high- and low-frequency words, illustrating higher uncertainty for low-frequency words.
2. Comparison with Document Bootstrap: The GloVe-V method offers a computationally efficient alternative to the document bootstrap, providing variances that are more sensitive to word frequency.
3. Nearest Neighbors and Model Performance: Incorporating uncertainties changes not only nearest neighbor rankings and performance metrics on standard NLP tasks but also highlights the statistical significance of these changes.
4. Bias Measurement: GloVe-V allows for statistically robust measurement of biases in word embeddings, as demonstrated through gender and ethnic bias analyses.

Implications and Future Directions

Practical Implications

• Robustness in NLP Applications: Integrating GloVe-V variances can substantiate model evaluations and bias measurements, ensuring that conclusions are not artifacts of data sparsity.
• Hypothesis Testing: Researchers can use these variances to perform rigorous hypothesis tests, fostering greater statistical rigor in the field of NLP.

Theoretical Implications

• Foundation for Future Work on Embedding Models: This framework can potentially be extended or adapted to other embedding models, including those used in transformer-based architectures, adding a new dimension to how statistical uncertainty is accounted for.

Speculation on Future Developments in AI

Future advancements in AI could see widespread adoption of statistical uncertainty measures in various NLP tasks. This will likely accelerate as computational resources become cheaper and more accessible. Improved uncertainty quantification can lead to more robust models, better interpretability, and more reliable deployment in sensitive domains such as healthcare, law, and social science research.

Conclusion

The paper presents GloVe-V, an important advancement in the treatment of statistical uncertainty in word embeddings. By providing a scalable and computationally efficient method for estimating variances in GloVe embeddings, the authors significantly enhance the robustness and interpretability of downstream NLP tasks. This work sets the stage for incorporating rigorous statistical hypothesis testing into the assessment of word embeddings, ultimately contributing to more reliable and generalizable insights in computational linguistics and beyond.