We give the first single-pass streaming algorithm for Column Subset Selection with respect to the entrywise $\ell_p$-norm with $1 \leq p < 2$. We study the $\ell_p$ norm loss since it is often considered more robust to noise than the standard Frobenius norm. Given an input matrix $A \in \mathbb{R}^{d \times n}$ ($n \gg d$), our algorithm achieves a multiplicative $k^{\frac{1}{p} - \frac{1}{2}}\poly(\log nd)$-approximation to the error with respect to the \textit{best possible column subset} of size $k$. Furthermore, the space complexity of the streaming algorithm is optimal up to a logarithmic factor. Our streaming algorithm also extends naturally to a 1-round distributed protocol with nearly optimal communication cost. A key ingredient in our algorithms is a reduction to column subset selection in the $\ell_{p,2}$-norm, which corresponds to the $p$-norm of the vector of Euclidean norms of each of the columns of $A$. This enables us to leverage strong coreset constructions for the Euclidean norm, which previously had not been applied in this context. We also give the first provable guarantees for greedy column subset selection in the $\ell_{1, 2}$ norm, which can be used as an alternative, practical subroutine in our algorithms. Finally, we show that our algorithms give significant practical advantages on real-world data analysis tasks.

As natural language processing methods are increasingly deployed in real-world scenarios such as healthcare, legal systems, and social science, it becomes necessary to recognize the role they potentially play in shaping social biases and stereotypes.Previous work has revealed the presence of social biases in widely used word embeddings involving gender, race, religion, and other social constructs.While some methods were proposed to debias these word-level embeddings, there is a need to perform debiasing at the sentence-level given the recent shift towards new contextualized sentence representations such as ELMo and BERT.In this paper, we investigate the presence of social biases in sentence-level representations and propose a new method, SENT-DEBIAS, to reduce these biases.We show that SENT-DEBIAS is effective in removing biases, and at the same time, preserves performance on sentence-level downstream tasks such as sentiment analysis, linguistic acceptability, and natural language understanding.We hope that our work will inspire future research on characterizing and removing social biases from widely adopted sentence representations for fairer NLP.