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Word vector embeddings have been shown to contain and amplify biases in the data they are extracted from. Consequently, many techniques have been proposed to identify, mitigate, and attenuate these biases in word representations. In this paper, we utilize interactive visualization to increase the interpretability and accessibility of a collection of state-of-the-art debiasing techniques. To aid this, we present the Visualization of Embedding Representations for deBiasing (“VERB”) system, an open-source web-based visualization tool that helps users gain a technical understanding and visual intuition of the inner workings of debiasing techniques, with a focus on their geometric properties. In particular, VERB offers easy-to-follow examples that explore the effects of these debiasing techniques on the geometry of high-dimensional word vectors. To help understand how various debiasing techniques change the underlying geometry, VERB decomposes each technique into interpretable sequences of primitive transformations and highlights their effect on the word vectors using dimensionality reduction and interactive visual exploration. VERB is designed to target natural language processing (NLP) practitioners who are designing decision-making systems on top of word embeddings, and also researchers working with the fairness and ethics of machine learning systems in NLP. It can also serve as a visual medium for education, which helps an NLP novice understand and mitigate biases in word embeddings. 

Abstract Metabolism is intertwined with various cellular processes, including controlling cell fate, influencing tumorigenesis, participating in stress responses and more. Metabolism is a complex, interdependent network, and local perturbations can have indirect effects that are pervasive across the metabolic network. Current analytical and technical limitations have long created a bottleneck in metabolic data interpretation. To address these shortcomings, we developed Metaboverse, a user-friendly tool to facilitate data exploration and hypothesis generation. Here we introduce algorithms that leverage the metabolic network to extract complex reaction patterns from data. To minimize the impact of missing measurements within the network, we introduce methods that enable pattern recognition across multiple reactions. Using Metaboverse, we identify a previously undescribed metabolite signature that correlated with survival outcomes in early stage lung adenocarcinoma patients. Using a yeast model, we identify metabolic responses suggesting an adaptive role of citrate homeostasis during mitochondrial dysfunction facilitated by the citrate transporter, Ctp1. We demonstrate that Metaboverse augments the user’s ability to extract meaningful patterns from multi-omics datasets to develop actionable hypotheses. 

A mass spectrometry and dialysis method detects metabolite-protein interactions that help to control physiology. 

The mapper algorithm is a popular tool from topological data analysis for extracting topological summaries of high-dimensional datasets. In this paper, we present Mapper Interactive, a web-based framework for the interactive analysis and visualization of high-dimensional point cloud data. It implements the mapper algorithm in an interactive, scalable, and easily extendable way, thus supporting practical data analysis. In particular, its command-line API can compute mapper graphs for 1 million points of 256 dimensions in about 3 minutes (4 times faster than the vanilla implementation). Its visual interface allows on-the-fly computation and manipulation of the mapper graph based on user-specified parameters and supports the addition of new analysis modules with a few lines of code. Mapper Interactive makes the mapper algorithm accessible to nonspecialists and accelerates topological analytics workflows. 

Abstract We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space $${\mathbb {X}}$$ X equipped with a continuous function $$f: {\mathbb {X}}\rightarrow \mathbb {R}$$ f : X → R . We first give a categorification of the mapper graph and the Reeb graph by interpreting them in terms of cosheaves and stratified covers of the real line $$\mathbb {R}$$ R . We then introduce a variant of the classic mapper graph of Singh et al. (in: Eurographics symposium on point-based graphics, 2007), referred to as the enhanced mapper graph, and demonstrate that such a construction approximates the Reeb graph of $$({\mathbb {X}}, f)$$ ( X , f ) when it is applied to points randomly sampled from a probability density function concentrated on $$({\mathbb {X}}, f)$$ ( X , f ) . Our techniques are based on the interleaving distance of constructible cosheaves and topological estimation via kernel density estimates. Following Munch and Wang (In: 32nd international symposium on computational geometry, volume 51 of Leibniz international proceedings in informatics (LIPIcs), Dagstuhl, Germany, pp 53:1–53:16, 2016), we first show that the mapper graph of $$({\mathbb {X}}, f)$$ ( X , f ) , a constructible $$\mathbb {R}$$ R -space (with a fixed open cover), approximates the Reeb graph of the same space. We then construct an isomorphism between the mapper of $$({\mathbb {X}},f)$$ ( X , f ) to the mapper of a super-level set of a probability density function concentrated on $$({\mathbb {X}}, f)$$ ( X , f ) . Finally, building on the approach of Bobrowski et al. (Bernoulli 23 (1):288–328, 2017b), we show that, with high probability, we can recover the mapper of the super-level set given a sufficiently large sample. Our work is the first to consider the mapper construction using the theory of cosheaves in a probabilistic setting. It is part of an ongoing effort to combine sheaf theory, probability, and statistics, to support topological data analysis with random data.