Sublinear Time Approximation of Text Similarity Matrices

We study algorithms for approximating pairwise similarity matrices that arise in natural language processing. Generally, computing a similarity matrix for $n$ data points requires $\Omega(n^2)$ similarity computations. This quadratic scaling is a significant bottleneck, especially when similarities are computed via expensive functions, e.g., via transformer models. Approximation methods reduce this quadratic complexity, often by using a small subset of exactly computed similarities to approximate the remainder of the complete pairwise similarity matrix. Significant work focuses on the efficient approximation of positive semidefinite (PSD) similarity matrices, which arise e.g., in kernel methods. However, much less is understood about indefinite (non-PSD) similarity matrices, which often arise in NLP. Motivated by the observation that many of these matrices are still somewhat close to PSD, we introduce a generalization of the popular Nystr\"{o}m method to the indefinite setting. Our algorithm can be applied to any similarity matrix and runs in sublinear time in the size of the matrix, producing a rank-$s$ approximation with just $O(ns)$ similarity computations. We show that our method, along with a simple variant of CUR decomposition, performs very well in approximating a variety of similarity matrices arising in NLP tasks. We demonstrate high accuracy of the approximated similarity matrices in the downstream tasks of document classification, sentence similarity, and cross-document coreference.

Entity Linking and Discovery via Arborescence-based Supervised Clustering

Previous work has shown promising results in performing entity linking by measuring not only the affinities between mentions and entities but also those amongst mentions. In this paper, we present novel training and inference procedures that fully utilize mention-to-mention affinities by building minimum arborescences (i.e., directed spanning trees) over mentions and entities across documents in order to make linking decisions. We also show that this method gracefully extends to entity discovery, enabling the clustering of mentions that do not have an associated entity in the knowledge base. We evaluate our approach on the Zero-Shot Entity Linking dataset and MedMentions, the largest publicly available biomedical dataset, and show significant improvements in performance for both entity linking and discovery compared to identically parameterized models. We further show significant efficiency improvements with only a small loss in accuracy over previous work, which use more computationally expensive models.

Exact and Approximate Hierarchical Clustering Using A*

Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function that can be used to characterize the quality of the clustering. In those cases, hierarchical clustering can be seen as a combinatorial optimization problem. To that end, we introduce a new approach based on A* search. We overcome the prohibitively large search space by combining A* with a novel \emph{trellis} data structure. This combination results in an exact algorithm that scales beyond previous state of the art, from a search space with $10^{12}$ trees to $10^{15}$ trees, and an approximate algorithm that improves over baselines, even in enormous search spaces that contain more than $10^{1000}$ trees. We empirically demonstrate that our method achieves substantially higher quality results than baselines for a particle physics use case and other clustering benchmarks. We describe how our method provides significantly improved theoretical bounds on the time and space complexity of A* for clustering.

Model-Agnostic Graph Regularization for Few-Shot Learning

In many domains, relationships between categories are encoded in the knowledge graph. Recently, promising results have been achieved by incorporating knowledge graph as side information in hard classification tasks with severely limited data. However, prior models consist of highly complex architectures with many sub-components that all seem to impact performance. In this paper, we present a comprehensive empirical study on graph embedded few-shot learning. We introduce a graph regularization approach that allows a deeper understanding of the impact of incorporating graph information between labels. Our proposed regularization is widely applicable and model-agnostic, and boosts the performance of any few-shot learning model, including fine-tuning, metric-based, and optimization-based meta-learning. Our approach improves the performance of strong base learners by up to 2% on Mini-ImageNet and 6.7% on ImageNet-FS, outperforming state-of-the-art graph embedded methods. Additional analyses reveal that graph regularizing models result in a lower loss for more difficult tasks, such as those with fewer shots and less informative support examples.

Scalable Bottom-Up Hierarchical Clustering

Bottom-up algorithms such as the classic hierarchical agglomerative clustering, are highly effective for hierarchical as well as flat clustering. However, the large number of rounds and their sequential nature limit the scalability of agglomerative clustering. In this paper, we present an alternative round-based bottom-up hierarchical clustering, the Sub-Cluster Component Algorithm (SCC), that scales gracefully to massive datasets. Our method builds many sub-clusters in parallel in a given round and requires many fewer rounds -- usually an order of magnitude smaller than classic agglomerative clustering. Our theoretical analysis shows that, under a modest separability assumption, SCC will contain the optimal flat clustering. SCC also provides a 2-approx solution to the DP-means objective, thereby introducing a novel application of hierarchical clustering methods. Empirically, SCC finds better hierarchies and flat clusterings even when the data does not satisfy the separability assumption. We demonstrate the scalability of our method by applying it to a dataset of 30 billion points and showing that SCC produces higher quality clusterings than the state-of-the-art.

Clustering-based Inference for Zero-Shot Biomedical Entity Linking

Due to large number of entities in biomedical knowledge bases, only a small fraction of entities have corresponding labelled training data. This necessitates a zero-shot entity linking model which is able to link mentions of unseen entities using learned representations of entities. Existing zero-shot entity linking models however link each mention independently, ignoring the inter/intra-document relationships between the entity mentions. These relations can be very useful for linking mentions in biomedical text where linking decisions are often difficult due mentions having a generic or a highly specialized form. In this paper, we introduce a model in which linking decisions can be made not merely by linking to a KB entity but also by grouping multiple mentions together via clustering and jointly making linking predictions. In experiments on the largest publicly available biomedical dataset, we improve the best independent prediction for zero-shot entity linking by 2.5 points of accuracy, and our joint inference model further improves entity linking by 1.8 points.

Probabilistic Case-based Reasoning for Open-World Knowledge Graph Completion

A case-based reasoning (CBR) system solves a new problem by retrieving `cases' that are similar to the given problem. If such a system can achieve high accuracy, it is appealing owing to its simplicity, interpretability, and scalability. In this paper, we demonstrate that such a system is achievable for reasoning in knowledge-bases (KBs). Our approach predicts attributes for an entity by gathering reasoning paths from similar entities in the KB. Our probabilistic model estimates the likelihood that a path is effective at answering a query about the given entity. The parameters of our model can be efficiently computed using simple path statistics and require no iterative optimization. Our model is non-parametric, growing dynamically as new entities and relations are added to the KB. On several benchmark datasets our approach significantly outperforms other rule learning approaches and performs comparably to state-of-the-art embedding-based approaches. Furthermore, we demonstrate the effectiveness of our model in an "open-world" setting where new entities arrive in an online fashion, significantly outperforming state-of-the-art approaches and nearly matching the best offline method. Code available at https://github.com/ameyagodbole/Prob-CBR

Compact Representation of Uncertainty in Hierarchical Clustering

Hierarchical clustering is a fundamental task often used to discover meaningful structures in data, such as phylogenetic trees, taxonomies of concepts, subtypes of cancer, and cascades of particle decays in particle physics. When multiple hierarchical clusterings of the data are possible, it is useful to represent uncertainty in the clustering through various probabilistic quantities. Existing approaches represent uncertainty for a range of models; however, they only provide approximate inference. This paper presents dynamic-programming algorithms and proofs for exact inference in hierarchical clustering. We are able to compute the partition function, MAP hierarchical clustering, and marginal probabilities of sub-hierarchies and clusters. Our method supports a wide range of hierarchical models and only requires a cluster compatibility function. Rather than scaling with the number of hierarchical clusterings of $n$ elements ($\omega(n n! / 2^{n-1})$), our approach runs in time and space proportional to the significantly smaller powerset of $n$. Despite still being large, these algorithms enable exact inference in small-data applications and are also interesting from a theoretical perspective. We demonstrate the utility of our method and compare its performance with respect to existing approximate methods.

Scalable Hierarchical Clustering with Tree Grafting

We introduce Grinch, a new algorithm for large-scale, non-greedy hierarchical clustering with general linkage functions that compute arbitrary similarity between two point sets. The key components of Grinch are its rotate and graft subroutines that efficiently reconfigure the hierarchy as new points arrive, supporting discovery of clusters with complex structure. Grinch is motivated by a new notion of separability for clustering with linkage functions: we prove that when the model is consistent with a ground-truth clustering, Grinch is guaranteed to produce a cluster tree containing the ground-truth, independent of data arrival order. Our empirical results on benchmark and author coreference datasets (with standard and learned linkage functions) show that Grinch is more accurate than other scalable methods, and orders of magnitude faster than hierarchical agglomerative clustering.