Related papers: Accelerating the Convergence of Higher-Order Coupl…
This paper studies high-dimensional regression models with lasso when data is sampled under multi-way clustering. First, we establish convergence rates for the lasso and post-lasso estimators. Second, we propose a novel inference method…
In the era of large language models (LLMs), supervised neural methods remain the state-of-the-art (SOTA) for Coreference Resolution. Yet, their full potential is underexplored, particularly in incremental clustering, which faces the…
We study the supervised clustering problem under the two-component anisotropic Gaussian mixture model in high dimensions and in the non-asymptotic setting. We first derive a lower and a matching upper bound for the minimax risk of…
Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for…
We address the problem of clustering a set of points in $\mathbb{R}^d$ with axis-parallel clusters. Previous exact approaches to this problem are mostly based on integer programming formulations and can only solve to optimality instances of…
Acceleration is a celebrated cornerstone of convex optimization, enabling gradient-based algorithms to converge sublinearly in the condition number. A major open question is whether an analogous acceleration phenomenon is possible for…
Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. In this paper, we introduce a method that simultaneously learns an embedding space along…
The high dimensionality of hyperspectral images often results in the degradation of clustering performance. Due to the powerful ability of deep feature extraction and non-linear feature representation, the clustering algorithm based on deep…
A dynamical formulation of coupled cluster theory is derived using a variational principle. By allowing time-dependent single-particle functions, a high degree of adaptivity is introduced, allowing complex systems to be simulated with high…
The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate…
One potential solution to combat the scarcity of tail observations in extreme value analysis is to integrate information from multiple datasets sharing similar tail properties, for instance, a common extreme value index. In other words, for…
In this paper, we introduce a \textit{Bi-level OPTimization} (BiOPT) framework for minimizing the sum of two convex functions, where both can be nonsmooth. The BiOPT framework involves two levels of methodologies. At the upper level of…
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy conserving problems and prove convergence of the WaveHoltz…
Dimensionality reduction and clustering techniques are frequently used to analyze complex data sets, but their results are often not easy to interpret. We consider how to support users in interpreting apparent cluster structure on scatter…
We present a novel acceleration technique for improving the convergence of source iteration for discrete ordinates transport calculations. Our approach uses the idea of the dynamic mode decomposition (DMD) to estimate the slowly decaying…
One of the most widely used techniques for data clustering is agglomerative clustering. Such algorithms have been long used across many different fields ranging from computational biology to social sciences to computer vision in part…
Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…
A new method that accurately describes strongly correlated states and captures dynamical correlation is presented. It is derived as a modification of coupled-cluster theory with single and double excitations (CCSD) through consideration of…
In this paper we extend an earlier result within Dempster-Shafer theory ["Fast Dempster-Shafer Clustering Using a Neural Network Structure," in Proc. Seventh Int. Conf. Information Processing and Management of Uncertainty in Knowledge-Based…
This article presents a class of new relaxation modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). Using two positive diagonal matrices, we formulate a fixed-point equation and prove that…