Related papers: Matrix Multiplication and Binary Space Partitionin…

The perturbative approach to quantum field theories has made it possible to obtain incredibly accurate theoretical predictions in high-energy physics. Although various techniques have been developed to boost the efficiency of these…

A large fraction of the arithmetic operations required to evaluate deep neural networks (DNNs) consists of matrix multiplications, in both convolution and fully connected layers. We perform end-to-end learning of low-cost approximations of…

This paper explores hierarchical clustering in the case where pairs of points have dissimilarity scores (e.g. distances) as a part of the input. The recently introduced objective for points with dissimilarity scores results in every tree…

We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…

We propose a novel application of coded computing to the problem of the nearest neighbor estimation using MatDot Codes [Fahim. et.al. 2017], that are known to be optimal for matrix multiplication in terms of recovery threshold under storage…

Co-clustering simultaneously clusters rows and columns, revealing more fine-grained groups. However, existing co-clustering methods suffer from poor scalability and cannot handle large-scale data. This paper presents a novel and scalable…

We describe a subroutine that improves the running time of any subdivision algorithm for real root isolation. The subroutine first detects clusters of roots using a result of Ostrowski, and then uses Newton iteration to converge to them.…

We present an axiomatic framework for analyzing the algorithmic properties of decision trees. This framework supports the classification of decision tree problems through structural and ancestral constraints within a rigorous mathematical…

Identifying clusters of similar elements in a set is a common task in data analysis. With the immense growth of data and physical limitations on single processor speed, it is necessary to find efficient parallel algorithms for clustering…

Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…

Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is…

We introduce an algorithm that performs a one-directional mesh overset of a parallel forest of octrees with another distributed mesh of unrelated partition. The forest mesh consists of several adaptively refined octrees. Individual smooth…

The tree inclusion problem is, given two node-labeled trees $P$ and $T$ (the ``pattern tree'' and the ``target tree''), to locate every minimal subtree in $T$ (if any) that can be obtained by applying a sequence of node insertion operations…

The quest for non-commutative matrix multiplication algorithms in small dimensions has seen a lot of recent improvements recently. In particular, the number of scalar multiplications required to multiply two $4\times4$ matrices was first…

Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…

We extend the four-dimensional unsubtraction method, which is based on the loop-tree duality (LTD), to deal with processes involving heavy particles. The method allows to perform the summation over degenerate IR configurations directly at…

We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…

We consider sketched approximate matrix multiplication and ridge regression in the novel setting of localized sketching, where at any given point, only part of the data matrix is available. This corresponds to a block diagonal structure on…

Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise…

The issue of internal fragmentation in data structures is a fundamental challenge in database design. A seminal result of Yao in this field shows that evenly splitting the leaves of a B-tree against a workload of uniformly random insertions…