相关论文: Matrix Multiplication and Binary Space Partitionin…
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…
It is known that the multiplication of an $N \times M$ matrix with an $M \times P$ matrix can be performed using fewer multiplications than what the naive $NMP$ approach suggests. The most famous instance of this is Strassen's algorithm for…
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
Biclustering is a class of techniques that simultaneously clusters the rows and columns of a matrix to sort heterogeneous data into homogeneous blocks. Although many algorithms have been proposed to find biclusters, existing methods suffer…
Several efficient distributed algorithms have been developed for matrix-matrix multiplication: the 3D algorithm, the 2D SUMMA algorithm, and the 2.5D algorithm. Each of these algorithms was independently conceived and they trade-off memory…
We propose splitting methods for the computation of the exponential of perturbed matrices which can be written as the sum $A=D+\varepsilon B$ of a sparse and efficiently exponentiable matrix $D$ with sparse exponential $e^D$ and a dense…
Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…
We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and…
One important tool is the optimal clustering of data into useful categories. Dividing similar objects into a smaller number of clusters is of importance in many applications. These include search engines, monitoring of academic performance,…
We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the rooted Subtree…
The Binary Space Partitioning~(BSP)-Tree process is proposed to produce flexible 2-D partition structures which are originally used as a Bayesian nonparametric prior for relational modelling. It can hardly be applied to other learning tasks…
Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…
In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by…
We present a protocol for the Boolean matrix product of two $n\times b$ Boolean matrices on the congested clique designed for the situation when the rows of the first matrix or the columns of the second matrix are highly clustered in the…
Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
This paper discusses the topic of dimensionality reduction for $k$-means clustering. We prove that any set of $n$ points in $d$ dimensions (rows in a matrix $A \in \RR^{n \times d}$) can be projected into $t = \Omega(k / \eps^2)$…
Matrix multiplication is the foundation from much of the success from high performance technologies like deep learning, scientific simulations, and video graphics. High level programming languages like Python and R rely on highly optimized…