相关论文: An efficient algorithm for computing the Baker-Cam…
In this paper we propose a novel algorithm to combine two or more cellular complexes, providing a minimal fragmentation of the cells of the resulting complex. We introduce here the idea of arrangement generated by a collection of cellular…
The main component of (constructive) recognition algorithms for black box groups of Lie type in computational group theory is the construction of unipotent elements. In the existing algorithms unipotent elements are found by random search…
Dynamic programming is widely used for exact computations based on tree decompositions of graphs. However, the space complexity is usually exponential in the treewidth. We study the problem of designing efficient dynamic programming…
This article presents the \emph{Serial and Unserial Methods} (SUM). The algorithms are strongly related to the first part of a classical reference in combinatorics, the \emph{Combinatorial algorithms for computers and calculators}, from…
Bilevel optimization has arisen as a powerful tool in modern machine learning. However, due to the nested structure of bilevel optimization, even gradient-based methods require second-order derivative approximations via Jacobian- or/and…
Many modern clustering methods scale well to a large number of data items, N, but not to a large number of clusters, K. This paper introduces PERCH, a new non-greedy algorithm for online hierarchical clustering that scales to both massive N…
The biggest cost of computing with large matrices in any modern computer is related to memory latency and bandwidth. The average latency of modern RAM reads is 150 times greater than a clock step of the processor. Throughput is a little…
Shapley values are a standard tool for explaining predictions of tree ensembles, with Path-Dependent SHAP being the most widely used variant. Despite substantial progress, existing methods still exhibit trade-offs between depth-dependent…
We extend the herding algorithm to continuous spaces by using the kernel trick. The resulting "kernel herding" algorithm is an infinite memory deterministic process that learns to approximate a PDF with a collection of samples. We show that…
Performing inference in Bayesian models requires sampling algorithms to draw samples from the posterior. This becomes prohibitively expensive as the size of data sets increase. Constructing approximations to the posterior which are cheap to…
We propose the ultra-fast numerical approach to large-scale inhomogeneous superconductors, which we call the Localized Krylov Bogoliubov-de Gennes method (LK-BdG). In the LK-BdG method, the computational complexity of the local Green's…
Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fi t a model to data without relying on the computation of the model likelihood. They instead require to…
We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…
In this paper, we present the first study of the computational complexity of converting an automata-based text index structure, called the Compact Directed Acyclic Word Graph (CDAWG), of size $e$ for a text $T$ of length $n$ into other text…
In this paper, we consider the problem of classification of $M$ high dimensional queries $y^1,\cdots,y^M\in B^S$ to $N$ high dimensional classes $x^1,\cdots,x^N\in A^S$ where $A$ and $B$ are discrete alphabets and the probabilistic model…
Best rank-one approximation is one of the most fundamental tasks in tensor computation. In order to fully exploit modern multi-core parallel computers, it is necessary to develop decoupling algorithms for computing the best rank-one…
This paper introduces two new algorithms for Lie algebras over finite fields and applies them to the investigate the known simple Lie algebras of dimension at most $20$ over the field $\mathbb{F}_2$ with two elements. The first algorithm is…
This work introduces a kernel-independent, multilevel, adaptive algorithm for efficiently evaluating a discrete convolution kernel with a given source distribution. The method is based on linear algebraic tools such as low rank…
We develop Lie's correspondence and an explicit Baker-Campbell-Hausdorff formula for commutative automorphic formal loops.
Recent work has developed Bayesian methods for the automatic statistical analysis and description of single time series as well as of homogeneous sets of time series data. We extend prior work to create an interpretable kernel embedding for…