相关论文: The Schreier-Sims algorithm for matrix groups

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

We present a formal analysis, in Isabelle/HOL, of optimisation algorithms for matroids, which are useful generalisations of combinatorial structures that occur in optimisation, and greedoids, which are a generalisation of matroids. Although…

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…

The randomized group-greedy method and its customized method for large-scale sensor selection problems are proposed. The randomized greedy sensor selection algorithm is applied straightforwardly to the group-greedy method, and a customized…

The Set Cover problem (SCP) and Set Packing problem (SPP) are standard NP-hard combinatorial optimization problems. Their decision problem versions are shown to be NP-Complete in Karp's 1972 paper. We specify a rough guide to constructing…

We present GRIP, a graph neural network accelerator architecture designed for low-latency inference. AcceleratingGNNs is challenging because they combine two distinct types of computation: arithmetic-intensive vertex-centric operations and…

Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…

Matrix recovery is the problem of recovering a low-rank matrix from a few linear measurements. Recently, this problem has gained a lot of attention as it is employed in many applications such as Netflix prize problem, seismic data…

In high dimensional settings, sparse structures are crucial for efficiency, either in term of memory, computation or performance. In some contexts, it is natural to handle more refined structures than pure sparsity, such as for instance…

In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…

The proposed distributed dynamic clustering algorithm enables to group agents based on their pre-selected feature states. The clusters are determined by comparing the distance of the agents' current feature states with average estimates of…

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

This paper studies how to efficiently update the saddle-point strategy, or security strategy of one player in a matrix game when the other player develops new actions in the game. It is well known that the saddle-point strategy of one…

This is a collection of examples showing how the GAP system can be used to compute information about the generating graphs of finite groups. It includes all examples that were needed for the computational results in the paper "Hamiltonian…

We derive new discrete event simulation algorithms for marked time point processes. The main idea is to couple a special structure, namely the associated local independence graph, as defined by Didelez arXiv:0710.5874, with the activity…

Modern Machine Learning (ML) training on large-scale datasets is a very time-consuming workload. It relies on the optimization algorithm Stochastic Gradient Descent (SGD) due to its effectiveness, simplicity, and generalization performance.…

In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously…

Complex multi-robot missions often require heterogeneous teams to jointly optimize task allocation, scheduling, and path planning to improve team performance under strict constraints. We formalize these complexities into a new class of…