Related papers: An algorithm for scaling vectors by the reciprocal…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
Vector programming is an important topic in many Introduction to Computer Science courses. Despite the importance of vectors, learning vector programming is a source for frustration to many students given that they feel left adrift when it…
In appropriate frameworks, automatic differentiation is transparent to the user at the cost of being a significant computational burden when the number of operations is large. For iterative algorithms, implicit differentiation alleviates…
We describe an exact algorithm to solve linear systems of the form $Hx=b$ where $H$ is the Hessian of a deep net. The method computes Hessian-inverse-vector products without storing the Hessian or its inverse. It requires time and storage…
The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…
The inverse power method is a numerical algorithm to obtain the eigenvectors of a matrix. In this work, we develop an iteration algorithm, based on the inverse power method, to numerically solve the Schr\"odinger equation that couples an…
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…
This work studies a fully distributed algorithm for computing the PageRank vector, which is inspired by the Matching Pursuit and features: 1) a fully distributed implementation 2) convergence in expectation with exponential rate 3) low…
Singular value decomposition is widely used in modal analysis, such as proper orthogonal decomposition and resolvent analysis, to extract key features from complex problems. SVD derivatives need to be computed efficiently to enable the…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
Object detection in aerial imagery presents a significant challenge due to large scale variations among objects. This paper proposes an evolutionary reinforcement learning agent, integrated within a coarse-to-fine object detection…
Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
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…
The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all…
Current automatic vision systems face two major challenges: scalability and extreme variability of appearance. First, the computational time required to process an image typically scales linearly with the number of pixels in the image,…
Modern algorithms for binary classification rely on an intermediate regression problem for computational tractability. In this paper, we establish a geometric distinction between classification and regression that allows risk in these two…
In this paper, a scalable iterative projection-type algorithm for solving non-stationary systems of linear inequalities is considered. A non-stationary system is understood as a large-scale system of inequalities in which coefficients and…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
We introduce the Vector Fitting algorithm for the creation of reduced-order models from the sampled response of a linear time-invariant system. This data-driven approach to reduction is particularly useful when the system under modeling is…