Related papers: A Critical Path Approach to Analyzing Parallelism …
Effective resistance, which originates from the field of circuits analysis, is an important graph distance in spectral graph theory. It has found numerous applications in various areas, such as graph data mining, spectral graph…
We develop and analyze several different second-order algorithms for computing a near-optimal solution path of a convex parametric optimization problem with smooth Hessian. Our algorithms are inspired by a differential equation perspective…
In the recent years it can be observed increasing popularity of parallel processing using multi-core processors, local clusters, GPU and others. Moreover, currently one of the main requirements the IT users is the reduction of maintaining…
We present a novel approach to differential cost analysis that, given a program revision, attempts to statically bound the difference in resource usage, or cost, between the two program versions. Differential cost analysis is particularly…
Mixed-effects models are widely used to model data with hierarchical grouping structures and high-cardinality categorical predictor variables. However, for high-dimensional crossed random effects, current standard computations relying on…
The PC algorithm is the state-of-the-art algorithm for causal structure discovery on observational data. It can be computationally expensive in the worst case due to the conditional independence tests are performed in an…
This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature. Although prior work has established convergence results for algorithms that integrate both descent…
This paper proposes and analyzes an a posteriori error estimator for the finite element multi-scale discretization approximation of the Steklov eigenvalue problem. Based on the a posteriori error estimates, an adaptive algorithm of shifted…
We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…
Cyclomatic complexity is an incompletely specified but mathematically principled software metric that can be usefully applied to both source and binary code. We consider the application of path homology as a stronger analogue of cyclomatic…
We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a…
The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…
Algorithms involving Gaussian processes or determinantal point processes typically require computing the determinant of a kernel matrix. Frequently, the latter is computed from the Cholesky decomposition, an algorithm of cubic complexity in…
The on-line shortest path problem is considered under various models of partial monitoring. Given a weighted directed acyclic graph whose edge weights can change in an arbitrary (adversarial) way, a decision maker has to choose in each…
Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a…
In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…
Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…
In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This is a fundamental problem in query complexity, and appears in many contexts, particularly…
We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and…
We show that the Variational Quantum-Classical Simulation algorithm admits a finite circuit depth scaling collapse when targeting the critical point of the transverse field Ising chain. The order parameter only collapses on one side of the…