Related papers: A continuation method for computing the multilinea…
PageRank is a widespread model for analysing the relative relevance of nodes within large graphs arising in several applications. In the current paper, we present a cost-effective Hessenberg-type method built upon the Hessenberg process for…
Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of…
When machine learning systems meet real world applications, accuracy is only one of several requirements. In this paper, we assay a complementary perspective originating from the increasing availability of pre-trained and regularly…
A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
The Bayesian Mallows model is a flexible tool for analyzing data in the form of complete or partial rankings, and transitive or intransitive pairwise preferences. In many potential applications of preference learning, data arrive…
Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models, the predicted choice probabilities often form a bounded and…
Counterfactual explanations are viewed as an effective way to explain machine learning predictions. This interest is reflected by a relatively young literature with already dozens of algorithms aiming to generate such explanations. These…
Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on…
Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…
This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank (PPR) computation. At each stage of the process, we employ a localized inexact proximal point iteration to solve a simplified…
In this paper, we propose three methods to solve the PageRank problem for the transition matrices with both row and column sparsity. Our methods reduce the PageRank problem to the convex optimization problem over the simplex. The first…
We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…
The Multiquadric Radial Basis Function (MQ) Method is a meshless collocation method with global basis functions. It is known to have exponentional convergence for interpolation problems. We descretize nonlinear elliptic PDEs by the MQ…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of…
The continuation method is a popular approach in non-convex optimization and computer vision. The main idea is to start from a simple function that can be minimized efficiently, and gradually transform it to the more complicated original…
The Parameter Continuation Theorem is the theoretical foundation for polynomial homotopy continuation, which is one of the main tools in computational algebraic geometry. In this note, we give a short proof using Gr\"obner bases. Our…
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…
This work presents a comprehensive framework for capturing bifurcating phenomena and detecting bifurcation curves in nonlinear multiparametric partial differential equations, where the system exhibits multiple coexisting solutions for given…