Related papers: On the choice of initial guesses for the Newton-Ra…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
Algorithmic systems are often called upon to assist in high-stakes decision making. In light of this, algorithmic recourse, the principle wherein individuals should be able to take action against an undesirable outcome made by an…
Non-conjugate Gaussian processes (NCGPs) define a flexible probabilistic framework to model categorical, ordinal and continuous data, and are widely used in practice. However, exact inference in NCGPs is prohibitively expensive for large…
Traditional recommendation algorithms develop techniques that can help people to choose desirable items. However, in many real-world applications, along with a set of recommendations, it is also essential to quantify each recommendation's…
Robots working in real environments need to adapt to unexpected changes to avoid failures. This is an open and complex challenge that requires robots to timely predict and identify the causes of failures to prevent them. In this paper, we…
We study a class of two-stage stochastic programs in which the second stage includes a set of components with uncertain capacity, and the expression for the distribution function of the uncertain capacity includes first-stage variables.…
We present a novel statistical inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a…
We extend a multi-agent convex-optimization algorithm named Newton-Raphson consensus to a network scenario that involves directed, asynchronous and lossy communications. We theoretically analyze the stability and performance of the…
We consider an adaptive finite element method with arbitrary but fixed polynomial degree $p \ge 1$, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [Diening et al, Found.…
Some fractional Newton methods have been proposed in order to find roots of nonlinear equations using fractional derivatives. In this paper we introduce a fractional Newton method with order $\alpha+1$ and compare with another fractional…
Making accurate inferences about data is a key task in science and mathematics. Here we study the problem of \emph{retrodiction}, inferring past values of a series, in the context of chaotic dynamical systems. Specifically, we are…
Untrained large neural networks, just after random initialization, tend to favour a small subset of classes, assigning high predicted probabilities to these few classes and approximately zero probability to all others. This bias, termed…
We show how probabilistic numerics can be used to convert an initial value problem into a Gauss--Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in…
We consider minimization of a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of distributed…
In the algorithm selection research, the discussion surrounding algorithm features has been significantly overshadowed by the emphasis on problem features. Although a few empirical studies have yielded evidence regarding the effectiveness…
Stochastic optimization algorithms have been successfully applied in several domains to find optimal solutions. Because of the ever-growing complexity of the integrated systems, novel stochastic algorithms are being proposed, which makes…
In celestial mechanics, proper orbits related to missions are obtained by solving two-point boundary value problems. Since a selection method of initial value affects the convergence of the solution, developing an effective method to find…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
This paper proposes and tests the first-ever reduced basis warm-start iterative method for the parametrized linear systems, exemplified by those discretizing the parametric partial differential equations. Traditional iterative methods are…
Repeated computations on the same molecular system, but with different geometries, are often performed in quantum chemistry, for instance, in ab-initio molecular dynamics simulations or geometry optimizations. While many efficient…