Related papers: Reciprocal first-order second-moment method
The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all…
Classical first passage under resetting is a paradigm in the search process. Despite its multitude of applications across interdisciplinary sciences, experimental realizations of such resetting processes posit practical challenges in…
The paper proposes a linesearch for a primal-dual method. Each iteration of the linesearch requires to update only the dual (or primal) variable. For many problems, in particular for regularized least squares, the linesearch does not…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…
We present a simple scheme for restarting first-order methods for convex optimization problems. Restarts are made based only on achieving specified decreases in objective values, the specified amounts being the same for all optimization…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturally leads to multi-parameter models for which adequate…
In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…
A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity…
We propose a projection based multi-moment matching method for model order reduction of quadratic-bilinear systems. The goal is to construct a reduced system that ensures higher-order moment matching for the multivariate transfer functions…
It is proposed that to the usual probability theory, three definitions and a new theorem are added, the resulting theory allows one to displace the central role usually given to the notion of conditional probability. When a mapping $\phi$…
Effective operators have been used extensively to understand small deviations from the Standard Model in the search for new physics. So far there has been no general method to fit for small parameters when higher order corrections in these…
Probability functions appear in constraints of many optimization problems in practice and have become quite popular. Understanding their first-order properties has proven useful, not only theoretically but also in implementable algorithms,…
Statistical matching methods are widely used in the social and health sciences to estimate causal effects using observational data. Often the objective is to find comparable groups with similar covariate distributions in a dataset, with the…
Real-world recommendation systems often consist of two phases. In the first phase, multiple predictive models produce the probability of different immediate user actions. In the second phase, these predictions are aggregated according to a…
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…
This paper is devoted to a new first order Taylor-like formula where the corresponding remainder is strongly reduced in comparison with the usual one which appears in the classical Taylor's formula. To derive this new formula, we introduce…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
Recursion formulae are derived for the calculation of two centre matrix elements of a radial function in relativistic quantum mechanics. The recursions are obtained between not necessarily diagonal radial eigensates using arbitrary radial…