Related papers: Efficiency of the Multisection Method
While well-known methods to list the intersections of either a list of segments or a complex polygon aim at achieving optimal time-complexity they often do so at the cost of memory comsumption and complex code. Real-life software…
The Frank-Wolfe algorithm is a method for constrained optimization that relies on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational…
An MT2 calculation algorithm is described. It is shown to achieve better precision than the fastest and most popular existing bisection-based methods. Most importantly, it is also the first algorithm to be able to reliably calculate…
We propose a second-order method for unconditional minimization of functions $f(z)$ of complex arguments. We call it the Mixed Newton Method due to the use of the mixed Wirtinger derivative $\frac{\partial^2f}{\partial\bar z\partial z}$ for…
Two methods to reduce the CPU time needed for the numerical evaluation of cross-sections and similar quantities are discussed.
We consider the problem of detecting multiple changepoints in large data sets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example in genetics as we analyse larger regions of the…
We shed new light on the \textit{smoothness} of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the…
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…
Multi-label document classification is a traditional task in NLP. Compared to single-label classification, each document can be assigned multiple classes. This problem is crucially important in various domains, such as tagging scientific…
This short paper describes a numerical method for optimising the conservative confidence bound on the reliability of a system based on tests of its individual components. This is an alternative to the algorithmic approaches identified in…
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…
We present a new method that includes three key components of distributed optimization and federated learning: variance reduction of stochastic gradients, partial participation, and compressed communication. We prove that the new method has…
We present the first mini-batch algorithm for maximizing a non-negative monotone decomposable submodular function, $F=\sum_{i=1}^N f^i$, under a set of constraints. We consider two sampling approaches: uniform and weighted. We first show…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…
Multiclass probability estimation is the problem of estimating conditional probabilities of a data point belonging to a class given its covariate information. It has broad applications in statistical analysis and data science. Recently a…
This paper considers the simple bilevel optimization (SBO) problem, which minimizes a composite convex function over the optimal solution set of another composite convex minimization problem. We first show that this bilevel problem is…
This paper revisits the parametric analysis of semidefinite optimization problems with respect to the perturbation of the objective function along a fixed direction. We review the notions of invariancy set, nonlinearity interval, and…