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A common method of generalizing binary to multi-class classification is the error correcting code (ECC). ECCs may be optimized in a number of ways, for instance by making them orthogonal. Here we test two types of orthogonal ECCs on seven…
Dyadic prediction methods operate on pairs of objects (dyads), aiming to infer labels for out-of-sample dyads. We consider the full and almost full cold start problem in dyadic prediction, a setting that occurs when both objects in an…
Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…
Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…
Our paper "Solving Third Order Linear Difference Equations in Terms of Second Order Equations" gave two algorithms for solving difference equations in terms of lower order equations: an algorithm for absolute factorization, and an algorithm…
We present a new microscopic ODE-based model for pedestrian dynamics: the Gradient Navigation Model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is…
Selecting an effective step-size is a fundamental challenge in first-order optimization, especially for problems with non-Euclidean geometries. This paper presents a novel adaptive step-size strategy for optimization algorithms that rely on…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
We consider a general class of nonsmooth optimal control problems with partial differential equation (PDE) constraints, which are very challenging due to its nonsmooth objective functionals and the resulting high-dimensional and…
We propose adaptive, line search-free second-order methods with optimal rate of convergence for solving convex-concave min-max problems. By means of an adaptive step size, our algorithms feature a simple update rule that requires solving…
The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of…
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…
We study a fixed step-size noisy distributed gradient descent algorithm for solving optimization problems in which the objective is a finite sum of smooth but possibly non-convex functions. Random perturbations are introduced to the…
We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…
Gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs). Motivated by the fact that existing ODEs do not distinguish between two fundamentally different…
Designing and analyzing optimization methods via continuous-time models expressed as ordinary differential equations (ODEs) is a promising approach for its intuitiveness and simplicity. A key concern, however, is that the convergence rates…
Machine learning models support decision-making, yet the reasons behind their predictions are opaque. Clear and reliable explanations help users make informed decisions and avoid blindly trusting model outputs. However, many existing…
Numerous variable selection methods rely on a two-stage procedure, where a sparsity-inducing penalty is used in the first stage to predict the support, which is then conveyed to the second stage for estimation or inference purposes. In this…
This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…