Related papers: Rational minimax approximation via adaptive baryce…
We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…
In this paper, we propose Riemannian conditional gradient methods for minimizing composite functions, i.e., those that can be expressed as the sum of a smooth function and a retraction-based convex function. We analyze the convergence of…
Collecting and aggregating information from several probability measures or histograms is a fundamental task in machine learning. One of the popular solution methods for this task is to compute the barycenter of the probability measures…
Rational best approximations (in a Chebyshev sense) to real functions are characterized by an equioscillating approximation error. Similar results do not hold true for rational best approximations to complex functions in general. In the…
We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where…
We show how rational function approximations to the logarithm, such as $\log z \approx (z^2 - 1)/(z^2 + 6z + 1)$, can be turned into fast algorithms for approximating the determinant of a very large matrix. We empirically demonstrate that…
Discrete barycenters are the optimal solutions to mass transport problems for a set of discrete measures. Such transport problems arise in many applications of operations research and statistics. The best known algorithms for exact…
B\'ezier simplex fitting algorithms have been recently proposed to approximate the Pareto set/front of multi-objective continuous optimization problems. These new methods have shown to be successful at approximating various shapes of Pareto…
We revisit the problem of recovering a low-rank positive semidefinite matrix from rank-one projections using tools from optimal transport. More specifically, we show that a variational formulation of this problem is equivalent to computing…
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
When developing robust preconditioners for multiphysics problems, fractional functions of the Laplace operator often arise and need to be inverted. Rational approximation in the uniform norm can be used to convert inverting those fractional…
In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately…
This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has…
In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent…
We propose a simple and effective method for designing approximation formulas for weighted analytic functions. We consider spaces of such functions according to weight functions expressing the decay properties of the functions. Then, we…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to…
Piecewise linearization is a key technique for solving nonlinear problems in transportation network design and other optimization fields, in which generating breakpoints is a fundamental task. This paper proposes an optimal breakpoint…