Related papers: $(n D+1)$ Pad\'e approximation
In this paper we develop an optimisation based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: multivariate polynomial approximation and multivariate generalised rational approximation. In the…
Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on…
We study reduction schemes for functions of "many" variables into system of functions in one variable. Our setting includes infinite-dimensions. Following Cybenko-Kolmogorov, the outline for our results is as follows: We present explicit…
Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…
We reformulate the Cavity Approximation (CA), a class of algorithms recently introduced for improving the Bethe approximation estimates of marginals in graphical models. In our new formulation, which allows for the treatment of multivalued…
We present a novel method for calculating Pad\'e approximants that is capable of eliminating spurious poles placed at the point of development and of identifying and eliminating spurious poles created by precision limitations and/or noisy…
Dempster-Shafer theory is widely applied in uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. A distance between two basic probability assignments(BPAs) presents a measure of performance…
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of…
The paper deals with the problem of approximating the functions of several variables by branched continued fractions, in particular, multidimensional A- and J-fractions with independent variables. A generalization of Gragg's algorithm is…
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…
The use of approximants of Pad\`e type are employed to develop a method aimed at opening new perspectives in the theory of Appell polynomials $a_n(x)$, specified by the generating function \sum_{n=0}^{\infty} \frac{t^n}{n!} a_n(x) = A(t)…
Multiview varieties are mathematical models for the set of image feature correspondences that can be produced by a given camera arrangement. They possess an invariant known as their Euclidean distance (ED) degree, which measures the…
Frequency estimation is a fundamental problem in many areas. The well-known A&M and its variant estimators have established an estimation framework by iteratively interpolating the discrete Fourier transform (DFT) coefficients. In general,…
This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…
Variational Bayes (VB) is a recent approximate method for Bayesian inference. It has the merit of being a fast and scalable alternative to Markov Chain Monte Carlo (MCMC) but its approximation error is often unknown. In this paper, we…
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…
Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…
We introduce a bottleneck method for learning data representations based on information deficiency, rather than the more traditional information sufficiency. A variational upper bound allows us to implement this method efficiently. The…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…