Related papers: Approximating functions on ${\mathbb R}^+$ by expo…
This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuously specified Gaussian random field. We show that for…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
In this paper, we present a rigorous framework for rational minimax approximation of matrix-valued functions that generalizes classical scalar approximation theory. Given sampled data $\{(x_\ell, {F}(x_\ell))\}_{\ell=1}^m$ where…
We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
We obtain the best approximation in $L^1(\R)$, by entire functions of exponential type, for a class of even functions that includes $e^{-\lambda|x|}$, where $\lambda >0$, $\log |x|$ and $|x|^{\alpha}$, where $-1 < \alpha < 1$. We also give…
We construct a new scheme of approximation of any multivalued algebraic function $f(z)$ by a sequence $\{r_{n}(z)\}_{n\in \mathbb{N}}$ of rational functions. The latter sequence is generated by a recurrence relation which is completely…
The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
We consider the minimization of a sum of a smooth function with a nonsmooth composite function, where the composition is applied on a random linear mapping. This random composite model encompasses many problems, and can especially capture…
Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In…
In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…
In this work a general approach to compute a compressed representation of the exponential $\exp(h)$ of a high-dimensional function $h$ is presented. Such exponential functions play an important role in several problems in Uncertainty…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some methods of this approximation for functions in a class induced by the convolution with a given function,…