Related papers: Reconstruction of rational functions made simple
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…
Computational approaches in historical linguistics have been increasingly applied during the past decade and many new methods that implement parts of the traditional comparative method have been proposed. Despite these increased efforts,…
Recovering frequency-localized functions from pointwise data is a fundamental task in signal processing. We examine this problem from an approximation-theoretic perspective, focusing on least squares and deep learning-based methods. First,…
This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the…
Text Simplification improves the readability of sentences through several rewriting transformations, such as lexical paraphrasing, deletion, and splitting. Current simplification systems are predominantly sequence-to-sequence models that…
In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from…
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents…
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
We design and analyze an algorithm for computing solutions with coefficients in a finite field $\mathbb{F}_q$ of underdetermined systems defined over $\mathbb{F}_q$. The algorithm is based on reductions to zero-dimensional searches. The…
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…
The method of Symmetries of Feynman Integrals defines for any Feynman diagram a set of partial differential equations. On some locus in parameter space the equations imply that the diagram can be reduced to a linear combination of simpler…
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…
This paper studies the data-driven reconstruction of firing rate dynamics of brain activity described by linear-threshold network models. Identifying the system parameters directly leads to a large number of variables and a highly…
Sampling is a fundamental technique, and sampling without replacement is often desirable when duplicate samples are not beneficial. Within machine learning, sampling is useful for generating diverse outputs from a trained model. We present…
Although some recent works show potential complementarity among different state-of-the-art systems, few works try to investigate this problem in text summarization. Researchers in other areas commonly refer to the techniques of reranking or…
Machine learning is rapidly making its path into natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a…
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…
Functional methods like Dyson-Schwinger equations, the nPI effective action formalism, bound state equations and the functional renormalization group are versatile tools to study quantum field theories. They are exact, nonperturbative…
Many tasks in image processing can be tackled by modeling an appropriate data fidelity term $\Phi: \mathbb{R}^n \rightarrow \mathbb{R} \cup \{+\infty\}$ and then solve one of the regularized minimization problems \begin{align*}…