Related papers: Parameter selection and numerical approximation pr…
We introduce a continuous analog of the Fourier ratio for compactly supported Borel measures. For a measure \(\mu\) on \(\mathbb{R}^d\) and \(f\in L^2(\mu)\), the Fourier ratio compares \(L^1\) and \(L^2\) norms of a regularized Fourier…
A variety of techniques have been developed for the approximation of non-periodic functions. In particular, there are approximation techniques based on rank-$1$ lattices and transformed rank-$1$ lattices, including methods that use sampling…
The ability to resolve detail in the object that is being imaged, named by resolution, is the core parameter of an imaging system. Super-resolution is a class of techniques that can enhance the resolution of an imaging system and even…
In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…
Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…
Approximate pattern matching is a natural and well-studied problem on strings: Given a text $T$, a pattern $P$, and a threshold $k$, find (the starting positions of) all substrings of $T$ that are at distance at most $k$ from $P$. We…
Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…
Quantitative helio- and asteroseismology require very precise measurements of the frequencies, amplitudes, and lifetimes of the global modes of stellar oscillation. It is common knowledge that the precision of these measurements depends on…
We consider the problem of approximating a truncated Gaussian kernel using Fourier (trigonometric) functions. The computation-intensive bilateral filter can be expressed using fast convolutions by applying such an approximation to its range…
While evolutionary algorithms are known to be very successful for a broad range of applications, the algorithm designer is often left with many algorithmic choices, for example, the size of the population, the mutation rates, and the…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
Many Bayesian network modelling applications suffer from the issue of data scarcity. Hence the use of expert judgement often becomes necessary to determine the parameters of the conditional probability tables (CPTs) throughout the network.…
In recent years, many design automation methods have been developed to routinely create approximate implementations of circuits and programs that show excellent trade-offs between the quality of output and required resources. This paper…
One-dimensional function approximation is a fundamental problem in scientific computing and engineering applications. While neural networks possess powerful universal approximation capabilities, their optimization process is often hindered…
This article describes a robust algorithm to estimate a conditional probability density f(t|x) as a non-parametric smooth regression function. It is based on a neural network and the Bayesian interpretation of the network output as a…
Fine-tuning pre-trained models has been ubiquitously proven to be effective in a wide range of NLP tasks. However, fine-tuning the whole model is parameter inefficient as it always yields an entirely new model for each task. Currently, many…
A Fixed-Parameter Tractable (\FPT) $\rho$-approximation algorithm for a minimization (resp. maximization) parameterized problem $P$ is an FPT algorithm that, given an instance $(x, k)\in P$ computes a solution of cost at most $k \cdot…
A supervised learning problem is to find a function in a hypothesis function space given values on isolated data points. Inspired by the frequency principle in neural networks, we propose a Fourier-domain variational formulation for…
We study an expansion method for high-dimensional parabolic PDEs which constructs accurate approximate solutions by decomposition into solutions to lower-dimensional PDEs, and which is particularly effective if there are a low number of…
It is well known that approximation of functions on $[0,1]$ whose periodic extension is not continuous fail to converge uniformly due to rapid Gibbs oscillations near the boundary. Among several approaches that have been proposed toward the…