相关论文: Approximation of Functions on Manifolds in High Di…
Function approximation is widely used in reinforcement learning to handle the computational difficulties associated with very large state spaces. However, function approximation introduces errors which may lead to instabilities when using…
Recently, a framework for the approximation of the entire set of $\epsilon$-efficient solutions (denote by $E_\epsilon$) of a multi-objective optimization problem with stochastic search algorithms has been proposed. It was proven that such…
We introduce Noisy Feature Mixup (NFM), an inexpensive yet effective method for data augmentation that combines the best of interpolation based training and noise injection schemes. Rather than training with convex combinations of pairs of…
We address the problem of minimizing a smooth function $f^0(x)$ over a compact set $D$ defined by smooth functional constraints $f^i(x)\leq 0,~ i = 1,\ldots, m$ given noisy value measurements of $f^i(x)$. This problem arises in…
This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains to a worst-case setting tied to a symmetric, convex, and…
We consider the problem of reconstructing a low rank matrix from noisy observations of a subset of its entries. This task has applications in statistical learning, computer vision, and signal processing. In these contexts, "noise"…
This work explores the neural network approximation capabilities for functions within the spectral Barron space $\mathscr{B}^s$, where $s$ is the smoothness index. We demonstrate that for functions in $\mathscr{B}^{1/2}$, a shallow neural…
In computer graphics, smooth data reconstruction on 2D or 3D manifolds usually refers to subdivision problems. Such a method is only valid based on dense sample points. The manifold usually needs to be triangulated into meshes (or patches)…
A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The…
Meshfree methods based on radial basis function (RBF) approximation are of interest for numerical solution of partial differential equations (PDEs) because they are flexible with respect to the geometry of the computational domain, they can…
Recent work on approximate linear programming (ALP) techniques for first-order Markov Decision Processes (FOMDPs) represents the value function linearly w.r.t. a set of first-order basis functions and uses linear programming techniques to…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to…
Image restoration has been an extensively researched topic in numerous fields. With the advent of deep learning, a lot of the current algorithms were replaced by algorithms that are more flexible and robust. Deep networks have demonstrated…
The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…
Approximations of non-smooth multivariate functions return low-order approximations in the vicinities of the singularities. Most prior works solve this problem for univariate functions. In this work we introduce a method for approximating…
Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to its ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the…
This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…
Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…