Related papers: Building Function Approximators on top of Haar Sca…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
Feature extraction and matching are among central problems of computer vision. It is inefficent to search features over all locations and scales. Neurophysiological evidence shows that to locate objects in a digital image the human visual…
High-dimensional representations, such as radial basis function networks or tile coding, are common choices for policy evaluation in reinforcement learning. Learning with such high-dimensional representations, however, can be expensive,…
Learning graph-structured data with graph neural networks (GNNs) has been recently emerging as an important field because of its wide applicability in bioinformatics, chemoinformatics, social network analysis and data mining. Recent GNN…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is…
In this paper we describe an approach to construct large extendable collections of vectors in predefined spaces of given dimensions. These collections are useful for neural network latent space configuration and training. For classification…
This paper proposes a novel localized Fourier extension method for approximating non-periodic functions via domain segmentation. By partitioning the computational domain into subregions with uniform discretization scales, the method…
Learning on sets is increasingly gaining attention in the machine learning community, due to its widespread applicability. Typically, representations over sets are computed by using fixed aggregation functions such as sum or maximum.…
A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there…
Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the…
An enriched approximation space is the span of a conventional basis with a few extra functions included, for example to capture known features of the solution to a computational problem. Adding functions to a basis makes it overcomplete…
We study the problem of constructing a linear sketch of minimum dimension that allows approximation of a given real-valued function $f \colon \mathbb{F}_2^n \rightarrow \mathbb R$ with small expected squared error. We develop a general…
The A* algorithm is commonly used to solve NP-hard combinatorial optimization problems. When provided with a completely informed heuristic function, A* solves many NP-hard minimum-cost path problems in time polynomial in the branching…
In this note we extend kernel function approximation results for neural networks with Gaussian-distributed weights to single-layer networks initialized using Haar-distributed random orthogonal matrices (with possible rescaling). This is…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
Choosing a suitable filtering function for the Mapper algorithm can be difficult due to its arbitrariness and domain-specific requirements. Finding a general filtering function that can be applied across domains is therefore of interest,…
There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types…
We propose a highly structured neural network architecture for semantic segmentation with an extremely small model size, suitable for low-power embedded and mobile platforms. Specifically, our architecture combines i) a Haar wavelet-based…