Related papers: Vector Fitting for Matrix-valued Rational Approxim…
The objective of this paper is to design an embedding method that maps local features describing an image (e.g. SIFT) to a higher dimensional representation useful for the image retrieval problem. First, motivated by the relationship…
We propose a method for designing policies for convex stochastic control problems characterized by random linear dynamics and convex stage cost. We consider policies that employ quadratic approximate value functions as a substitute for the…
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…
A widely used approach to compute the action $f(A)v$ of a matrix function $f(A)$ on a vector $v$ is to use a rational approximation $r$ for $f$ and compute $r(A)v$ instead. If $r$ is not computed adaptively as in rational Krylov methods,…
We consider the following basic problem: given an $n$-variate degree-$d$ homogeneous polynomial $f$ with real coefficients, compute a unit vector $x \in \mathbb{R}^n$ that maximizes $|f(x)|$. Besides its fundamental nature, this problem…
Following the success of dot-product attention in Transformers, numerous approximations have been recently proposed to address its quadratic complexity with respect to the input length. However, all approximations thus far have ignored the…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to non-empty compact subsets of $\mathbb{R}^d$, $F: [a,b] \to K(\mathbb{R}^d)$, we discuss the problem of computing good approximations of F. We…
We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…
In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
Kernel methods are a highly effective and widely used collection of modern machine learning algorithms. A fundamental limitation of virtually all such methods are computations involving the kernel matrix that naively scale quadratically…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
Vectorization of images is a key concern uniting computer graphics and computer vision communities. In this paper we are presenting a novel idea for efficient, customizable vectorization of raster images, based on Catmull Rom spline…
Quantization is a fundamental optimization for many machine-learning use cases, including compressing gradients, model weights and activations, and datasets. The most accurate form of quantization is \emph{adaptive}, where the error is…
We introduce a new approximate solution technique for first-order Markov decision processes (FOMDPs). Representing the value function linearly w.r.t. a set of first-order basis functions, we compute suitable weights by casting the…
Multidimensional fitting (MDF) method is a multivariate data analysis method recently developed and based on the fitting of distances. Two matrices are available: one contains the coordinates of the points and the second contains the…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar…
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,…
This paper introduce a novel metric of an objective function f, we say VC (value change) to measure the difficulty and approximation affection when conducting an neural network approximation task, and it numerically supports characterizing…