Constant-Time Algorithms for Continuous Optimization Problems

Yuichi Yoshida

doi:10.1007/978-981-16-4095-7_3

Abstract

AbstractIn this chapter, we consider constant-time algorithms for continuous optimization problems. Specifically, we consider quadratic function minimization and tensor decomposition, both of which have numerous applications in machine learning and data mining. The key component in our analysis isgraph limit theory, which was originally developed to study graphs analytically.

Highlights

We turn our attention to constant-time algorithms for continuous optimization problems
This section reviews the basic concepts of graph limit theory
They formulated the estimation problem as the minimization of a squared loss and showed that the Pearson divergence can be estimated from the minimum value

Summary

Introduction

We turn our attention to constant-time algorithms for continuous optimization problems. We consider quadratic function minimization and tensor decomposition, both of which have numerous applications in machine learning and data mining. The key component in our analysis is graph limit theory, which was originally developed to study graphs analytically. Throughout this chapter, we assume the real RAM model, in which we can perform basic algebraic operations on real numbers in one step. For a positive integer n, let [n] denote the set {1, 2, . The algorithms and analysis presented in this chapter are based on [5, 6]

Graph Limit Theory

Background

Preliminaries