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Classification and Regression Error Bounds for Inhomogenous Data With Applications to Wireless Networks

Ghurumuruhan Ganesan

TL;DR

This paper considers classification of data in the presence of non-stationary noise and establishes ergodic type sufficient conditions that guarantee the achievability of the Bayes error bound, using universal rules.

Abstract

In this paper, we study classification and regression error bounds for inhomogenous data that are independent but not necessarily identically distributed. First, we consider classification of data in the presence of non-stationary noise and establish ergodic type sufficient conditions that guarantee the achievability of the Bayes error bound, using universal rules. We then perform a similar analysis for $k$-nearest neighbour regression and obtain optimal error bounds for the same. Finally, we illustrate applications of our results in the context of wireless networks.

Classification and Regression Error Bounds for Inhomogenous Data With Applications to Wireless Networks

TL;DR

This paper considers classification of data in the presence of non-stationary noise and establishes ergodic type sufficient conditions that guarantee the achievability of the Bayes error bound, using universal rules.

Abstract

In this paper, we study classification and regression error bounds for inhomogenous data that are independent but not necessarily identically distributed. First, we consider classification of data in the presence of non-stationary noise and establish ergodic type sufficient conditions that guarantee the achievability of the Bayes error bound, using universal rules. We then perform a similar analysis for -nearest neighbour regression and obtain optimal error bounds for the same. Finally, we illustrate applications of our results in the context of wireless networks.
Paper Structure (4 sections, 3 theorems, 72 equations)

This paper contains 4 sections, 3 theorems, 72 equations.

Table of Contents

  1. Introduction
  2. Regression of Inhomogenous Data
  3. Classification of Inhomogenous Data
  4. Applications and Future Directions

Key Result

Theorem 2.1

If $h$ is uniformly continuous and as $n \rightarrow \infty,$ where $f$ is a uniformly continuous density, then there is a universally consistent regressor that achieves (err_less).

Theorems & Definitions (3)

  • Theorem 2.1
  • Theorem 3.1
  • Lemma 3.1