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Quantum Random Forest for the Regression Problem

Kamil Khadiev, Liliya Safina

Abstract

The Random Forest model is one of the popular models of Machine learning. We present a quantum algorithm for testing (forecasting) process of the Random Forest machine learning model for the Regression problem. The presented algorithm is more efficient (in terms of query complexity or running time) than the classical counterpart.

Quantum Random Forest for the Regression Problem

Abstract

The Random Forest model is one of the popular models of Machine learning. We present a quantum algorithm for testing (forecasting) process of the Random Forest machine learning model for the Regression problem. The presented algorithm is more efficient (in terms of query complexity or running time) than the classical counterpart.
Paper Structure (12 sections, 3 theorems, 19 equations, 4 figures, 3 tables)

This paper contains 12 sections, 3 theorems, 19 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Basics of Machine Learning. Supervised Learning
  4. Random Forest Model
  5. Basics of Quantum Computing
  6. Quantum Query Model
  7. Quantum Algorithm for Testing Process of Random Forest
  8. Tools
  9. Algorithm for One Decision Tree
  10. Algorithm for the Random Forest Model
  11. On Circuit Implementation
  12. Conclusion

Key Result

Lemma 1

Let ${\cal U}$ be a (classical or quantum) algorithm which aims to estimate some quantity $\beta$, and whose output $\tilde{\beta}$ satisfies $|\beta-\tilde{\beta}|\leq \varepsilon$ except with probability $\gamma$ , for some fixed $\gamma<0.5$. Then, for any $\delta>0$, it suffices to repeat the ${

Figures (4)

  • Figure 1: Quantum gate circuits
  • Figure 2: Quantum random forest forecasting circuit
  • Figure 3: Quantum tree forecasting circuit
  • Figure 4: The operator of multiplication by 2 circuit

Theorems & Definitions (3)

  • Lemma 1: Powering lemma jvv1986 or success probability boosting technique
  • Lemma 2: Amplitude estimation bhmt2002
  • Theorem 1