Quantum algorithm for logistic regression

TL;DR

This paper introduces a quantum algorithm for logistic regression that significantly accelerates training by efficiently computing gradients, especially beneficial for high-dimensional data, enabling faster classification in machine learning tasks.

Contribution

The paper presents a quantum algorithm that achieves exponential speedup in training logistic regression models by efficiently computing gradients, applicable when data dimension grows polylogarithmically with data size.

Findings

Achieves exponential speedup over classical algorithms in gradient computation.

Applicable when data dimension M is O(polylog N).

Allows fast classification after training.

Abstract

Logistic regression (LR) is an important machine learning model for classification, with wide applications in text classification, image analysis and medicine diagnosis, etc. However, training LR generally entails an iterative gradient descent method, and is quite time consuming when processing big data sets. To solve this problem, we present a quantum algorithm for LR to implement the key task of the gradient descent method, obtaining the classical gradients in each iteration. It is shown that our algorithm achieves exponential speedup over its classical counterpart in each iteration when the dimension of each data point M grows polylogarithmically with the number of data points N, i.e.,M=O(polylog N). It is worth noting that the optimal model parameters are finally derived by performing simple calculations on the obtained gradients. So once the optimal model parameters are determined, one can use them to classify new data at little cost.