Quantum algorithm for logistic regression
arXiv:1906.03834
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.
We have just found that our core algorithm is similar to the algorithm of a published paper (Shao C. Physical Review A, 2019, 99(4): 042325.),which makes our algorithm less innovative, so we apply for retraction
References in corpus (17)
- Quantum Machine Learning
- Quantum Mechanics helps in searching for a needle in a haystack
- Quantum algorithm for solving linear systems of equations
- Quantum support vector machine for big data classification
- Quantum machine learning in feature Hilbert spaces
- Quantum principal component analysis
- Quantum random access memory
- Quantum Data Fitting
- Quantum algorithms for supervised and unsupervised machine learning
- A quantum linear system algorithm for dense matrices
- Quantum Hopfield neural network
- Quantum Algorithm for Linear Regression
- Quantum Discriminant Analysis for Dimensionality Reduction and Classification
- Quantum algorithm for association rules mining
- Quantum algorithm for association rules mining
- Asymptotic Quantum Algorithm for the Toeplitz Systems
- Quantum Conditional Random Field