Models For Regression Problems Research Articles

Quantum algorithm for Gaussian process regression

The Gaussian process is a widely used model for regression problems in supervised machine learning. However, predicting new inputs via a Gaussian process model becomes computationally inefficient when training a large data set. This paper proposes a fast quantum algorithm for prediction based on the Gaussian process regression. The proposed quantum algorithm consists of two subalgorithms: the first one aims to efficiently prepare the squared exponential covariance matrices and covariance functions vector with annihilation and creation operators; the other is to obtain predictive mean values and covariance values for new inputs. Evidence is also shown that the proposed quantum Gaussian process regression algorithm can achieve quadratic speedup over the classical counterpart.

Comparative Evaluation and Comprehensive Analysis of Machine Learning Models for Regression Problems

Abstract Artificial intelligence and machine learning applications are of significant importance almost in every field of human life to solve problems or support human experts. However, the determination of the machine learning model to achieve a superior result for a particular problem within the wide real-life application areas is still a challenging task for researchers. The success of a model could be affected by several factors such as dataset characteristics, training strategy and model responses. Therefore, a comprehensive analysis is required to determine model ability and the efficiency of the considered strategies. This study implemented ten benchmark machine learning models on seventeen varied datasets. Experiments are performed using four different training strategies 60:40, 70:30, and 80:20 hold-out and five-fold cross-validation techniques. We used three evaluation metrics to evaluate the experimental results: mean squared error, mean absolute error, and coefficient of determination (R2 score). The considered models are analyzed, and each model's advantages, disadvantages, and data dependencies are indicated. As a result of performed excess number of experiments, the deep Long-Short Term Memory (LSTM) neural network outperformed other considered models, namely, decision tree, linear regression, support vector regression with a linear and radial basis function kernels, random forest, gradient boosting, extreme gradient boosting, shallow neural network, and deep neural network. It has also been shown that cross-validation has a tremendous impact on the results of the experiments and should be considered for the model evaluation in regression studies where data mining or selection is not performed.

Quantum-assisted Gaussian process regression

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] can be applied to Gaussian process regression (GPR), leading to an exponential reduction in computation time in some instances. We show that even in some cases not ideally suited to the quantum linear systems algorithm, a polynomial increase in efficiency still occurs.