Quantum Algorithms for Prediction Based on Ridge Regression

• URL: http://arxiv.org/abs/2104.13108v1
• Date: Tue, 27 Apr 2021 11:03:52 GMT
• Title: Quantum Algorithms for Prediction Based on Ridge Regression
• Authors: Menghan Chen, Chaohua Yu, Gongde Guo, and Song Lin
• Abstract summary: We propose a quantum algorithm based on ridge regression model, which get the optimal fitting parameters. The proposed algorithm has a wide range of application and the proposed algorithm can be used as a subroutine of other quantum algorithms.
• Score: 0.7612218105739107
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a quantum algorithm based on ridge regression model, which get the optimal fitting parameters w and a regularization hyperparameter {\alpha} by analysing the training dataset. The algorithm consists of two subalgorithms. One is generating predictive value for a new input, the way is to apply the phase estimation algorithm to the initial state |Xi and apply the controlled rotation to the eigenvalue register. The other is finding an optimal regularization hyperparameter {\alpha} , the way is to apply the phase estimation algorithm to the initial state |yi and apply the controlled rotation to the eigenvalue register. The second subalgorithm can compute the whole training dataset in parallel that improve the efficiency. Compared with the classical ridge regression algorithm, our algorithm overcome multicollinearity and overfitting. Moreover, it have exponentially faster. What's more, our algorithm can deal with the non-sparse matrices in comparison to some existing quantum algorithms and have slightly speedup than the existing quantum counterpart. At present, the quantum algorithm has a wide range of application and the proposed algorithm can be used as a subroutine of other quantum algorithms.

Related papers

• A quantum algorithm for advection-diffusion equation by a probabilistic imaginary-time evolution operator [0.0]
  We propose a quantum algorithm for solving the linear advection-diffusion equation by employing a new approximate probabilistic imaginary-time evolution (PITE) operator. We construct the explicit quantum circuit for realizing the imaginary-time evolution of the Hamiltonian coming from the advection-diffusion equation. Our algorithm gives comparable result to the Harrow-Hassidim-Lloyd (HHL) algorithm with similar gate complexity, while we need much less ancillary qubits.
  arXiv  Detail & Related papers  (2024-09-27T08:56:21Z)
• An adaptive Bayesian quantum algorithm for phase estimation [0.0]
  We present a coherence-based phase-estimation algorithm which can achieve the optimal quadratic scaling in the mean absolute error and the mean squared error. In the presence of noise, our algorithm produces errors that approach the theoretical lower bound.
  arXiv  Detail & Related papers  (2023-03-02T19:00:01Z)
• Accelerated First-Order Optimization under Nonlinear Constraints [73.2273449996098]
  We exploit between first-order algorithms for constrained optimization and non-smooth systems to design a new class of accelerated first-order algorithms. An important property of these algorithms is that constraints are expressed in terms of velocities instead of sparse variables.
  arXiv  Detail & Related papers  (2023-02-01T08:50:48Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Ising formulation of integer optimization problems for utilizing quantum annealing in iterative improvement strategy [1.14219428942199]
  We propose an Ising formulation of integer optimization problems to utilize quantum annealing in the iterative improvement strategy. We analytically show that a first-order phase transition is successfully avoided for a fully connected ferro Potts model if the overlap between a ground state and a candidate solution exceeds a threshold.
  arXiv  Detail & Related papers  (2022-11-08T02:12:49Z)
• Classical and Quantum Iterative Optimization Algorithms Based on Matrix Legendre-Bregman Projections [1.5736899098702972]
  We consider Legendre-Bregman projections defined on the Hermitian matrix space and design iterative optimization algorithms based on them. We study both exact and approximate Bregman projection algorithms. In particular, our approximate iterative algorithm gives rise to the non-commutative versions of the generalized iterative scaling (GIS) algorithm for maximum entropy inference.
  arXiv  Detail & Related papers  (2022-09-28T15:59:08Z)
• Gradient-Free optimization algorithm for single-qubit quantum classifier [0.3314882635954752]
  A gradient-free optimization algorithm is proposed to overcome the effects of barren plateau caused by quantum devices. The proposed algorithm is demonstrated for a classification task and is compared with that using Adam. The proposed gradient-free optimization algorithm can reach a high accuracy faster than that using Adam.
  arXiv  Detail & Related papers  (2022-05-10T08:45:03Z)
• A Fully Single Loop Algorithm for Bilevel Optimization without Hessian Inverse [121.54116938140754]
  We propose a new Hessian inverse free Fully Single Loop Algorithm for bilevel optimization problems. We show that our algorithm converges with the rate of $O(epsilon-2)$.
  arXiv  Detail & Related papers  (2021-12-09T02:27:52Z)
• Provably Faster Algorithms for Bilevel Optimization [54.83583213812667]
  Bilevel optimization has been widely applied in many important machine learning applications. We propose two new algorithms for bilevel optimization. We show that both algorithms achieve the complexity of $mathcalO(epsilon-1.5)$, which outperforms all existing algorithms by the order of magnitude.
  arXiv  Detail & Related papers  (2021-06-08T21:05:30Z)
• Single-Timescale Stochastic Nonconvex-Concave Optimization for Smooth Nonlinear TD Learning [145.54544979467872]
  We propose two single-timescale single-loop algorithms that require only one data point each step. Our results are expressed in a form of simultaneous primal and dual side convergence.
  arXiv  Detail & Related papers  (2020-08-23T20:36:49Z)
• Accelerated Message Passing for Entropy-Regularized MAP Inference [89.15658822319928]
  Maximum a posteriori (MAP) inference in discrete-valued random fields is a fundamental problem in machine learning. Due to the difficulty of this problem, linear programming (LP) relaxations are commonly used to derive specialized message passing algorithms. We present randomized methods for accelerating these algorithms by leveraging techniques that underlie classical accelerated gradient.
  arXiv  Detail & Related papers  (2020-07-01T18:43:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.