.png){kind=icon}
.png){kind=icon}
Return
Quantum algorithms for structured prediction
.png){kind=icon}
PRE
AI
DOI：10.1007/s42484-022-00078-w.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the structured prediction problem with a runtime that scales with the square root of the size of the label space, and in similar to O (1/..) with respect to the precision,.., of the solution. Motivated by robust inference techniques in machine learning, we then introduce another quantum algorithm that solves a smooth approximation of the structured prediction problem with a similar quantum speedup in the size of the label space and a similar scaling in the precision parameter. In doing so, we analyze a variant of stochastic gradient descent for convex optimization in the presence of an additive error in the calculation of the gradients, and show that its convergence rate does not deteriorate if the additive errors are of the order O(v root epsilon). This algorithm uses quantum Gibbs sampling at temperature O(epsilon) as a subroutine. Based on these theoretical observations, we propose a method for using quantum Gibbs samplers to combine feedforward neural networks with probabilistic graphical models for quantum machine learning. Our numerical results using Monte Carlo simulations on an image tagging task demonstrate the benefit of the approach.
Keywords:
Quantum algorithms
Statistical learning
Structured prediction
Support vector machines
Computational complexity
Query complexity
Quantum minimum finding
Quantum Gibbs sampling
Stochastic gradient descent
Stochastic subgradient methods
Stochastic average gradient methods
Smooth approximation
Journal
Q
IF:
4.4
Papers:
427
Citations:
796