SVRLoss

class SVRLoss(**kwargs)[source]

Bases: KernelLoss

This class provides a kernel loss function for regression tasks by fitting an SVR model from scikit-learn. Given training samples, \(x_{i}\), with labels, \(y_{i}\), and a kernel, \(K_{θ}\), parameterized by values, \(θ\), the loss is defined as:

\[SVRLoss = -0.5 \sum_{i,j} \beta_i \beta_j K_θ(x_i, x_j) - \epsilon \sum_{i} |\beta_i| + \sum_{i} y_i \beta_i\]

where \(\beta_i = \alpha_i - \alpha_i^*\) are the optimal Lagrange multipliers found by solving the standard SVR quadratic program. Note that the hyper-parameters C and epsilon can be specified through the keyword args.

Minimizing this loss over the parameters, \(θ\), of the kernel is equivalent to minimizing the optimized dual objective of the SVR, which is a proxy for the primal objective (a combination of the model complexity and the training error).

See https://arxiv.org/abs/2105.03406 for further details on kernel training (though it focuses on classification, the principle applies to regression).

Parameters:

**kwargs – Arbitrary keyword arguments to pass to SVR constructor within SVRLoss evaluation.

Methods

evaluate(parameter_values, quantum_kernel, data, labels)[source]

An abstract method for evaluating the loss of a kernel function on a labeled dataset.

Parameters:

  • parameter_values (Sequence[float]) – An array of values to assign to the user params

  • quantum_kernel (TrainableKernel) – A trainable quantum kernel object to evaluate

  • data (ndarray) – An (N, M) matrix containing the data N = # samples, M = dimension of data

  • labels (ndarray) – A length-N array containing the truth labels

Returns:

A loss value

Return type:

float