cherab.inversion.regularization.criteria.PRESS¶

class cherab.inversion.regularization.criteria.PRESSSource¶

Bases: Criterion

Predicted Residual Error Sum of Squares (PRESS) criterion.

The PRESS criterion, also known as ordinary cross-validation, selects the regularization parameter \(\lambda\) by minimizing the leave-one-out cross-validation error.

Note

The theory and implementation of the PRESS criterion are described in the PRESS theory page.

Methods

optimize(solver, bounds[, stepsize])	Find the optimal parameter by minimizing PRESS with basinhopping.
plot_press()	Plot PRESS as a function of the regularization parameter.
press(solver, beta)	Calculate the PRESS criterion function.

press(solver: _SVDBase, beta: float) → floatSource¶

Calculate the PRESS criterion function.

The PRESS function \(\mathcal{P}(\lambda)\) can be expressed with SVD components as:

\[\mathcal{P}(\lambda) = \left\| \left[ \mathrm{Diag}\!\left( \mathbf{I} - \mathbf{U}\mathbf{F}_\lambda\mathbf{U}^\mathsf{T} \right) \right]^{-1} \!\left( \mathbf{I} - \mathbf{U}\mathbf{F}_\lambda\mathbf{U}^\mathsf{T} \right)\hat{\mathbf{b}} \right\|_2^2,\]

where \(\hat{\mathbf{b}} = \mathbf{B}\mathbf{b}\) (or simply \(\mathbf{b}\) when \(\mathbf{B} = \mathbf{I}\)) and \(\mathrm{Diag}(\mathbf{M})\) denotes the diagonal matrix formed from the diagonal entries of \(\mathbf{M}\).

Parameters:

solver: _SVDBase¶

An _SVDBase instance providing U, filter, data, etc.

beta: float¶

Regularization parameter \(\lambda\).

Returns:

float – Value of PRESS function at a given regularization parameter.

Raises:

RuntimeError – If solver.data is not set.

optimize(solver: _SVDBase, bounds: tuple[float, float], stepsize: float = 10, **kwargs: Any) → tuple[float, OptimizeResult]Source¶

Find the optimal parameter by minimizing PRESS with basinhopping.

Parameters:

solver: _SVDBase¶

An _SVDBase instance.

bounds: tuple[float, float]¶

(log10_lower, log10_upper) search interval.

stepsize: float = 10¶

Step-size for the underlying global optimizer.

**kwargs: Any¶

Extra arguments forwarded to the optimizer.

Returns:

• lambda_opt (float) – Optimal regularization parameter.

• result (OptimizeResult) – Optimizer result object returned by basinhopping.

plot_press(solver: _SVDBase | None = None, axes: None = None, bounds: Collection[float | None] | None = None, n_beta: int = 500, show_min_line: bool = True) → tuple[Axes, Figure]Source¶

plot_press(solver: _SVDBase | None = None, axes: Axes | None = None, bounds: Collection[float | None] | None = None, n_beta: int = 500, show_min_line: bool = True) → Axes

Plot PRESS as a function of the regularization parameter.

Parameters:

solver: _SVDBase | None = None¶

An _SVDBase instance. If None, the last solver used in optimize() is used.

axes: None = None¶

axes: Axes | None = None

Matplotlib axes to plot on. If None, a new figure and axes are created.

bounds: Collection[float | None] | None = None¶

Boundary pair of log10 of regularization parameters, by default None. If None, the bounds are generated by the solver as described in SVD._generate_bounds(). If you set the bounds like (-10, None), the higher bound is set to \(\log_{10}\sigma_1^2\). Raise an error if a >= b in (a, b).

n_beta: int = 500¶

Number of regularization parameters, by default 500.

show_min_line: bool = True¶

Whether to show a vertical line at the optimal regularization parameter.

Returns:

• axes (Axes) – A matplotlib Axes object.

• fig (Figure) – A matplotlib figure object if axes is None, otherwise None.