Approximation, interpolation and surface sensitivities¶

ASRQuant 1.0.0 distinguishes interpolation, regression, smoothing, extrapolation, simulation, optimization and validation.

Available methods¶

Operation	ASRQuant function
Linear interpolation	`linear_interpolation`
Bilinear regular-grid interpolation	`bilinear_interpolation`
Cubic spline	`cubic_spline`
Gaussian kernel regression	`kernel_regression`
Radial-basis interpolation	`rbf_interpolation`
Gaussian-process surrogate	`gaussian_process`
Linear response regression	`response_regression(..., method="linear")`
Polynomial response regression	`response_regression(..., method="polynomial")`
Ridge response regression	`response_regression(..., method="ridge")`
Lasso response regression	`response_regression(..., method="lasso")`
RMSE, MAE and R-squared	`regression_metrics`
Finite-difference gradient	`finite_difference_gradient`
Finite-difference Hessian	`finite_difference_hessian`
Grid-surface gradient	`SurfaceResult.gradient()`
Grid-surface Hessian	`SurfaceResult.hessian()`

Interpolation¶

import asrquant as asr

curve = asr.linear_interpolation(
    x=[0.00, 0.01, 0.02, 0.04],
    y=[4.8, 5.5, 7.2, 10.6],
)
print(curve.predict([0.015]))

For a regular two-dimensional grid:

surface_model = asr.bilinear_interpolation(
    x_values=cost_grid,
    y_values=volatility_grid,
    z_values=cvar_matrix,
)
value = surface_model.predict([[0.0015, 0.25]])

Smoothing and irregular data¶

spline = asr.cubic_spline(maturities, zero_rates)
kernel = asr.kernel_regression(points, values, bandwidth=0.4)
rbf = asr.rbf_interpolation(points, values, smoothing=1e-6)

Gaussian-process surrogate and uncertainty¶

gp = asr.gaussian_process(points, expensive_model_values, noise=1e-6)
mean, standard_deviation = gp.predict_with_uncertainty(new_points)

The Gaussian process provides both a predictive mean and predictive standard deviation. It is useful for sparse expensive experiments, calibration and Bayesian-optimization workflows.

Extrapolation control¶

Predictions outside the observed domain fail by default:

model.predict(outside_points)

Explicit extrapolation requires:

model.predict(outside_points, allow_extrapolation=True)

ASRQuant emits a warning because extrapolation is structurally less reliable than interpolation.

Gradient and Hessian¶

For a callable:

gradient = asr.finite_difference_gradient(function, [x0, y0])
hessian = asr.finite_difference_hessian(function, [x0, y0])

For an evaluated SurfaceResult:

surface = lab.parameter_surface(...)
first_order = surface.gradient()
second_order = surface.hessian()

first_order["transaction_cost"].plot("heatmap")
second_order["transaction_costvolatility"].plot("surface")

These objects preserve axis names and can use the same 3D, heatmap and contour renderers as the original surface.