approx_hsgp_hyperparams#

pymc_marketing.mmm.hsgp.approx_hsgp_hyperparams(x, x_center, lengthscale_range, cov_func)[source]#

Use heuristics for minimum m and c values.

Based on recommendations from Ruitort-Mayol et. al.

In practice, you need to choose c large enough to handle the largest lengthscales, and m large enough to accommodate the smallest lengthscales.

NOTE: These recommendations are based on a one-dimensional GP.

Parameters:

xtensor_like: The x values the HSGP will be evaluated over.
x_centertensor_like: The center of the data.
lengthscale_rangetuple[float, float]: The range of the lengthscales. Should be a list with two elements [lengthscale_min, lengthscale_max].
cov_funcLiteral[“expquad”, “matern32”, “matern52”]: The covariance function to use. Supported options are “expquad”, “matern52”, and “matern32”.

Returns:

- `m`int: Number of basis vectors. Increasing it helps approximate smaller lengthscales, but increases computational cost.
- `c`float: Scaling factor such that L = c * S, where L is the boundary of the approximation. Increasing it helps approximate larger lengthscales, but may require increasing m.

Raises:

ValueError: If either x_range or lengthscale_range is not in the correct order.

References

[1]

Ruitort-Mayol, G., Anderson, M., Solin, A., Vehtari, A. (2022).

Practical Hilbert Space Approximate Bayesian Gaussian Processes for Probabilistic Programming