HSGP

pydantic model pymc_marketing.mmm.hsgp.HSGP

HSGP component.

Examples

Literature recommended HSGP configuration:

import numpy as np
import pandas as pd

import matplotlib.pyplot as plt

from pymc_marketing.mmm import HSGP

seed = sum(map(ord, "Out of the box GP"))
rng = np.random.default_rng(seed)

n = 52
X = np.arange(n)

hsgp = HSGP.parameterize_from_data(
    X=X,
    dims="time",
)

dates = pd.date_range("2022-01-01", periods=n, freq="W-MON")
coords = {
    "time": dates,
}
prior = hsgp.sample_prior(coords=coords, random_seed=rng)
curve = prior["f"]
hsgp.plot_curve(curve, random_seed=rng)
plt.show()

(Source code, png, hires.png, pdf)

Using a demeaned basis to remove “intercept” effect of first basis:

import numpy as np
import pandas as pd
import xarray as xr

import matplotlib.pyplot as plt

from pymc_marketing.mmm import HSGP
from pymc_marketing.plot import plot_curve

seed = sum(map(ord, "Out of the box GP"))
rng = np.random.default_rng(seed)

n = 52
X = np.arange(n)

kwargs = dict(X=X, ls=25, eta=1, dims="time", m=200, L=150, drop_first=False)

hsgp = HSGP(demeaned_basis=False, **kwargs)
hsgp_demeaned = HSGP(demeaned_basis=True, **kwargs)

dates = pd.date_range("2022-01-01", periods=n, freq="W-MON")
coords = {"time": dates}

def sample_curve(hsgp):
    return hsgp.sample_prior(coords=coords, random_seed=rng)["f"]

non_demeaned = sample_curve(hsgp).rename("False")
demeaned = sample_curve(hsgp_demeaned).rename("True")

combined = xr.merge([non_demeaned, demeaned]).to_array("demeaned")
_, axes = combined.pipe(plot_curve, "time", same_axes=True)
axes[0].set(title="Demeaned the intercepty first basis")
plt.show()

(Source code, png, hires.png, pdf)

HSGP with different covariance function

import numpy as np
import pandas as pd

import matplotlib.pyplot as plt

from pymc_marketing.mmm import HSGP

seed = sum(map(ord, "Change of covariance function"))
rng = np.random.default_rng(seed)

n = 52
X = np.arange(n)

hsgp = HSGP.parameterize_from_data(
    X=X,
    cov_func="matern32",
    dims="time",
)

dates = pd.date_range("2022-01-01", periods=n, freq="W-MON")
coords = {
    "time": dates,
}
prior = hsgp.sample_prior(coords=coords, random_seed=rng)
curve = prior["f"]
hsgp.plot_curve(curve, random_seed=rng)
plt.show()

(Source code, png, hires.png, pdf)

HSGP with different link function via transform argument

Note

The transform parameter must be registered or from either pytensor.tensor or pymc.math namespaces. See the pymc_extras.prior.register_tensor_transform()

import numpy as np
import pandas as pd

import matplotlib.pyplot as plt

from pymc_marketing.mmm import HSGP

seed = sum(map(ord, "Change of covariance function"))
rng = np.random.default_rng(seed)

n = 52
X = np.arange(n)

hsgp = HSGP.parameterize_from_data(
    X=X,
    dims="time",
    transform="sigmoid",
)

dates = pd.date_range("2022-01-01", periods=n, freq="W-MON")
coords = {
    "time": dates,
}
prior = hsgp.sample_prior(coords=coords, random_seed=rng)
curve = prior["f"]
hsgp.plot_curve(curve, random_seed=rng)
plt.show()

(Source code, png, hires.png, pdf)

New data predictions with HSGP

import numpy as np
import pandas as pd

import pymc as pm

import matplotlib.pyplot as plt

from pymc_marketing.mmm import HSGP
from pymc_extras.prior import Prior

seed = sum(map(ord, "New data predictions"))
rng = np.random.default_rng(seed)

eta = Prior("Exponential", lam=1)
ls = Prior("InverseGamma", alpha=2, beta=1)
hsgp = HSGP(
    eta=eta,
    ls=ls,
    m=20,
    L=150,
    dims=("time", "channel"),
)

n = 52
X = np.arange(n)

dates = pd.date_range("2022-01-01", periods=n, freq="W-MON")
coords = {"time": dates, "channel": ["A", "B"]}
with pm.Model(coords=coords) as model:
    data = pm.Data("data", X, dims="time")
    hsgp.register_data(data).create_variable("f", xdist=True)
    idata = pm.sample_prior_predictive(random_seed=rng)

prior = idata.prior

n_new = 10
X_new = np.arange(n, n + n_new)
new_dates = pd.date_range("2023-01-01", periods=n_new, freq="W-MON")

with model:
    pm.set_data(
        new_data={
            "data": X_new,
        },
        coords={"time": new_dates},
    )
    post = pm.sample_posterior_predictive(
        prior,
        var_names=["f"],
        random_seed=rng,
    )

chain, draw = 0, 50
colors = ["C0", "C1"]

def get_sample(curve):
    return curve.loc[chain, draw].to_series().unstack()

ax = prior["f"].pipe(get_sample).plot(color=colors)
post.posterior_predictive["f"].pipe(get_sample).plot(
    ax=ax, color=colors, linestyle="--", legend=False
)
ax.set(xlabel="time", ylabel="f", title="New data predictions")
plt.show()

(Source code, png, hires.png, pdf)

Higher dimensional HSGP

import numpy as np
import pymc as pm

import matplotlib.pyplot as plt

from pymc_marketing.mmm import HSGP

seed = sum(map(ord, "Higher dimensional HSGP"))
rng = np.random.default_rng(seed)

n = 52
X = np.arange(n)

hsgp = HSGP.parameterize_from_data(
    X=X,
    dims=("time", "channel", "product"),
)

coords = {
    "time": range(n),
    "channel": ["A", "B"],
    "product": ["X", "Y", "Z"],
}
prior = hsgp.sample_prior(coords=coords, random_seed=rng)
curve = prior["f"]
fig, _ = hsgp.plot_curve(
    curve,
    random_seed=rng,
    subplot_kwargs={"figsize": (12, 8), "ncols": 3},
)
fig.suptitle("Higher dimensional HSGP prior")
plt.show()

(Source code, png, hires.png, pdf)

Methods

HSGP.__init__(**data)	Create a new model by parsing and validating input data from keyword arguments.
HSGP.create_variable(name[, xdist])	Create a variable from HSGP configuration.
HSGP.deterministics_to_replace(name)	Name of the Deterministic variables that are replaced with pm.Flat for out-of-sample.
HSGP.from_dict(data)	Create an object from a dictionary.
HSGP.parameterize_from_data(X, dims[, ...])	Create a HSGP informed by the data with literature-based recommendations.
HSGP.plot_curve(curve[, n_samples, ...])	Plot the curve.
HSGP.register_data(X)	Register the data to be used in the model.
HSGP.sample_prior([coords])	Sample from the prior distribution.
HSGP.to_dict([_orig])	Convert the object to a dictionary.

field L: float [Required]

Extent of basis functions

Constraints:

• gt = 0

field X: InstanceOf[XTensorVariable] | InstanceOf[DataArray] | InstanceOf[np.ndarray] | None = None

The data to be used in the model

field X_mid: float | None = None

The mean of the training data

field centered: bool = False

Whether the model is centered or not

field cov_func: CovFunc = CovFunc.ExpQuad

The covariance function

field demeaned_basis: bool = False

Whether each basis has its mean subtracted from it.

field dims: Dims [Required]

The dimensions of the variable

field drop_first: bool = True

Whether to drop the first basis function

field eta: InstanceOf[VariableFactory] | DeferredFactory | float [Required]

Prior for the variance

field ls: InstanceOf[VariableFactory] | DeferredFactory | float [Required]

Prior for the lengthscales

field m: int [Required]

Number of basis functions

field transform: str | None = None

Optional transformation for the variable. Must be registered or from either pytensor.tensor or pymc.math namespaces.