HSGPPeriodic

pydantic model pymc_marketing.mmm.hsgp.HSGPPeriodic

HSGP component for periodic data.

Examples

HSGPPeriodic with default configuration:

import numpy as np
import pandas as pd

import matplotlib.pyplot as plt

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

seed = sum(map(ord, "Periodic GP"))
rng = np.random.default_rng(seed)

n = 52 * 3
dates = pd.date_range("2023-01-01", periods=n, freq="W-MON")
X = np.arange(n)
coords = {
    "time": dates,
}
scale = Prior("HalfNormal", sigma=1)
ls = Prior("InverseGamma", alpha=2, beta=1)

hsgp = HSGPPeriodic(
    scale=scale,
    m=20,
    cov_func="periodic",
    ls=ls,
    period=52,
    dims="time",
)
hsgp.register_data(X)

prior = hsgp.sample_prior(coords=coords, random_seed=rng)
curve = prior["f"]
fig, axes = hsgp.plot_curve(
    curve,
    n_samples=3,
    random_seed=rng,
)
ax = axes[0]
ax.set(xlabel="Date", ylabel="f", title="HSGP with period of 52 weeks")
plt.show()

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

HSGPPeriodic with 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 HSGPPeriodic
from pymc_extras.prior import Prior

seed = sum(map(ord, "Periodic GP"))
rng = np.random.default_rng(seed)

n = 52 * 3
dates = pd.date_range("2023-01-01", periods=n, freq="W-MON")
X = np.arange(n)
coords = {
    "time": dates,
}
scale = Prior("Gamma", mu=0.25, sigma=0.1)
ls = Prior("InverseGamma", alpha=2, beta=1)

hsgp = HSGPPeriodic(
    scale=scale,
    m=20,
    cov_func="periodic",
    ls=ls,
    period=52,
    dims="time",
    transform="exp",
)
hsgp.register_data(X)

prior = hsgp.sample_prior(coords=coords, random_seed=rng)
curve = prior["f"]
fig, axes = hsgp.plot_curve(
    curve,
    n_samples=3,
    random_seed=rng,
)
ax = axes[0]
ax.set(xlabel="Date", ylabel="f", title="HSGP with period of 52 weeks")
plt.show()

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

Demeaned basis for HSGPPeriodic

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

import matplotlib.pyplot as plt

from pymc_marketing.mmm import HSGPPeriodic
from pymc_marketing.plot import plot_curve

seed = sum(map(ord, "Periodic GP"))
rng = np.random.default_rng(seed)

scale = 0.25
ls = 1
kwargs = dict(ls=ls, scale=scale, period=52, cov_func="periodic", dims="time", m=20)

n = 52 * 3
dates = pd.date_range("2023-01-01", periods=n, freq="W-MON")
X = np.arange(n)
coords = {"time": dates}

hsgp = HSGPPeriodic(demeaned_basis=False, **kwargs).register_data(X)
hsgp_demeaned = HSGPPeriodic(demeaned_basis=True, **kwargs).register_data(X)

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)

Higher dimensional HSGPPeriodic with periodic data

import numpy as np
import pandas as pd

import pymc as pm

import matplotlib.pyplot as plt

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

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

n = 52 * 3
dates = pd.date_range("2023-01-01", periods=n, freq="W-MON")
X = np.arange(n)

scale = Prior("HalfNormal", sigma=1)
ls = Prior("InverseGamma", alpha=2, beta=1)

hsgp = HSGPPeriodic(
    X=X,
    scale=scale,
    ls=ls,
    m=20,
    cov_func="periodic",
    period=52,
    dims=("time", "channel", "product"),
)

coords = {
    "time": dates,
    "channel": ["A", "B"],
    "product": ["X", "Y", "Z"],
}
prior = hsgp.sample_prior(coords=coords, random_seed=rng)
curve = prior["f"]
fig, axes = hsgp.plot_curve(
    curve,
    n_samples=3,
    random_seed=rng,
    subplot_kwargs={"figsize": (12, 8), "ncols": 3},
)
plt.show()

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

Methods

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

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 cov_func: PeriodicCovFunc = PeriodicCovFunc.Periodic

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

Prior for the lengthscale

field m: int [Required]

Number of basis functions

field period: float [Required]

The period of the function

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

Prior for the scale

field transform: str | None = None

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