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# SPDX-License-Identifier: Apache-2.0
import argparse
import functools
from pathlib import Path
from typing import Optional
import numpy as np
from gluonts.dataset.arrow import ArrowWriter
from joblib import Parallel, delayed
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import (
RBF,
ConstantKernel,
DotProduct,
ExpSineSquared,
Kernel,
RationalQuadratic,
WhiteKernel,
)
from tqdm.auto import tqdm
LENGTH = 1024
KERNEL_BANK = [
ExpSineSquared(periodicity=24 / LENGTH), # H
ExpSineSquared(periodicity=48 / LENGTH), # 0.5H
ExpSineSquared(periodicity=96 / LENGTH), # 0.25H
ExpSineSquared(periodicity=24 * 7 / LENGTH), # H
ExpSineSquared(periodicity=48 * 7 / LENGTH), # 0.5H
ExpSineSquared(periodicity=96 * 7 / LENGTH), # 0.25H
ExpSineSquared(periodicity=7 / LENGTH), # D
ExpSineSquared(periodicity=14 / LENGTH), # 0.5D
ExpSineSquared(periodicity=30 / LENGTH), # D
ExpSineSquared(periodicity=60 / LENGTH), # 0.5D
ExpSineSquared(periodicity=365 / LENGTH), # D
ExpSineSquared(periodicity=365 * 2 / LENGTH), # 0.5D
ExpSineSquared(periodicity=4 / LENGTH), # W
ExpSineSquared(periodicity=26 / LENGTH), # W
ExpSineSquared(periodicity=52 / LENGTH), # W
ExpSineSquared(periodicity=4 / LENGTH), # M
ExpSineSquared(periodicity=6 / LENGTH), # M
ExpSineSquared(periodicity=12 / LENGTH), # M
ExpSineSquared(periodicity=4 / LENGTH), # Q
ExpSineSquared(periodicity=4 * 10 / LENGTH), # Q
ExpSineSquared(periodicity=10 / LENGTH), # Y
DotProduct(sigma_0=0.0),
DotProduct(sigma_0=1.0),
DotProduct(sigma_0=10.0),
RBF(length_scale=0.1),
RBF(length_scale=1.0),
RBF(length_scale=10.0),
RationalQuadratic(alpha=0.1),
RationalQuadratic(alpha=1.0),
RationalQuadratic(alpha=10.0),
WhiteKernel(noise_level=0.1),
WhiteKernel(noise_level=1.0),
ConstantKernel(),
]
def random_binary_map(a: Kernel, b: Kernel):
"""
Applies a random binary operator (+ or *) with equal probability
on kernels ``a`` and ``b``.
Parameters
----------
a
A GP kernel.
b
A GP kernel.
Returns
-------
The composite kernel `a + b` or `a * b`.
"""
binary_maps = [lambda x, y: x + y, lambda x, y: x * y]
return np.random.choice(binary_maps)(a, b)
def sample_from_gp_prior(
kernel: Kernel, X: np.ndarray, random_seed: Optional[int] = None
):
"""
Draw a sample from a GP prior.
Parameters
----------
kernel
The GP covaraince kernel.
X
The input "time" points.
random_seed, optional
The random seed for sampling, by default None.
Returns
-------
A time series sampled from the GP prior.
"""
if X.ndim == 1:
X = X[:, None]
assert X.ndim == 2
gpr = GaussianProcessRegressor(kernel=kernel)
ts = gpr.sample_y(X, n_samples=1, random_state=random_seed)
return ts
def sample_from_gp_prior_efficient(
kernel: Kernel,
X: np.ndarray,
random_seed: Optional[int] = None,
method: str = "eigh",
):
"""
Draw a sample from a GP prior. An efficient version that allows specification
of the sampling method. The default sampling method used in GaussianProcessRegressor
is based on SVD which is significantly slower that alternatives such as `eigh` and
`cholesky`.
Parameters
----------
kernel
The GP covaraince kernel.
X
The input "time" points.
random_seed, optional
The random seed for sampling, by default None.
method, optional
The sampling method for multivariate_normal, by default `eigh`.
Returns
-------
A time series sampled from the GP prior.
"""
if X.ndim == 1:
X = X[:, None]
assert X.ndim == 2
cov = kernel(X)
ts = np.random.default_rng(seed=random_seed).multivariate_normal(
mean=np.zeros(X.shape[0]), cov=cov, method=method
)
return ts
def generate_time_series(max_kernels: int = 5):
"""Generate a synthetic time series from KernelSynth.
Parameters
----------
max_kernels, optional
The maximum number of base kernels to use for each time series, by default 5
Returns
-------
A time series generated by KernelSynth.
"""
while True:
X = np.linspace(0, 1, LENGTH)
# Randomly select upto max_kernels kernels from the KERNEL_BANK
selected_kernels = np.random.choice(
KERNEL_BANK, np.random.randint(1, max_kernels + 1), replace=True
)
# Combine the sampled kernels using random binary operators
kernel = functools.reduce(random_binary_map, selected_kernels)
# Sample a time series from the GP prior
try:
ts = sample_from_gp_prior(kernel=kernel, X=X)
except np.linalg.LinAlgError as err:
print("Error caught:", err)
continue
# The timestamp is arbitrary
return {"start": np.datetime64("2000-01-01 00:00", "s"), "target": ts.squeeze()}
if __name__ == "__main__":
parser = argparse.ArgumentParser()
parser.add_argument("-N", "--num-series", type=int, default=1000_000)
parser.add_argument("-J", "--max-kernels", type=int, default=5)
args = parser.parse_args()
path = Path(__file__).parent / "kernelsynth-data.arrow"
generated_dataset = Parallel(n_jobs=-1)(
delayed(generate_time_series)(max_kernels=args.max_kernels)
for _ in tqdm(range(args.num_series))
)
ArrowWriter(compression="lz4").write_to_file(
generated_dataset,
path=path,
)
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