def precompute_gaussian_model(cls,
ts: np.ndarray,
random_state: t.Optional[int] = None,
**kwargs) -> t.Dict[str, t.Any]:
"""Precompute a gaussian process model.
Parameters
----------
ts : :obj:`np.ndarray`
One-dimensional time-series values.
random_state : int, optional
Random seed to optimize the gaussian process model, to keep
the results reproducible.
kwargs:
Additional arguments and previous precomputed items. May
speed up this precomputation.
Returns
-------
dict
The following precomputed item is returned:
* ``gaussian_model`` (:obj:`GaussianProcessRegressor`):
Gaussian process fitted model.
* ``gaussian_resid`` (:obj:`np.ndarray`): Gaussian process
model residuals (diference from the original time-series).
The following item is necessary and, therefore, also precomputed
if necessary:
* ``ts_scaled`` (:obj:`np.ndarray`): standardized time-series
values (z-score).
"""
precomp_vals = {} # type: t.Dict[str, t.Any]
ts_scaled = kwargs.get("ts_scaled")
if ts_scaled is None:
precomp_vals["ts_scaled"] = _utils.standardize_ts(ts=ts)
ts_scaled = precomp_vals["ts_scaled"]
if "gaussian_model" not in kwargs:
gaussian_model = _utils.fit_gaussian_process(
ts=ts, ts_scaled=ts_scaled, random_state=random_state)
precomp_vals["gaussian_model"] = gaussian_model
gaussian_model = kwargs.get("gaussian_model",
precomp_vals["gaussian_model"])
if "gaussian_resid" not in kwargs:
gaussian_resid = _utils.fit_gaussian_process(
ts=ts,
ts_scaled=ts_scaled,
gaussian_model=gaussian_model,
return_residuals=True)
precomp_vals["gaussian_resid"] = gaussian_resid
return precomp_vals
def ft_gaussian_r_sqr(
cls,
ts: np.ndarray,
random_state: t.Optional[int] = None,
ts_scaled: t.Optional[np.ndarray] = None,
gaussian_model: t.Optional[
sklearn.gaussian_process.GaussianProcessRegressor] = None,
) -> float:
"""R^2 from a gaussian process model.
Parameters
----------
ts : :obj:`np.ndarray`
One-dimensional time-series values.
random_state : int, optional
Random seed to optimize the gaussian process model, to keep
the results reproducible.
ts_scaled : :obj:`np.ndarray`, optional
Standardized time-series values. Used to take advantage of
precomputations.
gaussian_model : :obj:`GaussianProcessRegressor`, optional
A fitted model of a gaussian process. Used to take advantage of
precomputations.
Returns
-------
float
R^2 of a gaussian process model.
References
----------
.. [1] B.D. Fulcher and N.S. Jones, "hctsa: A Computational Framework
for Automated Time-Series Phenotyping Using Massive Feature
Extraction, Cell Systems 5: 527 (2017).
DOI: 10.1016/j.cels.2017.10.001
.. [2] B.D. Fulcher, M.A. Little, N.S. Jones, "Highly comparative
time-series analysis: the empirical structure of time series and
their methods", J. Roy. Soc. Interface 10(83) 20130048 (2013).
DOI: 10.1098/rsif.2013.0048
"""
ts_scaled = _utils.standardize_ts(ts=ts, ts_scaled=ts_scaled)
gaussian_model = _utils.fit_gaussian_process(
ts=ts_scaled,
random_state=random_state,
gaussian_model=gaussian_model,
ts_scaled=ts_scaled)
X = np.linspace(0, 1, ts_scaled.size).reshape(-1, 1)
r_squared = gaussian_model.score(X=X, y=ts_scaled)
return r_squared
def ft_gresid_lbtest(
cls,
ts: np.ndarray,
nlags: int = 8,
return_pval: bool = True,
random_state: t.Optional[int] = None,
ts_scaled: t.Optional[np.ndarray] = None,
gaussian_resid: t.Optional[np.ndarray] = None,
gaussian_model: t.Optional[
sklearn.gaussian_process.GaussianProcessRegressor] = None,
) -> np.ndarray:
"""Ljung–Box test in the residuals of a gaussian process model.
Parameters
----------
ts : :obj:`np.ndarray`
One-dimensional time-series values.
nlags : int, optional (default=8)
Number of lags evaluated in the Ljung-Box test.
return_pval : bool, optional (default=True)
If True, return the p-value of the test instead of the test
statistic.
random_state : int, optional
Random seed to optimize the gaussian process model, to keep
the results reproducible.
ts_scaled : :obj:`np.ndarray`, optional
Standardized time-series values. Used to take advantage of
precomputations. Used only if ``gaussian_resid`` is None.
gaussian_resid : :obj:`np.ndarray`, optional
Residuals of a gaussian process. Used to take advantage of
precomputations.
gaussian_model : :obj:`GaussianProcessRegressor`, optional
A fitted model of a gaussian process. Used to take advantage of
precomputations. Used only if ``gaussian_resid`` is None.
Returns
-------
:obj:`np.ndarray`
If `return_pval` is False, Ljung-Box test statistic for each lag
of the gaussian process residuals.
If `return_pval` is True, p-value associated with the Ljung-Box
test statistic for each lag of the gaussian process residuals.
References
----------
.. [1] B.D. Fulcher and N.S. Jones, "hctsa: A Computational Framework
for Automated Time-Series Phenotyping Using Massive Feature
Extraction, Cell Systems 5: 527 (2017).
DOI: 10.1016/j.cels.2017.10.001
.. [2] B.D. Fulcher, M.A. Little, N.S. Jones, "Highly comparative
time-series analysis: the empirical structure of time series and
their methods", J. Roy. Soc. Interface 10(83) 20130048 (2013).
DOI: 10.1098/rsif.2013.0048
"""
if gaussian_resid is None:
gaussian_resid = _utils.fit_gaussian_process(
ts=ts,
ts_scaled=ts_scaled,
random_state=random_state,
gaussian_model=gaussian_model,
return_residuals=True)
gaussian_lb_test = stat_tests.MFETSStatTests.ft_test_lb(
ts_residuals=gaussian_resid,
max_nlags=nlags,
return_pval=return_pval)
return gaussian_lb_test
def ft_gresid_autocorr(
cls,
ts: np.ndarray,
nlags: int = 8,
unbiased: bool = True,
random_state: t.Optional[int] = None,
ts_scaled: t.Optional[np.ndarray] = None,
gaussian_resid: t.Optional[np.ndarray] = None,
gaussian_model: t.Optional[
sklearn.gaussian_process.GaussianProcessRegressor] = None,
) -> np.ndarray:
"""Autocorrelation function of the gaussian process model residuals.
Parameters
----------
ts : :obj:`np.ndarray`
One-dimensional time-series values.
nlags : int, optional (default=8)
Number of lags evaluated in the autocorrelation function.
unbiased : bool, optional (default=True)
If True, the autocorrelation function is corrected for statistical
bias.
random_state : int, optional
Random seed to optimize the gaussian process model, to keep
the results reproducible.
ts_scaled : :obj:`np.ndarray`, optional
Standardized time-series values. Used to take advantage of
precomputations. Used only if ``gaussian_resid`` is None.
gaussian_resid : :obj:`np.ndarray`, optional
Residuals of a gaussian process. Used to take advantage of
precomputations.
gaussian_model : :obj:`GaussianProcessRegressor`, optional
A fitted model of a gaussian process. Used to take advantage of
precomputations. Used only if ``gaussian_resid`` is None.
Returns
-------
:obj:`np.ndarray`
Autocorrelation function of the gaussian process residuals up
to ``nlags``.
References
----------
.. [1] B.D. Fulcher and N.S. Jones, "hctsa: A Computational Framework
for Automated Time-Series Phenotyping Using Massive Feature
Extraction, Cell Systems 5: 527 (2017).
DOI: 10.1016/j.cels.2017.10.001
.. [2] B.D. Fulcher, M.A. Little, N.S. Jones, "Highly comparative
time-series analysis: the empirical structure of time series and
their methods", J. Roy. Soc. Interface 10(83) 20130048 (2013).
DOI: 10.1098/rsif.2013.0048
"""
if gaussian_resid is None:
gaussian_resid = _utils.fit_gaussian_process(
ts=ts,
ts_scaled=ts_scaled,
random_state=random_state,
gaussian_model=gaussian_model,
return_residuals=True)
gaussian_resid_acf = cls._calc_acf(ts=gaussian_resid,
nlags=nlags,
unbiased=unbiased)
return gaussian_resid_acf