def pred_CV(goal_datum,
data_sources,
n_folds=1,
bootstrap=False,
lin_reg_intercept=False):
r"""Test the performance of the linear regression model using
cross-validation.
Parameters
----------
goal_datum : dictionary
The gold standard data source, which is the dependent variable in the
linear regression.
data_sources : list
List of data sources that will be evaluated. Each data source is a
dictionary, which is an independent variable in the linear
regression model.
n_folds : integer
Number of fold in k-fold cross-validation
bootstrap : boolean
Whether or not to use bootstrap data sets, which are created by sampling
with replacement and the same size as the original training dataset.
lin_reg_intercept: whether to include an intercept in the linear regression
(and prediction)
Returns
-------
pred_series_CV : dictionary
Gold standard values predicted from independent variables (data
sources).
"""
if n_folds > 1:
# kf = KFold(dm.length(goal_datum), n_folds)
kf_p = KFold(n_folds)
kf = list(kf_p.split(range(dm.length(goal_datum))))
else:
v = range(dm.length(goal_datum))
kf = [(v, v)]
pred_series_CV_list = []
for train, test in kf:
if bootstrap:
train = np.random.choice(train, len(train))
train_f, test_f = tt.index_to_filter(train), tt.index_to_filter(test)
coef = tt.train_on_filter(lin_reg,
goal_datum,
data_sources,
train_f,
lin_reg_intercept=lin_reg_intercept)
pred_series = tt.test_on_filter(partial(lin_pred, coefficients=coef),
data_sources, test_f)
pred_series_CV_list.append(pred_series)
pred_series_CV = {}
pred_series_CV['data'] = {}
pred_series_CV['data']['values'] = np.concatenate(pred_series_CV_list,
axis=0)
pred_series_CV['data']['times'] = goal_datum['data']['times']
return pred_series_CV
def EED(data_sources, alg, h, auto_reset=False, len_outbreak=8):
r"""Generalized Early Event Detection (EED) method with chose update method
and optional reset.
Parameters
----------
data_sources : list
List of data sources that will be evaluated. Each data source is a
dictionary.
alg : string
An early event detection method, including MEWMA, cCUSUM, MCUSUM.
h : number
A value below which an alarm will not be triggered (no outbreak).
auto_reset : boolean, optional
If the updated S statistic should be reset. The default is False.
len_outbreak : integer, optional
The length of the outbreak. The default length is 8.
Returns
-------
alarm : array (boolean data type)
Indicate which time an EED method signals.
S : list
Elements in the list are arrays. Each element is the updated S statistic
at each time step.
E : list
Elements in the list are the EED method test statistic E values at each
time step.
"""
S, E = [], []
S_prev = np.zeros(len(data_sources))
for t in range(dm.length(data_sources[0])):
series_list = [d['data']['values'] for d in data_sources]
Y_t = np.array(series_list)[:, t]
S_next, E_next = alg(S_prev, Y_t)
S.append(S_next)
E.append(E_next)
S_prev = S_next
if auto_reset:
len_regression = int(round(len_outbreak / 2))
slope, _, _, p_value, _ = stats.linregress(
range(len(E[-len_regression:])), E[-len_regression:])
reset = (E[-1] > h) * (slope < 0) * (p_value < 0.05)
S_prev = (not reset) * S_prev
alarm = (np.array(E) >= h)
return alarm, S, E
def cross_validate(train_func,
test_func,
goal_datum,
data_sources,
num_folds=1):
# kf = KFold(dm.length(goal_datum), n_folds)
kf_p = KFold(n_folds)
kf = list(kf_p.split(range(dm.length(goal_datum))))
pred_series_CV_list = []
for train, test in kf:
train_f, test_f = tt.index_to_filter(train), tt.index_to_filter(test)
params = tt.train_on_filter(train_func, goal_datum, data_sources,
train_f)
pred_series_CV = tt.test_on_filter(
partial(test_func, train_params=params), data_sources, test_f)
pred_series_CV_list.append(pred_series_CV)
pred_series_CV = np.concatenate(pred_series_CV_list, axis=0)
return 0
def pred_CV_candidate(goal_datum,
data_sources,
threshold,
l,
h,
auto_reset=False,
len_outbreak=8,
n_folds=1,
bootstrap=False):
r"""Cross-validated train/test function for early detection.
Parameters
----------
goal_datum : dictionary
The gold standard data source.
data_sources : list
List of data sources that will be evaluated. Each data source is a
dictionary.
threshold : float
Event baseline. When the value is larger than the threshold, there is
an event. Otherwise, there is no event.
l : float
The smoothing parameter. A parameter in EED method MEWMA.
h : number
A value below which an alarm will not be triggered (no event).
auto_reset : boolean
If the updated S statistic should be reset. The default is False.
len_outbreak : integer
The length of the outbreak. The default length is 8.
n_folds : integer
Number of fold in k-fold cross-validation
bootstrap : boolean
Whether or not to use bootstrap data sets, which are created by sampling
with replacement and has the same size as the original training dataset.
Returns
-------
alarm_CV : dictionary
Including date and whether or not alarm is triggered at that date.
S_CV : ndarray
Elements in the array are lists. Each element includes the updated S
statistic for each fold.
E_CV : array
Elements in the array are the EED method test statistic E values for
each fold.
"""
if n_folds > 1:
# kf = KFold(dm.length(goal_datum), n_folds)
kf_p = KFold(n_folds)
kf = list(kf_p.split(range(dm.length(goal_datum))))
else:
v = range(dm.length(goal_datum))
kf = [(v, v)]
alarm_CV_list, S_CV_list, E_CV_list = [], [], []
for train, test in kf:
if bootstrap:
train = np.random.choice(train, len(train))
train_f, test_f = tt.index_to_filter(train), tt.index_to_filter(test)
_, mu_0, inv_Sigma_0 = tt.train_on_filter(
partial(null_dist, threshold=threshold), goal_datum, data_sources,
train_f)
EED_MEWMA = partial(EED,
alg=partial(MEWMA,
mu_0=mu_0,
inv_Sigma_0=inv_Sigma_0,
l=l),
h=h,
auto_reset=auto_reset,
len_outbreak=len_outbreak)
alarm, S, E = tt.test_on_filter(EED_MEWMA, data_sources, test_f)
alarm_CV_list.append(alarm)
S_CV_list.append(S)
E_CV_list.append(E)
S_CV = np.concatenate(S_CV_list, axis=0)
E_CV = np.concatenate(E_CV_list, axis=0)
alarm_CV = {}
alarm_CV['data'] = {}
alarm_CV['data']['values'] = np.concatenate(alarm_CV_list, axis=0)
alarm_CV['data']['times'] = goal_datum['data']['times']
return alarm_CV, S_CV, E_CV