def fit(self,
frequency,
recency,
T,
iterative_fitting=1,
initial_params=None,
verbose=False,
tol=1e-4,
index=None):
"""
This methods fits the data to the BG/NBD model.
Parameters:
frequency: the frequency vector of customers' purchases (denoted x in literature).
recency: the recency vector of customers' purchases (denoted t_x in literature).
T: the vector of customers' age (time since first purchase)
iterative_fitting: perform iterative_fitting fits over random/warm-started initial params
initial_params: set the initial parameters for the fitter.
verbose: set to true to print out convergence diagnostics.
index: index for resulted DataFrame which is accessible via self.data
Returns:
self, with additional properties and methods like params_ and predict
"""
frequency = asarray(frequency)
recency = asarray(recency)
T = asarray(T)
_check_inputs(frequency, recency, T)
self._scale = _scale_time(T)
scaled_recency = recency * self._scale
scaled_T = T * self._scale
params, self._negative_log_likelihood_ = _fit(
self._negative_log_likelihood,
[frequency, scaled_recency, scaled_T, self.penalizer_coef],
iterative_fitting, initial_params, 4, verbose, tol)
self.params_ = OrderedDict(zip(['r', 'alpha', 'a', 'b'], params))
self.params_['alpha'] /= self._scale
self.data = DataFrame(vconcat[frequency, recency, T],
columns=['frequency', 'recency', 'T'])
if index is not None:
self.data.index = index
self.generate_new_data = lambda size=1: beta_geometric_nbd_model(
T, *self._unload_params('r', 'alpha', 'a', 'b'), size=size)
self.predict = self.conditional_expected_number_of_purchases_up_to_time
return self
def fit(self, frequency, recency, T, iterative_fitting=1, initial_params=None, verbose=False):
"""
This methods fits the data to the BG/NBD model.
Parameters:
frequency: the frequency vector of customers' purchases (denoted x in literature).
recency: the recency vector of customers' purchases (denoted t_x in literature).
T: the vector of customers' age (time since first purchase)
iterative_fitting: perform `iterative_fitting` additional fits to find the best
parameters for the model. Setting to 0 will improve peformance but possibly
hurt estimates.
initial_params: set the initial parameters for the fitter.
verbose: set to true to print out convergence diagnostics.
Returns:
self, with additional properties and methods like params_ and predict
"""
frequency = asarray(frequency)
recency = asarray(recency)
T = asarray(T)
_check_inputs(frequency, recency, T)
self._scale = _scale_time(T)
scaled_recency = recency * self._scale
scaled_T = T * self._scale
params, self._negative_log_likelihood_ = _fit(
self._negative_log_likelihood,
frequency,
scaled_recency,
scaled_T,
iterative_fitting,
self.penalizer_coef,
initial_params,
verbose,
)
self.params_ = OrderedDict(zip(["r", "alpha", "a", "b"], params))
self.params_["alpha"] /= self._scale
self.data = DataFrame(vconcat[frequency, recency, T], columns=["frequency", "recency", "T"])
self.generate_new_data = lambda size=1: beta_geometric_nbd_model(
T, *self._unload_params("r", "alpha", "a", "b"), size=size
)
self.predict = self.conditional_expected_number_of_purchases_up_to_time
return self
def fit(self,
frequency,
recency,
T,
iterative_fitting=1,
initial_params=None,
verbose=False):
"""
This methods fits the data to the BG/NBD model.
Parameters:
frequency: the frequency vector of customers' purchases (denoted x in literature).
recency: the recency vector of customers' purchases (denoted t_x in literature).
T: the vector of customers' age (time since first purchase)
iterative_fitting: perform `iterative_fitting` additional fits to find the best
parameters for the model. Setting to 0 will improve peformance but possibly
hurt estimates.
initial_params: set the initial parameters for the fitter.
verbose: set to true to print out convergence diagnostics.
Returns:
self, with additional properties and methods like params_ and predict
"""
frequency = asarray(frequency)
recency = asarray(recency)
T = asarray(T)
_check_inputs(frequency, recency, T)
self._scale = _scale_time(T)
scaled_recency = recency * self._scale
scaled_T = T * self._scale
params, self._negative_log_likelihood_ = _fit(
self._negative_log_likelihood, frequency, scaled_recency, scaled_T,
iterative_fitting, self.penalizer_coef, initial_params, verbose)
self.params_ = OrderedDict(zip(['r', 'alpha', 'a', 'b'], params))
self.params_['alpha'] /= self._scale
self.data = DataFrame(vconcat[frequency, recency, T],
columns=['frequency', 'recency', 'T'])
self.generate_new_data = lambda size=1: beta_geometric_nbd_model(
T, *self._unload_params('r', 'alpha', 'a', 'b'), size=size)
self.predict = self.conditional_expected_number_of_purchases_up_to_time
return self
def fit(self, frequency, recency, T, iterative_fitting=1, initial_params=None, verbose=False, tol=1e-4):
"""
This methods fits the data to the BG/NBD model.
Parameters:
frequency: the frequency vector of customers' purchases (denoted x in literature).
recency: the recency vector of customers' purchases (denoted t_x in literature).
T: the vector of customers' age (time since first purchase)
iterative_fitting: perform iterative_fitting fits over random/warm-started initial params
initial_params: set the initial parameters for the fitter.
verbose: set to true to print out convergence diagnostics.
Returns:
self, with additional properties and methods like params_ and predict
"""
frequency = asarray(frequency)
recency = asarray(recency)
T = asarray(T)
_check_inputs(frequency, recency, T)
self._scale = _scale_time(T)
scaled_recency = recency * self._scale
scaled_T = T * self._scale
params, self._negative_log_likelihood_ = _fit(self._negative_log_likelihood,
[frequency, scaled_recency, scaled_T, self.penalizer_coef],
iterative_fitting,
initial_params,
4,
verbose,
tol)
self.params_ = OrderedDict(zip(['r', 'alpha', 'a', 'b'], params))
self.params_['alpha'] /= self._scale
self.data = DataFrame(vconcat[frequency, recency, T], columns=['frequency', 'recency', 'T'])
self.generate_new_data = lambda size=1: beta_geometric_nbd_model(T, *self._unload_params('r', 'alpha', 'a', 'b'), size=size)
self.predict = self.conditional_expected_number_of_purchases_up_to_time
return self
def test_scale_time():
max_T = 200.
T = np.arange(max_T)
assert utils._scale_time(T) == 10. / (max_T-1)
def fit(self,
frequency,
recency,
T,
weights=None,
iterative_fitting=1,
initial_params=None,
verbose=False,
tol=1e-4,
index=None,
fit_method="Nelder-Mead",
maxiter=2000,
**kwargs):
"""
Pareto/NBD model fitter.
Parameters
----------
frequency: array_like
the frequency vector of customers' purchases
(denoted x in literature).
recency: array_like
the recency vector of customers' purchases
(denoted t_x in literature).
T: array_like
customers' age (time units since first purchase)
weights: None or array_like
Number of customers with given frequency/recency/T,
defaults to 1 if not specified. Fader and
Hardie condense the individual RFM matrix into all
observed combinations of frequency/recency/T. This
parameter represents the count of customers with a given
purchase pattern. Instead of calculating individual
log-likelihood, the log-likelihood is calculated for each
pattern and multiplied by the number of customers with
that pattern.
iterative_fitting: int, optional
perform iterative_fitting fits over random/warm-started initial params
initial_params: array_like, optional
set the initial parameters for the fitter.
verbose : bool, optional
set to true to print out convergence diagnostics.
tol : float, optional
tolerance for termination of the function minimization process.
index: array_like, optional
index for resulted DataFrame which is accessible via self.data
fit_method : string, optional
fit_method to passing to scipy.optimize.minimize
maxiter : int, optional
max iterations for optimizer in scipy.optimize.minimize will be
overwritten if set in kwargs.
kwargs:
key word arguments to pass to the scipy.optimize.minimize
function as options dict
Returns
-------
ParetoNBDFitter
with additional properties like ``params_`` and methods like ``predict``
"""
frequency = asarray(frequency).astype(int)
recency = asarray(recency)
T = asarray(T)
if weights is None:
weights = np.ones(recency.shape[0], dtype=np.int64)
else:
weights = asarray(weights)
_check_inputs(frequency, recency, T)
self._scale = _scale_time(T)
scaled_recency = recency * self._scale
scaled_T = T * self._scale
params, self._negative_log_likelihood_ = self._fit(
(frequency, scaled_recency, scaled_T, weights,
self.penalizer_coef), iterative_fitting, initial_params, 4,
verbose, tol, fit_method, maxiter, **kwargs)
self._hessian_ = None
self.params_ = pd.Series(*(params, ["r", "alpha", "s", "beta"]))
self.params_["alpha"] /= self._scale
self.params_["beta"] /= self._scale
self.data = DataFrame(
{
"frequency": frequency,
"recency": recency,
"T": T,
"weights": weights
},
index=index)
self.generate_new_data = lambda size=1: pareto_nbd_model(
T, *self._unload_params("r", "alpha", "s", "beta"), size=size)
self.predict = self.conditional_expected_number_of_purchases_up_to_time
return self
def test_scale_time():
max_T = 200.
T = np.arange(max_T)
assert utils._scale_time(T) == 10. / (max_T - 1)
def fit(self,
frequency,
recency,
T,
weights=None,
iterative_fitting=1,
initial_params=None,
verbose=False,
tol=1e-4,
index=None,
fit_method="Nelder-Mead",
maxiter=2000,
covariates=None,
dropout_rate_scale_parameter_covariates=None,
**kwargs):
"""
Pareto/NBD model fitter.
Parameters
----------
frequency: array_like
the frequency vector of customers' purchases
(denoted x in literature).
recency: array_like
the recency vector of customers' purchases
(denoted t_x in literature).
T: array_like
customers' age (time units since first purchase)
weights: None or array_like
Number of customers with given frequency/recency/T,
defaults to 1 if not specified. Fader and
Hardie condense the individual RFM matrix into all
observed combinations of frequency/recency/T. This
parameter represents the count of customers with a given
purchase pattern. Instead of calculating individual
log-likelihood, the log-likelihood is calculated for each
pattern and multiplied by the number of customers with
that pattern.
iterative_fitting: int, optional
perform iterative_fitting fits over random/warm-started initial params
initial_params: array_like, optional
set the initial parameters for the fitter.
verbose : bool, optional
set to true to print out convergence diagnostics.
tol : float, optional
tolerance for termination of the function minimization process.
index: array_like, optional
index for resulted DataFrame which is accessible via self.data
fit_method : string, optional
fit_method to passing to scipy.optimize.minimize
maxiter : int, optional
max iterations for optimizer in scipy.optimize.minimize will be
overwritten if set in kwargs.
covariates: array_like, optional
Array of time-independent customer features (n_customers x n_covariates).
dropout_rate_scale_parameter_covariates: array_like, optional
Array of time-independent customer features (n_customers x n_covariates)
used exclusively for the dropout rate's scale parameter (denoted beta in
the literature). If this is None and `covariates` isn't, the latter's
values are used for both the transaction and dropout rate scale
parameter derivation.
kwargs:
key word arguments to pass to the scipy.optimize.minimize
function as options dict
Returns
-------
ParetoNBDwithCovariatesFitter
with additional properties like ``params_`` and methods like ``predict``
"""
frequency = asarray(frequency).astype(int)
recency = asarray(recency)
T = asarray(T)
if weights is None:
weights = np.ones(recency.shape[0], dtype=np.int64)
else:
weights = asarray(weights)
_check_inputs(frequency, recency, T)
self._scale = _scale_time(T)
scaled_recency = recency * self._scale
scaled_T = T * self._scale
params_size = 6
self.covariates = covariates
self.dropout_rate_scale_parameter_covariates = dropout_rate_scale_parameter_covariates
self.covariates_size = [1, 1]
if self.covariates is not None:
covariates_size = self.covariates.shape[1]
params_size += (covariates_size - 1)
self.covariates_size = [covariates_size, covariates_size]
if self.dropout_rate_scale_parameter_covariates is not None:
dropout_rate_scale_parameter_covariates_size = self.dropout_rate_scale_parameter_covariates.shape[
1]
params_size += (dropout_rate_scale_parameter_covariates_size - 1)
self.covariates_size[
1] = dropout_rate_scale_parameter_covariates_size
params, self._negative_log_likelihood_ = self._fit(
minimizing_function_args=(frequency, scaled_recency, scaled_T,
weights, self.penalizer_coef),
iterative_fitting=iterative_fitting,
initial_params=initial_params,
params_size=params_size,
disp=verbose,
tol=tol,
fit_method=fit_method,
maxiter=maxiter,
**kwargs)
params = tuple(params[:4]) + \
(params[4:4+self.covariates_size[0]], ) + \
(params[4+self.covariates_size[0]:4+self.covariates_size[0]+self.covariates_size[1]], )
self._hessian_ = None
self.params_ = pd.Series(
*(params, ["r", "alpha_0", "s", "beta_0", "gamma_1", "gamma_2"]))
self.params_["alpha_0"] /= self._scale
self.params_["beta_0"] /= self._scale
self.data = DataFrame(
{
"frequency": frequency,
"recency": recency,
"T": T,
"weights": weights
},
index=index)
self.generate_new_data = lambda size=1: pareto_nbd_model(
T,
*self._convert_parameters(
self._unload_params("r", "alpha_0", "s", "beta_0", "gamma_1",
"gamma_2")),
size=size)
self.predict = self.conditional_expected_number_of_purchases_up_to_time
return self
