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some possible perf improvements
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@CamDavidsonPilon
CamDavidsonPilon committed Oct 6, 2016
1 parent 5b4f7de commit e5c9d0a
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Showing 2 changed files with 22 additions and 22 deletions.
42 changes: 21 additions & 21 deletions lifetimes/estimation.py
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Expand Up @@ -6,7 +6,7 @@
isinf, isnan, ones_like
from pandas import DataFrame

from scipy import special
from scipy.special import gammaln, hyp2f1, beta, gamma
from scipy import misc

from lifetimes.utils import _fit, _scale_time, _check_inputs, customer_lifetime_value
Expand Down Expand Up @@ -52,7 +52,7 @@ def _negative_log_likelihood(params, frequency, avg_monetary_value, penalizer_co
x = frequency
m = avg_monetary_value

negative_log_likelihood_values = special.gammaln(p * x + q) - special.gammaln(p * x) - special.gammaln(q)\
negative_log_likelihood_values = gammaln(p * x + q) - gammaln(p * x) - gammaln(q)\
+ q * np.log(v) + (p * x - 1) * np.log(m) + (p * x) * np.log(x) - (p * x + q) * np.log(x * m + v)

penalizer_term = penalizer_coef * log(params).sum()
Expand Down Expand Up @@ -175,8 +175,8 @@ def _log_A_0(params, freq, recency, age):
abs_alpha_beta = max_of_alpha_beta - min_of_alpha_beta

rsf = r + s + freq
p_1, q_1 = special.hyp2f1(rsf, t, rsf + 1., abs_alpha_beta / (max_of_alpha_beta + recency)), (max_of_alpha_beta + recency)
p_2, q_2 = special.hyp2f1(rsf, t, rsf + 1., abs_alpha_beta / (max_of_alpha_beta + age)), (max_of_alpha_beta + age)
p_1, q_1 = hyp2f1(rsf, t, rsf + 1., abs_alpha_beta / (max_of_alpha_beta + recency)), (max_of_alpha_beta + recency)
p_2, q_2 = hyp2f1(rsf, t, rsf + 1., abs_alpha_beta / (max_of_alpha_beta + age)), (max_of_alpha_beta + age)

try:
size = len(freq)
Expand All @@ -198,7 +198,7 @@ def _negative_log_likelihood(params, freq, rec, T, penalizer_coef):

r_s_x = r + s + x

A_1 = special.gammaln(r + x) - special.gammaln(r) + r * log(alpha) + s * log(beta)
A_1 = gammaln(r + x) - gammaln(r) + r * log(alpha) + s * log(beta)
log_A_0 = ParetoNBDFitter._log_A_0(params, freq, rec, T)

A_2 = logaddexp(-(r + x) * log(alpha + T) - s * log(beta + T), log(s) + log_A_0 - log(r_s_x))
Expand Down Expand Up @@ -264,7 +264,7 @@ def conditional_expected_number_of_purchases_up_to_time(self, t, frequency, rece
r, alpha, s, beta = params

likelihood = exp(-self._negative_log_likelihood(params, x, t_x, T, 0))
first_term = (special.gamma(r + x) / special.gamma(r)) * (alpha ** r * beta ** s) / (alpha + T) ** (r + x) / (beta + T) ** s
first_term = (gamma(r + x) / gamma(r)) * (alpha ** r * beta ** s) / (alpha + T) ** (r + x) / (beta + T) ** s
second_term = (r + x) * (beta + T) / (alpha + T) / (s - 1)
third_term = 1 - ((beta + T) / (beta + T + t)) ** (s - 1)
return first_term * second_term * third_term / likelihood
Expand Down Expand Up @@ -356,8 +356,8 @@ def _negative_log_likelihood(params, freq, rec, T, penalizer_coef):

r, alpha, a, b = params

A_1 = special.gammaln(r + freq) - special.gammaln(r) + r * log(alpha)
A_2 = special.gammaln(a + b) + special.gammaln(b + freq) - special.gammaln(b) - special.gammaln(a + b + freq)
A_1 = gammaln(r + freq) - gammaln(r) + r * log(alpha)
A_2 = gammaln(a + b) + gammaln(b + freq) - gammaln(b) - gammaln(a + b + freq)
A_3 = -(r + freq) * log(alpha + T)

d = vconcat[ones_like(freq), (freq > 0)]
Expand All @@ -377,7 +377,7 @@ def expected_number_of_purchases_up_to_time(self, t):
Returns: a scalar or array
"""
r, alpha, a, b = self._unload_params('r', 'alpha', 'a', 'b')
hyp = special.hyp2f1(r, b, a + b - 1, t / (alpha + t))
hyp = hyp2f1(r, b, a + b - 1, t / (alpha + t))
return (a + b - 1) / (a - 1) * (1 - hyp * (alpha / (alpha + t)) ** r)

def conditional_expected_number_of_purchases_up_to_time(self, t, frequency, recency, T):
Expand All @@ -396,7 +396,7 @@ def conditional_expected_number_of_purchases_up_to_time(self, t, frequency, rece
x = frequency
r, alpha, a, b = self._unload_params('r', 'alpha', 'a', 'b')

hyp_term = special.hyp2f1(r + x, b + x, a + b + x - 1, t / (alpha + T + t))
hyp_term = hyp2f1(r + x, b + x, a + b + x - 1, t / (alpha + T + t))
first_term = (a + b + x - 1) / (a - 1)
second_term = (1 - hyp_term * ((alpha + T) / (alpha + t + T)) ** (r + x))
numerator = first_term * second_term
Expand Down Expand Up @@ -454,10 +454,10 @@ def probability_of_n_purchases_up_to_time(self, t, n):

r, alpha, a, b = self._unload_params('r', 'alpha', 'a', 'b')

first_term = special.beta(a, b + n) / special.beta(a, b) * special.gamma(r + n) / special.gamma(r) / special.gamma(n + 1) * (alpha / (alpha + t)) ** r * (t / (alpha + t)) ** n
first_term = beta(a, b + n) / beta(a, b) * gamma(r + n) / gamma(r) / gamma(n + 1) * (alpha / (alpha + t)) ** r * (t / (alpha + t)) ** n
if n > 0:
finite_sum = np.sum([special.gamma(r + j) / special.gamma(r) / special.gamma(j + 1) * (t / (alpha + t)) ** j for j in range(0, n)])
second_term = special.beta(a + 1, b + n - 1) / special.beta(a, b) * (1 - (alpha / (alpha + t)) ** r * finite_sum)
finite_sum = np.sum([gamma(r + j) / gamma(r) / gamma(j + 1) * (t / (alpha + t)) ** j for j in range(0, n)])
second_term = beta(a + 1, b + n - 1) / beta(a, b) * (1 - (alpha / (alpha + t)) ** r * finite_sum)
else:
second_term = 0
return first_term + second_term
Expand Down Expand Up @@ -511,13 +511,13 @@ def fit(self, frequency, recency, T, iterative_fitting=1, initial_params=None, v

@staticmethod
def _negative_log_likelihood(params, freq, rec, T, penalizer_coef):
if npany(asarray(params) <= 0):
if any(p <= 0 for p in params):
return np.inf

r, alpha, a, b = params

A_1 = special.gammaln(r + freq) - special.gammaln(r) + r * log(alpha)
A_2 = special.gammaln(a + b) + special.gammaln(b + freq + 1) - special.gammaln(b) - special.gammaln(a + b + freq + 1)
A_1 = gammaln(r + freq) - gammaln(r) + r * log(alpha)
A_2 = gammaln(a + b) + gammaln(b + freq + 1) - gammaln(b) - gammaln(a + b + freq + 1)
A_3 = -(r + freq) * log(alpha + T)
A_4 = log(a) - log(b + freq) + (r + freq) * (log(alpha + T) - log(alpha + rec))

Expand All @@ -535,7 +535,7 @@ def expected_number_of_purchases_up_to_time(self, t):
Returns: a scalar or array
"""
r, alpha, a, b = self._unload_params('r', 'alpha', 'a', 'b')
hyp = special.hyp2f1(r, b + 1, a + b, t / (alpha + t))
hyp = hyp2f1(r, b + 1, a + b, t / (alpha + t))
return b / (a - 1) * (1 - hyp * (alpha / (alpha + t)) ** r)

def conditional_expected_number_of_purchases_up_to_time(self, t, frequency, recency, T):
Expand All @@ -555,7 +555,7 @@ def conditional_expected_number_of_purchases_up_to_time(self, t, frequency, rece
x = frequency
r, alpha, a, b = self._unload_params('r', 'alpha', 'a', 'b')

hyp_term = special.hyp2f1(r + x, b + x + 1, a + b + x, t / (alpha + T + t))
hyp_term = hyp2f1(r + x, b + x + 1, a + b + x, t / (alpha + T + t))
first_term = (a + b + x) / (a - 1)
second_term = (1 - hyp_term * ((alpha + T) / (alpha + t + T)) ** (r + x))
numerator = first_term * second_term
Expand Down Expand Up @@ -603,8 +603,8 @@ def probability_of_n_purchases_up_to_time(self, t, n):

r, alpha, a, b = self._unload_params('r', 'alpha', 'a', 'b')

first_term = special.beta(a, b + n + 1) / special.beta(a, b) * special.gamma(r + n) / special.gamma(r) / special.gamma(n + 1) * (alpha / (alpha + t)) ** r * (t / (alpha + t)) ** n
finite_sum = np.sum([special.gamma(r + j) / special.gamma(r) / special.gamma(j + 1) * (t / (alpha + t)) ** j for j in range(0, n)])
second_term = special.beta(a + 1, b + n) / special.beta(a, b) * (1 - (alpha / (alpha + t)) ** r * finite_sum)
first_term = beta(a, b + n + 1) / beta(a, b) * gamma(r + n) / gamma(r) / gamma(n + 1) * (alpha / (alpha + t)) ** r * (t / (alpha + t)) ** n
finite_sum = np.sum([gamma(r + j) / gamma(r) / gamma(j + 1) * (t / (alpha + t)) ** j for j in range(0, n)])
second_term = beta(a + 1, b + n) / beta(a, b) * (1 - (alpha / (alpha + t)) ** r * finite_sum)

return first_term + second_term
2 changes: 1 addition & 1 deletion lifetimes/utils.py
View file
Expand Up @@ -212,7 +212,7 @@ def calculate_alive_path(model, transactions, datetime_col, t, freq='D'):
def _fit(minimizing_function, minimizing_function_args, iterative_fitting, initial_params, params_size, disp):
ll = []
sols = []
methods = ['Nelder-Mead', 'Powell', 'BFGS']
methods = ['Nelder-Mead', 'BFGS', 'Powell']

def _func_caller(params, func_args, function):
return function(params, *func_args)
Expand Down

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