def test_BGBB_fitting_time():
T = 100
sizes = [10, 100, 1000, 10000]
params = {'alpha': 1.2, 'beta': 0.7, 'gamma': 0.6, 'delta': 2.7}
compressed_data = {}
for size in sizes:
data = gen.bgbb_model(T,
params['alpha'],
params['beta'],
params['gamma'],
params['delta'],
size=size)
compressed_data[size] = compress_data(data)
times = {}
lengths = {}
for size in sizes:
fitter = est.BGBBFitter()
start_time = timeit.default_timer()
fitter.fit(compressed_data[size]['frequency'],
compressed_data[size]['recency'],
compressed_data[size]['T'],
N=compressed_data[size]['N'],
initial_params=params.values(),
jac=False)
t1 = timeit.default_timer() - start_time
times[size] = t1
lengths[size] = len(compressed_data[size])
print(params)
print(fitter.params_)
print(times)
print(lengths)
def test_BGBB_fitting_compressed_or_not():
T = 10
size = 1000
params = {'alpha': 1.2, 'beta': 0.7, 'gamma': 0.6, 'delta': 2.7}
data = gen.bgbb_model(T,
params['alpha'],
params['beta'],
params['gamma'],
params['delta'],
size=size)
compressed_data = compress_data(data)
fitter = est.BGBBFitter()
fitter_compressed = est.BGBBFitter()
fitter.fit(data['frequency'],
data['recency'],
data['T'],
initial_params=params.values())
fitter_compressed.fit(compressed_data['frequency'],
compressed_data['recency'],
compressed_data['T'],
N=compressed_data['N'],
initial_params=params.values())
print(params)
print(fitter.params_)
print(fitter_compressed.params_)
for par_name in params.keys():
assert math.fabs(fitter.params_[par_name] -
fitter_compressed.params_[par_name]) < 0.00001
def test_BGBB_integration_in_models_with_uncertainties():
T = 10
size = 100
params = {'alpha': 1.2, 'beta': 0.7, 'gamma': 0.6, 'delta': 2.7}
data = gen.bgbb_model(T,
params['alpha'],
params['beta'],
params['gamma'],
params['delta'],
size=size)
data = compress_data(data)
model = models.BGBBModel()
model.fit(data['frequency'],
data['recency'],
data['T'],
bootstrap_size=10,
N=data['N'],
initial_params=params.values())
print("Generation params")
print(params)
print("Fitted params")
print(model.params)
print(model.params_C)
print("Uncertain parameters")
print(model.uparams)
print("E[X(t)] as a function of t")
for t in [0, 1, 10, 100, 1000, 10000]:
uEx = model.expected_number_of_purchases_up_to_time(t)
print(t, uEx)
assert uEx.n >= -0.0001
assert uEx.s >= -0.0001
t = 10
print("E[X(t) = n] as a function of n, t = " + str(t))
tot_prob = 0.0
for n in range(t + 1):
prob = model.fitter.probability_of_n_purchases_up_to_time(t, n)
print(n, prob)
tot_prob += prob
assert 1 >= prob >= 0
uprob = model.probability_of_n_purchases_up_to_time(t, n)
print(uprob)
assert is_almost_equal(uprob.n, prob)
assert math.fabs(tot_prob - 1.0) < 0.00001
def test_BGBB_fitting_with_different_T_windows():
size = 10
params = {'alpha': 1.2, 'beta': 0.7, 'gamma': 0.6, 'delta': 2.7}
est_params = {}
T = range(1, 100 + 1)
data = gen.bgbb_model(T[0],
params['alpha'],
params['beta'],
params['gamma'],
params['delta'],
size=size)
for i in range(2, len(T)):
data_addendum = gen.bgbb_model(T[i],
params['alpha'],
params['beta'],
params['gamma'],
params['delta'],
size=size)
data = data.append(data_addendum)
data.index = range(len(data.index))
data = compress_data(data)
fitter = est.BGBBFitter()
T1s = [1, 15, 30, 45, 60, 75]
deltas = [30, 50, 60]
for T1 in T1s:
est_params[T1] = {}
for delta in deltas:
T2 = T1 + delta
filtered_data = filter_data_by_T(data, T1, T2)
fitter.fit(filtered_data['frequency'],
filtered_data['recency'],
filtered_data['T'],
N=filtered_data['N'])
est_params[T1][delta] = fitter.params_
print(est_params)
for T1 in T1s:
for delta in deltas:
current_params = est_params[T1][delta]
assert 'alpha' in current_params
assert 'beta' in current_params
assert 'gamma' in current_params
assert 'delta' in current_params
assert math.fabs(current_params['alpha'] -
params['alpha']) < 6 * params['alpha']
def test_BGBB_additional_functions():
T = 10
size = 100
params = {'alpha': 1.2, 'beta': 0.7, 'gamma': 0.6, 'delta': 2.7}
data = gen.bgbb_model(T,
params['alpha'],
params['beta'],
params['gamma'],
params['delta'],
size=size)
data = compress_data(data)
fitter = est.BGBBFitter()
fitter.fit(data['frequency'],
data['recency'],
data['T'],
N=data['N'],
initial_params=params.values())
print("Generation params")
print(params)
print("Fitted params")
print(fitter.params_)
print("E[X(t)] as a function of t")
for t in [0, 1, 10, 100, 1000, 10000]:
Ex = fitter.expected_number_of_purchases_up_to_time(t)
covariance_matrix = np.cov(
np.vstack([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0,
1]]))
Ex_err = fitter.expected_number_of_purchases_up_to_time_error(
t, covariance_matrix)
print(t, Ex, Ex_err)
assert Ex >= 0
assert Ex_err >= 0
t = 10
print("E[X(t) = n] as a function of n, t = " + str(t))
tot_prob = 0.0
for n in range(t + 1):
prob = fitter.probability_of_n_purchases_up_to_time(t, n)
print(n, prob)
tot_prob += prob
assert 1 >= prob >= 0
assert math.fabs(tot_prob - 1.0) < 0.00001
def test_goodness_of_test_BGBB():
params = {'alpha': 0.32, 'beta': 0.85, 'gamma': 5, 'delta': 3}
gen_data = compress_data(gen.bgbb_model(T=sample_T, size=100, **params))
test_n = multinomial_sample(gen_data['N'])
test_data = gen_data.copy(deep=True)
test_data['N'] = test_n
assert goodness_of_test(gen_data,
fitter_class=est.BGBBFitter,
verbose=True, test_data=test_data)
wrong_params = {'alpha': 3, 'beta': 0.1, 'gamma': 5, 'delta': 0.2}
wrong_test_data = gen.bgbb_model(T=sample_T, size=100, compressed=True, **wrong_params)
assert not goodness_of_test(gen_data,
fitter_class=est.BGBBFitter,
verbose=True,
test_data=wrong_test_data)
def test_BGBB_correlations_preserved():
T = 10
size = 100
params = {'alpha': 1.2, 'beta': 0.7, 'gamma': 0.6, 'delta': 2.7}
data = gen.bgbb_model(T,
params['alpha'],
params['beta'],
params['gamma'],
params['delta'],
size=size)
data = compress_data(data)
model = models.BGBBModel()
model.fit(data['frequency'],
data['recency'],
data['T'],
bootstrap_size=10,
N=data['N'],
initial_params=params.values())
print("Generation params")
print(params)
print("Fitted params")
print(model.params)
print(model.params_C)
print("Uncertain parameters")
print(model.uparams)
assert is_almost_equal(
correlation_matrix([model.uparams['alpha'],
model.uparams['alpha']])[0, 1], 1.0)
assert 1.0 > correlation_matrix([
model.uparams['alpha'] + ufloat(1, 1), model.uparams['alpha']
])[0, 1] > 0.0
# stub of profile
p1 = model.expected_number_of_purchases_up_to_time(1)
p2 = model.expected_number_of_purchases_up_to_time(2)
assert 1.0 > correlation_matrix([p1, p2])[0, 1] > 0.0
def test_BGBB_likelihood_compressed(T, size):
params = {'alpha': 0.56, 'beta': 1.17, 'gamma': 0.38, 'delta': 1.13}
data = gen.bgbb_model(T,
params['alpha'],
params['beta'],
params['gamma'],
params['delta'],
size=size)
data = compress_data(data)
model = models.BGBBModel()
n = len(data)
n_samples = ct.c_int(n)
int_n_size_array = ct.c_float * n
x = int_n_size_array(*data['frequency'])
tx = int_n_size_array(*data['recency'])
T = int_n_size_array(*data['T'])
N = int_n_size_array(*data['N'])
start_c = timeit.default_timer()
likelihood_c = model.fitter._c_negative_log_likelihood(
params.values(), x, tx, T, N, n_samples)
c_time = timeit.default_timer() - start_c
print("C_time: " + str(c_time))
print("Likelihood: " + str(likelihood_c))
start_py = timeit.default_timer()
likelihood_py = model.fitter._negative_log_likelihood(params.values(),
data['frequency'],
data['recency'],
data['T'],
penalizer_coef=0,
N=N)
py_time = timeit.default_timer() - start_py
print("Py_time: " + str(py_time))
print("Likelihood: " + str(likelihood_py))
def test_BGBB_fitting_with_jacobian():
T = 50
size = 5000
params = {'alpha': 1.2, 'beta': 0.7, 'gamma': 0.6, 'delta': 2.7}
data = gen.bgbb_model(T,
params['alpha'],
params['beta'],
params['gamma'],
params['delta'],
size=size)
compressed_data = compress_data(data)
fitter = est.BGBBFitter()
fitter.fit(compressed_data['frequency'],
compressed_data['recency'],
compressed_data['T'],
N=compressed_data['N'],
initial_params=params.values(),
jac=False)
print(params)
print("Without jacobian:")
print(fitter.params_)
fitter.fit(compressed_data['frequency'],
compressed_data['recency'],
compressed_data['T'],
N=compressed_data['N'],
initial_params=params.values(),
jac=True)
print(params)
print("With jacobian:")
print(fitter.params_)
def test_BGBBBGExt_fitting_on_simulated_quite_real_looking_data():
T = 10
T_lagged = 0
T0 = 52
sizes_installs = [500, 1000, 5000, 10000, 25000, 50000, 100000] # [500, 1000] #
n_sim = 10
iterative_fitting = 0
penalizer_coef = 0.1
success_fit_ratio = {}
success_fit = {}
arpd_estimates = {}
lifetime_estimates = {}
conversion_estimates = {}
appd_estimates = {}
apppu_estimates = {}
arppu_estimates = {}
for size_installs in sizes_installs:
success_fit[size_installs] = 0
arpd_estimates[size_installs] = []
lifetime_estimates[size_installs] = []
conversion_estimates[size_installs] = []
appd_estimates[size_installs] = []
apppu_estimates[size_installs] = []
arppu_estimates[size_installs] = []
for n in range(n_sim):
# size_installs = 5000
size_purchasers = size_installs / 20
a, b, g, d, e, z, c0, a2, b2, g2, d2 = 1.13, 0.32, 0.63, 3.2, 0.05, 6.78, 0.04, 0.33, 1.75, 1.88, 7.98
params_conversion = {'alpha': a, 'beta': b, 'gamma': g, 'delta': d, 'epsilon': e, 'zeta': z, 'c0': c0}
params_arppu = {'alpha': a2, 'beta': b2, 'gamma': g2, 'delta': d2}
n_cohorts = T - T_lagged + 1
data_conversion = gen.bgbbbgext_model(T, params_conversion['alpha'], params_conversion['beta'],
params_conversion['gamma'], params_conversion['delta'],
params_conversion['epsilon'],
params_conversion['zeta'], params_conversion['c0'],
size=size_installs / n_cohorts,
time_first_purchase=True)
data_arppu = gen.bgbb_model(T, params_arppu['alpha'], params_arppu['beta'],
params_arppu['gamma'], params_arppu['delta'],
size=size_purchasers / n_cohorts)
for Ti in range(T_lagged, T):
data_conversion_new = gen.bgbbbgext_model(Ti, params_conversion['alpha'], params_conversion['beta'],
params_conversion['gamma'], params_conversion['delta'],
params_conversion['epsilon'],
params_conversion['zeta'], params_conversion['c0'],
size=size_installs / n_cohorts,
time_first_purchase=True)
data_arppu_new = gen.bgbb_model(Ti, params_arppu['alpha'], params_arppu['beta'],
params_arppu['gamma'], params_arppu['delta'],
size=size_purchasers / n_cohorts)
data_conversion = pd.concat([data_conversion, data_conversion_new])
data_arppu = pd.concat([data_arppu, data_arppu_new])
mv_values = gen.sample_monetary_values(size_purchasers)
compressed_data_conversion = compress_session_session_before_conversion_data(data_conversion)
compressed_data_arppu = compress_data(data_arppu)
model_conversion = mod.BGBBBGExtModel(penalizer_coef)
model_conversion.fit(frequency=compressed_data_conversion['frequency'],
recency=compressed_data_conversion['recency'], T=compressed_data_conversion['T'],
frequency_before_conversion=compressed_data_conversion['frequency_before_conversion'],
N=compressed_data_conversion['N'], initial_params=params_conversion.values(),
iterative_fitting=iterative_fitting)
model_arppu = mod.BGBBModel(penalizer_coef)
model_arppu.fit(frequency=compressed_data_arppu['frequency'], recency=compressed_data_arppu['recency'],
T=compressed_data_arppu['T'],
N=compressed_data_arppu['N'], initial_params=params_arppu.values(),
iterative_fitting=iterative_fitting)
mv = ufloat(np.mean(mv_values), np.std(mv_values) / math.sqrt(len(mv_values)))
print("Conversion parameters")
print(params_conversion)
print(model_conversion.params)
print(model_conversion.uparams)
print("Arppu parameters")
print(params_arppu)
print(model_arppu.params)
print(model_arppu.uparams)
print("Monetary values")
print(mv)
ts = range(T0)
lifetime = [ufloat_to_tuple(model_conversion.expected_number_of_sessions_up_to_time(t)) for t in ts]
conversion_diff = [ufloat_to_tuple(model_conversion.expected_probability_of_converting_at_time(t)) for t in ts]
conversion = [ufloat_to_tuple(model_conversion.expected_probability_of_converting_within_time(t)) for t in ts]
apppu = [ufloat_to_tuple(model_arppu.expected_number_of_purchases_up_to_time(t)) for t in ts]
arppu = [ufloat_to_tuple((1.0 + apppu[i][0]) * mv) for i in range(len(apppu))]
appd = [ufloat_to_tuple(get_arpd_retention(model_conversion, model_arppu, t)) for t in ts]
arpd = [ufloat_to_tuple(appd[i][0] * mv) for i in range(len(appd))]
print(ts)
print(lifetime)
print(conversion_diff)
print(conversion)
print(apppu)
print(arppu)
print(appd)
print(arpd)
summary_df = pd.DataFrame({
'lifetime': [v[0] + 1 for v in lifetime],
'lifetime_err': [v[1] for v in lifetime],
'conversion_diff': [v[0] for v in conversion_diff],
'conversion_diff_err': [v[1] for v in conversion_diff],
'conversion': [v[0] for v in conversion],
'conversion_err': [v[1] for v in conversion],
'apppu': [v[0] + 1 for v in apppu],
'apppu_err': [v[1] for v in apppu],
'arppu': [v[0] for v in arppu],
'arppu_err': [v[1] for v in arppu],
'appd': [v[0] for v in appd],
'appd_err': [v[1] for v in appd],
'arpd': [v[0] for v in arpd],
'arpd_err': [v[1] for v in arpd],
'true_lifetime': [get_true_lifetime(a, b, g, d, t) for t in ts],
'true_conversion': [get_true_conversion(a, b, g, d, e, z, c0, t) for t in ts],
'true_apppu': [get_true_apppu(a2, b2, g2, d2, t) for t in ts],
'true_arppu': [get_true_arppu(a2, b2, g2, d2, true_mv, t) for t in ts],
'true_appd': [get_true_appd(a, b, g, d, e, z, c0, a2, b2, g2, d2, t) for t in ts],
'true_arpd': [get_true_arpd(a, b, g, d, e, z, c0, a2, b2, g2, d2, true_mv, t) for t in ts],
})
with open("/Users/marcomeneghelli/Desktop/arpd_simulations/" + str(size_installs) + "/pars_simdata_" + str(
size_installs) + "_" + str(
T) + "iterative_fitting" + str(iterative_fitting) + "_" + str(n) + ".txt", "w") as text_file:
text_file.write(str(model_conversion.params))
text_file.write(str(model_arppu.params))
text_file.write(str((mv)))
summary_df.to_csv(
"/Users/marcomeneghelli/Desktop/arpd_simulations/" + str(size_installs) + "/arpd_simdata_" + str(
size_installs) + "_" + str(
T) + "iterative_fitting" + str(iterative_fitting) + "_" + str(n) + ".csv")
last_arpd = arpd[-1][0]
last_lifetime = lifetime[-1][0]
last_conversion = conversion[-1][0]
last_appd = appd[-1][0]
last_apppu = apppu[-1][0]
last_arppu = arppu[-1][0]
if not (math.isnan(last_arpd) or last_arpd is None):
success_fit[size_installs] += 1
arpd_estimates[size_installs].append(last_arpd)
lifetime_estimates[size_installs].append(last_lifetime)
conversion_estimates[size_installs].append(last_conversion)
appd_estimates[size_installs].append(last_appd)
apppu_estimates[size_installs].append(last_apppu)
arppu_estimates[size_installs].append(last_arppu)
success_fit_ratio[size_installs] = float(success_fit[size_installs]) / n_sim
summary_size_installs_df = pd.DataFrame({
'success_fit_ratio': success_fit_ratio[size_installs],
'arpd_estimates': arpd_estimates[size_installs],
'lifetime_estimates': lifetime_estimates[size_installs],
'conversion_estimates': conversion_estimates[size_installs],
'appd_estimates': appd_estimates[size_installs],
'apppu_estimates': apppu_estimates[size_installs],
'arppu_estimates': arppu_estimates[size_installs],
})
summary_size_installs_df.to_csv(
"/Users/marcomeneghelli/Desktop/arpd_simulations/arpd_simdata_last_measurements_" + str(
size_installs) + "_" + str(
T) + "iterative_fitting" + str(iterative_fitting) + ".csv")
