def addPriors(self, prior_list):
"""
Add priors to the object, require prior_list contains priors
"""
self.prior_list = prior_list
(self.C, self.JC, self.c, self.H, self.JH, self.h, self.uprior,
self.gprior, self.lprior, self.C_list, self.JC_list, self.c_list,
self.H_list, self.JH_list, self.h_list, self.id_C_list,
self.id_C_var_list, self.id_H_list, self.id_H_var_list,
self.num_constraints_list,
self.num_regularizers_list) = utils.constructPrior(prior_list, self)
# renew uprior for gamma
if self.uprior is None:
self.uprior = np.array([[-np.inf] * self.k_beta +
[1e-7] * self.k_gamma, [np.inf] * self.k])
else:
uprior_beta = self.uprior[:, self.id_beta]
uprior_gamma = self.uprior[:, self.id_gamma]
uprior_gamma[0] = np.maximum(1e-7, uprior_gamma[0])
uprior_gamma[1] = np.maximum(uprior_gamma[0], uprior_gamma[1])
self.uprior = np.hstack((uprior_beta, uprior_gamma))
self.lt.C, self.lt.JC, self.lt.c = self.C, self.JC, self.c
self.lt.H, self.lt.JH, self.lt.h = self.H, self.JH, self.h
(self.lt.uprior, self.lt.gprior,
self.lt.lprior) = (self.uprior, self.gprior, self.lprior)
self.lt = LimeTr(self.study_sizes,
self.k_beta,
self.k_gamma,
self.obs_mean,
self.F,
self.JF,
self.Z,
self.obs_std,
C=self.C,
JC=self.JC,
c=self.c,
H=self.H,
JH=self.JH,
h=self.h,
uprior=self.uprior,
gprior=self.gprior,
lprior=self.lprior,
inlier_percentage=self.inlier_percentage)
def sample_params(self, n_samples=500):
if 'mr_list' in dir(self.mr):
# sample for each submodel
sample_size_list = self.mr.compute_sample_sizes(n_samples)
param_samples = [
LimeTr.sampleSoln(sub_mr.lt, sample_size=ss)
for sub_mr, ss in zip(self.mr.mr_list, sample_size_list)
]
given_samples = {
'given_beta_samples_list': [i[0] for i in param_samples],
'given_gamma_samples_list': [i[1] for i in param_samples]
}
else:
beta_samples, gamma_samples = LimeTr.sampleSoln(
self.mr.lt, sample_size=n_samples)
given_samples = {
'given_beta_samples': beta_samples,
'given_gamma_samples': gamma_samples
}
self.given_samples = given_samples
def get_parameter_samples(mr, n_samples=1000):
# sample for each submodel
sample_size_list = mr.compute_sample_sizes(n_samples)
param_samples = [
LimeTr.sampleSoln(sub_mr.lt, sample_size=ss)
for sub_mr, ss in zip(mr.mr_list, sample_size_list)
]
given_samples = {
'given_beta_samples_list': [i[0] for i in param_samples],
'given_gamma_samples_list': [i[1] for i in param_samples]
}
return given_samples
def __init__(self,
obs_mean,
obs_std,
study_sizes,
x_cov_list,
z_cov_list,
spline_list=[],
inlier_percentage=1.0,
rr_random_slope=False):
"""
Initialize the object and pass in the data, require
- obs_mean: observations
- obs_std: standard deviations for the observations
- study_sizes: all study sizes in a list
- x_cov_list: all x cov in a list
- z_cov_list: all z cov in a list
- spline_list: optional, all spline in a list
- inlier_percentage: optional, used for trimming
"""
# pass in data
self.obs_mean = obs_mean
self.obs_std = obs_std
self.study_sizes = study_sizes
self.num_studies = len(study_sizes)
self.num_obs = sum(study_sizes)
# construct x and z "covariates"
self.spline_list = spline_list
self.x_cov_list = x_cov_list
self.z_cov_list = z_cov_list
(self.F, self.JF, self.F_list, self.JF_list, self.id_beta_list,
self.id_spline_beta_list,
self.k_beta_list) = utils.constructXCov(x_cov_list,
spline_list=spline_list)
(self.Z, self.Z_list, self.id_gamma_list, self.id_spline_gamma_list,
self.k_gamma_list) = utils.constructZCov(z_cov_list,
spline_list=spline_list)
self.k_beta = int(sum(self.k_beta_list))
self.k_gamma = int(sum(self.k_gamma_list))
self.k = self.k_beta + self.k_gamma
self.id_beta = slice(0, self.k_beta)
self.id_gamma = slice(self.k_beta, self.k)
# if use the random slope model or not
self.rr_random_slope = rr_random_slope
if rr_random_slope:
valid_x_cov_id = [
i for i in range(len(x_cov_list)) if x_cov_list[i]['cov_type']
in ['log_ratio_spline', 'log_ratio_spline_integral']
]
if len(valid_x_cov_id) == 0:
raise Exception(
"Error: no suitable x cov for random slope model.")
if len(valid_x_cov_id) >= 2:
raise Exception(
"Error: multiple x cov for random slope model.")
x_cov = x_cov_list[valid_x_cov_id[0]]
mat = x_cov['mat']
if x_cov['cov_type'] == 'log_ratio_spline':
scaling = mat[0] - mat[1]
else:
scaling = 0.5 * (mat[0] + mat[1] - mat[2] - mat[3])
self.Z *= scaling.reshape(scaling.size, 1)
# create limetr object
self.inlier_percentage = inlier_percentage
self.lt = LimeTr(self.study_sizes,
self.k_beta,
self.k_gamma,
self.obs_mean,
self.F,
self.JF,
self.Z,
self.obs_std,
inlier_percentage=inlier_percentage)
class MR_BRT:
def __init__(self,
obs_mean,
obs_std,
study_sizes,
x_cov_list,
z_cov_list,
spline_list=[],
inlier_percentage=1.0,
rr_random_slope=False):
"""
Initialize the object and pass in the data, require
- obs_mean: observations
- obs_std: standard deviations for the observations
- study_sizes: all study sizes in a list
- x_cov_list: all x cov in a list
- z_cov_list: all z cov in a list
- spline_list: optional, all spline in a list
- inlier_percentage: optional, used for trimming
"""
# pass in data
self.obs_mean = obs_mean
self.obs_std = obs_std
self.study_sizes = study_sizes
self.num_studies = len(study_sizes)
self.num_obs = sum(study_sizes)
# construct x and z "covariates"
self.spline_list = spline_list
self.x_cov_list = x_cov_list
self.z_cov_list = z_cov_list
(self.F, self.JF, self.F_list, self.JF_list, self.id_beta_list,
self.id_spline_beta_list,
self.k_beta_list) = utils.constructXCov(x_cov_list,
spline_list=spline_list)
(self.Z, self.Z_list, self.id_gamma_list, self.id_spline_gamma_list,
self.k_gamma_list) = utils.constructZCov(z_cov_list,
spline_list=spline_list)
self.k_beta = int(sum(self.k_beta_list))
self.k_gamma = int(sum(self.k_gamma_list))
self.k = self.k_beta + self.k_gamma
self.id_beta = slice(0, self.k_beta)
self.id_gamma = slice(self.k_beta, self.k)
# if use the random slope model or not
self.rr_random_slope = rr_random_slope
if rr_random_slope:
valid_x_cov_id = [
i for i in range(len(x_cov_list)) if x_cov_list[i]['cov_type']
in ['log_ratio_spline', 'log_ratio_spline_integral']
]
if len(valid_x_cov_id) == 0:
raise Exception(
"Error: no suitable x cov for random slope model.")
if len(valid_x_cov_id) >= 2:
raise Exception(
"Error: multiple x cov for random slope model.")
x_cov = x_cov_list[valid_x_cov_id[0]]
mat = x_cov['mat']
if x_cov['cov_type'] == 'log_ratio_spline':
scaling = mat[0] - mat[1]
else:
scaling = 0.5 * (mat[0] + mat[1] - mat[2] - mat[3])
self.Z *= scaling.reshape(scaling.size, 1)
# create limetr object
self.inlier_percentage = inlier_percentage
self.lt = LimeTr(self.study_sizes,
self.k_beta,
self.k_gamma,
self.obs_mean,
self.F,
self.JF,
self.Z,
self.obs_std,
inlier_percentage=inlier_percentage)
def addPriors(self, prior_list):
"""
Add priors to the object, require prior_list contains priors
"""
self.prior_list = prior_list
(self.C, self.JC, self.c, self.H, self.JH, self.h, self.uprior,
self.gprior, self.lprior, self.C_list, self.JC_list, self.c_list,
self.H_list, self.JH_list, self.h_list, self.id_C_list,
self.id_C_var_list, self.id_H_list, self.id_H_var_list,
self.num_constraints_list,
self.num_regularizers_list) = utils.constructPrior(prior_list, self)
# renew uprior for gamma
if self.uprior is None:
self.uprior = np.array([[-np.inf] * self.k_beta +
[1e-7] * self.k_gamma, [np.inf] * self.k])
else:
uprior_beta = self.uprior[:, self.id_beta]
uprior_gamma = self.uprior[:, self.id_gamma]
uprior_gamma[0] = np.maximum(1e-7, uprior_gamma[0])
uprior_gamma[1] = np.maximum(uprior_gamma[0], uprior_gamma[1])
self.uprior = np.hstack((uprior_beta, uprior_gamma))
self.lt.C, self.lt.JC, self.lt.c = self.C, self.JC, self.c
self.lt.H, self.lt.JH, self.lt.h = self.H, self.JH, self.h
(self.lt.uprior, self.lt.gprior,
self.lt.lprior) = (self.uprior, self.gprior, self.lprior)
self.lt = LimeTr(self.study_sizes,
self.k_beta,
self.k_gamma,
self.obs_mean,
self.F,
self.JF,
self.Z,
self.obs_std,
C=self.C,
JC=self.JC,
c=self.c,
H=self.H,
JH=self.JH,
h=self.h,
uprior=self.uprior,
gprior=self.gprior,
lprior=self.lprior,
inlier_percentage=self.inlier_percentage)
def fitModel(self,
x0=None,
outer_verbose=False,
outer_max_iter=100,
outer_step_size=1.0,
outer_tol=1e-6,
inner_print_level=0,
inner_max_iter=20):
# initialization with gamma set to be zero
gamma_uprior = self.lt.uprior[:, self.lt.idx_gamma].copy()
self.lt.uprior[:, self.lt.idx_gamma] = 1e-6
self.lt.n = np.array([1] * self.num_obs)
norm_z_col = np.linalg.norm(self.lt.Z, axis=0)
self.lt.Z /= norm_z_col
if x0 is None:
if self.lprior is None:
x0 = np.array([1.0] * self.k_beta + [1e-6] * self.k_gamma)
else:
x0 = np.array([1.0] * self.k_beta * 2 +
[1e-6] * self.k_gamma * 2)
else:
if self.lprior is not None:
beta0 = x0[:self.k_beta]
gamma0 = x0[self.k_beta:self.k_beta + self.k_gamma]
x0 = np.hstack((beta0, np.abs(beta0), gamma0, gamma0))
(beta_0, gamma_0,
self.w_soln) = self.lt.fitModel(x0=x0,
outer_verbose=outer_verbose,
outer_max_iter=outer_max_iter,
outer_step_size=outer_step_size,
outer_tol=outer_tol,
inner_print_level=inner_print_level,
inner_max_iter=inner_max_iter)
# print("init obj", self.lt.objective(self.lt.soln))
# fit the model from the initial point
self.lt.uprior[:, self.lt.idx_gamma] = gamma_uprior
self.lt.n = self.study_sizes
if self.lprior is not None:
x0 = np.hstack((beta_0, np.abs(beta_0), gamma_0, gamma_0))
else:
x0 = np.hstack((beta_0, gamma_0))
self.lt.optimize(x0=x0, print_level=inner_print_level, max_iter=100)
self.lt.Z *= norm_z_col
self.lt.gamma /= norm_z_col**2
self.beta_soln = self.lt.beta
self.gamma_soln = self.lt.gamma
# print("final obj", self.lt.objective(self.lt.soln))
# print("------------------------------")
def predictData(self,
pred_x_cov_list,
pred_z_cov_list,
sample_size,
pred_study_sizes=None,
given_beta_samples=None,
given_gamma_samples=None,
ref_point=None,
include_random_effect=True):
# sample solutions
if given_beta_samples is None or given_gamma_samples is None:
beta_samples, gamma_samples = LimeTr.sampleSoln(
self.lt, sample_size=sample_size)
else:
beta_samples = given_beta_samples
gamma_samples = given_gamma_samples
# calculate the beta and gamma post cov
# self.beta_samples_mean = np.mean(beta_samples, axis=0)
# self.gamma_samples_mean = np.mean(gamma_samples, axis=0)
# self.beta_samples_cov = \
# beta_samples.T.dot(beta_samples)/sample_size - \
# np.outer(self.beta_samples_mean, self.beta_samples_mean)
# self.gamma_samples_cov = \
# gamma_samples.T.dot(gamma_samples)/sample_size - \
# np.outer(self.gamma_samples_mean, self.gamma_samples_mean)
# create x cov
(pred_F, pred_JF, pred_F_list, pred_JF_list,
pred_id_beta_list) = utils.constructPredXCov(pred_x_cov_list, self)
# create z cov
(pred_Z, pred_Z_list,
pred_id_gamma_list) = utils.constructPredZCov(pred_z_cov_list, self)
# num of studies
pred_num_obs = pred_Z.shape[0]
# create observation samples
y_samples = np.vstack([pred_F(beta) for beta in beta_samples])
if ref_point is not None:
x_cov_spline_id = [
x_cov['spline_id'] for x_cov in pred_x_cov_list
if 'spline' in x_cov['cov_type']
]
if len(x_cov_spline_id) == 0:
raise Exception("Error: no spline x cov")
if len(x_cov_spline_id) >= 2:
raise Exception("Error: multiple spline x covs")
spline = self.spline_list[x_cov_spline_id[0]]
ref_risk = spline.designMat(np.array([ref_point])).dot(
beta_samples[:,
self.id_spline_beta_list[x_cov_spline_id[0]]].T)
y_samples /= ref_risk.reshape(sample_size, 1)
pred_gamma = np.hstack([
self.gamma_soln[pred_id_gamma_list[i]]
for i in range(len(pred_id_gamma_list))
])
if include_random_effect:
if self.rr_random_slope:
u = np.random.randn(sample_size, self.k_gamma)*\
np.sqrt(self.gamma_soln)
# zu = np.sum(pred_Z*u, axis=1)
zu = u[:, 0]
valid_x_cov_id = [
i for i in range(len(pred_x_cov_list))
if pred_x_cov_list[i]['cov_type'] == 'spline'
]
if len(valid_x_cov_id) == 0:
raise Exception(
"Error: no suitable x cov for random slope model.")
if len(valid_x_cov_id) >= 2:
raise Exception(
"Error: multiple x cov for random slope model.")
mat = pred_x_cov_list[valid_x_cov_id[0]]['mat']
if ref_point is None:
y_samples *= np.exp(np.outer(zu, mat - mat[0]))
else:
y_samples *= np.exp(np.outer(zu, mat - ref_point))
else:
if pred_study_sizes is None:
pred_study_sizes = np.array([1] * pred_num_obs)
else:
assert sum(pred_study_sizes) == pred_num_obs
pred_num_studies = len(pred_study_sizes)
pred_Z_sub = np.split(pred_Z, np.cumsum(pred_study_sizes)[:-1])
u = [
np.random.multivariate_normal(
np.zeros(pred_study_sizes[i]),
(pred_Z_sub[i] * pred_gamma).dot(pred_Z_sub[i].T),
sample_size) for i in range(pred_num_studies)
]
U = np.hstack(u)
if np.any([
'log_ratio' in self.x_cov_list[i]['cov_type']
for i in range(len(self.x_cov_list))
]):
y_samples *= np.exp(U)
else:
y_samples += U
return y_samples, beta_samples, gamma_samples, pred_F, pred_Z
def predictData(self,
pred_x_cov_list,
pred_z_cov_list,
sample_size,
pred_study_sizes=None,
given_beta_samples=None,
given_gamma_samples=None,
ref_point=None,
include_random_effect=True):
# sample solutions
if given_beta_samples is None or given_gamma_samples is None:
beta_samples, gamma_samples = LimeTr.sampleSoln(
self.lt, sample_size=sample_size)
else:
beta_samples = given_beta_samples
gamma_samples = given_gamma_samples
# calculate the beta and gamma post cov
# self.beta_samples_mean = np.mean(beta_samples, axis=0)
# self.gamma_samples_mean = np.mean(gamma_samples, axis=0)
# self.beta_samples_cov = \
# beta_samples.T.dot(beta_samples)/sample_size - \
# np.outer(self.beta_samples_mean, self.beta_samples_mean)
# self.gamma_samples_cov = \
# gamma_samples.T.dot(gamma_samples)/sample_size - \
# np.outer(self.gamma_samples_mean, self.gamma_samples_mean)
# create x cov
(pred_F, pred_JF, pred_F_list, pred_JF_list,
pred_id_beta_list) = utils.constructPredXCov(pred_x_cov_list, self)
# create z cov
(pred_Z, pred_Z_list,
pred_id_gamma_list) = utils.constructPredZCov(pred_z_cov_list, self)
# num of studies
pred_num_obs = pred_Z.shape[0]
# create observation samples
y_samples = np.vstack([pred_F(beta) for beta in beta_samples])
if ref_point is not None:
x_cov_spline_id = [
x_cov['spline_id'] for x_cov in pred_x_cov_list
if 'spline' in x_cov['cov_type']
]
if len(x_cov_spline_id) == 0:
raise Exception("Error: no spline x cov")
if len(x_cov_spline_id) >= 2:
raise Exception("Error: multiple spline x covs")
spline = self.spline_list[x_cov_spline_id[0]]
ref_risk = spline.designMat(np.array([ref_point])).dot(
beta_samples[:,
self.id_spline_beta_list[x_cov_spline_id[0]]].T)
y_samples /= ref_risk.reshape(sample_size, 1)
pred_gamma = np.hstack([
self.gamma_soln[pred_id_gamma_list[i]]
for i in range(len(pred_id_gamma_list))
])
if include_random_effect:
if self.rr_random_slope:
u = np.random.randn(sample_size, self.k_gamma)*\
np.sqrt(self.gamma_soln)
# zu = np.sum(pred_Z*u, axis=1)
zu = u[:, 0]
valid_x_cov_id = [
i for i in range(len(pred_x_cov_list))
if pred_x_cov_list[i]['cov_type'] == 'spline'
]
if len(valid_x_cov_id) == 0:
raise Exception(
"Error: no suitable x cov for random slope model.")
if len(valid_x_cov_id) >= 2:
raise Exception(
"Error: multiple x cov for random slope model.")
mat = pred_x_cov_list[valid_x_cov_id[0]]['mat']
if ref_point is None:
y_samples *= np.exp(np.outer(zu, mat - mat[0]))
else:
y_samples *= np.exp(np.outer(zu, mat - ref_point))
else:
if pred_study_sizes is None:
pred_study_sizes = np.array([1] * pred_num_obs)
else:
assert sum(pred_study_sizes) == pred_num_obs
pred_num_studies = len(pred_study_sizes)
pred_Z_sub = np.split(pred_Z, np.cumsum(pred_study_sizes)[:-1])
u = [
np.random.multivariate_normal(
np.zeros(pred_study_sizes[i]),
(pred_Z_sub[i] * pred_gamma).dot(pred_Z_sub[i].T),
sample_size) for i in range(pred_num_studies)
]
U = np.hstack(u)
if np.any([
'log_ratio' in self.x_cov_list[i]['cov_type']
for i in range(len(self.x_cov_list))
]):
y_samples *= np.exp(U)
else:
y_samples += U
return y_samples, beta_samples, gamma_samples, pred_F, pred_Z
class MRBRT:
"""MR-BRT Object
"""
def __init__(self,
data: MRData,
cov_models: List[CovModel],
inlier_pct: float = 1.0):
"""Constructor of MRBRT.
Args:
data (MRData): Data for meta-regression.
cov_models (List[CovModel]): A list of covariates models.
inlier_pct (float, optional):
A float number between 0 and 1 indicate the percentage of inliers.
"""
self.data = data
self.cov_models = cov_models
self.inlier_pct = inlier_pct
self.check_input()
self.cov_model_names = [
cov_model.name for cov_model in self.cov_models
]
self.num_cov_models = len(self.cov_models)
self.cov_names = []
for cov_model in self.cov_models:
self.cov_names.extend(cov_model.covs)
self.num_covs = len(self.cov_names)
# attach data to cov_model
for cov_model in self.cov_models:
cov_model.attach_data(self.data)
# fixed effects size and index
self.x_vars_sizes = [
cov_model.num_x_vars for cov_model in self.cov_models
]
self.x_vars_indices = utils.sizes_to_indices(self.x_vars_sizes)
self.num_x_vars = sum(self.x_vars_sizes)
# random effects size and index
self.z_vars_sizes = [
cov_model.num_z_vars for cov_model in self.cov_models
]
self.z_vars_indices = utils.sizes_to_indices(self.z_vars_sizes)
self.num_z_vars = sum(self.z_vars_sizes)
self.num_vars = self.num_x_vars + self.num_z_vars
# number of constraints
self.num_constraints = sum(
[cov_model.num_constraints for cov_model in self.cov_models])
# number of regularizations
self.num_regularizations = sum(
[cov_model.num_regularizations for cov_model in self.cov_models])
# place holder for the limetr objective
self.lt = None
self.beta_soln = None
self.gamma_soln = None
self.u_soln = None
self.w_soln = None
self.re_soln = None
def check_input(self):
"""Check the input type of the attributes.
"""
assert isinstance(self.data, MRData)
assert isinstance(self.cov_models, list)
assert all(
[isinstance(cov_model, CovModel) for cov_model in self.cov_models])
assert (self.inlier_pct >= 0.0) and (self.inlier_pct <= 1.0)
def get_cov_model(self, name: str) -> CovModel:
"""Choose covariate model with name.
"""
index = self.get_cov_model_index(name)
return self.cov_models[index]
def get_cov_model_index(self, name: str) -> int:
"""From cov_model name get the index.
"""
matching_index = [
index for index, cov_model_name in enumerate(self.cov_model_names)
if cov_model_name == name
]
num_matching_index = len(matching_index)
assert num_matching_index == 1, f"Number of matching index is {num_matching_index}."
return matching_index[0]
def create_x_fun(self, data=None):
"""Create the fixed effects function, link with limetr.
"""
data = self.data if data is None else data
# create design functions
design_funs = [
cov_model.create_x_fun(data) for cov_model in self.cov_models
]
funs, jac_funs = list(zip(*design_funs))
def x_fun(beta, funs=funs):
return sum(
fun(beta[self.x_vars_indices[i]])
for i, fun in enumerate(funs))
def x_jac_fun(beta, jac_funs=jac_funs):
return np.hstack([
jac_fun(beta[self.x_vars_indices[i]])
for i, jac_fun in enumerate(jac_funs)
])
return x_fun, x_jac_fun
def create_z_mat(self, data=None):
"""Create the random effects matrix, link with limetr.
"""
data = self.data if data is None else data
mat = np.hstack(
[cov_model.create_z_mat(data) for cov_model in self.cov_models])
return mat
def create_c_mat(self):
"""Create the constraints matrices.
"""
c_mat = np.zeros((0, self.num_vars))
c_vec = np.zeros((2, 0))
for i, cov_model in enumerate(self.cov_models):
if cov_model.num_constraints != 0:
c_mat_sub = np.zeros(
(cov_model.num_constraints, self.num_vars))
c_mat_sub[:, self.x_vars_indices[
i]], c_vec_sub = cov_model.create_constraint_mat()
c_mat = np.vstack((c_mat, c_mat_sub))
c_vec = np.hstack((c_vec, c_vec_sub))
return c_mat, c_vec
def create_h_mat(self):
"""Create the regularizer matrices.
"""
h_mat = np.zeros((0, self.num_vars))
h_vec = np.zeros((2, 0))
for i, cov_model in enumerate(self.cov_models):
if cov_model.num_regularizations != 0:
h_mat_sub = np.zeros(
(cov_model.num_regularizations, self.num_vars))
h_mat_sub[:, self.x_vars_indices[
i]], h_vec_sub = cov_model.create_regularization_mat()
h_mat = np.vstack((h_mat, h_mat_sub))
h_vec = np.hstack((h_vec, h_vec_sub))
return h_mat, h_vec
def create_uprior(self):
"""Create direct uniform prior.
"""
uprior = np.array([[-np.inf] * self.num_vars,
[np.inf] * self.num_vars])
for i, cov_model in enumerate(self.cov_models):
uprior[:, self.x_vars_indices[i]] = cov_model.prior_beta_uniform
uprior[:, self.z_vars_indices[i] +
self.num_x_vars] = cov_model.prior_gamma_uniform
return uprior
def create_gprior(self):
"""Create direct gaussian prior.
"""
gprior = np.array([[0] * self.num_vars, [np.inf] * self.num_vars])
for i, cov_model in enumerate(self.cov_models):
gprior[:, self.x_vars_indices[i]] = cov_model.prior_beta_gaussian
gprior[:, self.z_vars_indices[i] +
self.num_x_vars] = cov_model.prior_gamma_gaussian
return gprior
def create_lprior(self):
"""Create direct laplace prior.
"""
lprior = np.array([[0] * self.num_vars, [np.inf] * self.num_vars])
for i, cov_model in enumerate(self.cov_models):
lprior[:, self.x_vars_indices[i]] = cov_model.prior_beta_laplace
lprior[:, self.z_vars_indices[i] +
self.num_x_vars] = cov_model.prior_gamma_laplace
return lprior
def fit_model(self, **fit_options):
"""Fitting the model through limetr.
Args:
x0 (np.ndarray): Initial guess for the optimization problem.
inner_print_level (int): If non-zero printing iteration information of the inner problem.
inner_max_iter (int): Maximum inner number of iterations.
inner_tol (float): Tolerance of the inner problem.
outer_verbose (bool): If `True` print out iteration information.
outer_max_iter (int): Maximum outer number of iterations.
outer_step_size (float): Step size of the outer problem.
outer_tol (float): Tolerance of the outer problem.
normalize_trimming_grad (bool): If `True`, normalize the gradient of the outer trimmign problem.
"""
# dimensions
n = self.data.study_sizes
k_beta = self.num_x_vars
k_gamma = self.num_z_vars
# data
y = self.data.obs
s = self.data.obs_se
# create x fun and z mat
x_fun, x_fun_jac = self.create_x_fun()
z_mat = self.create_z_mat()
# scale z_mat
z_scale = np.max(np.abs(z_mat), axis=0)
z_mat /= z_scale
# priors
c_mat, c_vec = self.create_c_mat()
h_mat, h_vec = self.create_h_mat()
c_fun, c_fun_jac = utils.mat_to_fun(c_mat)
h_fun, h_fun_jac = utils.mat_to_fun(h_mat)
uprior = self.create_uprior()
uprior[:, self.num_x_vars:self.num_vars] *= z_scale**2
gprior = self.create_gprior()
gprior[:, self.num_x_vars:self.num_vars] *= z_scale**2
lprior = self.create_lprior()
lprior[:, self.num_x_vars:self.num_vars] *= z_scale**2
if np.isneginf(uprior[0]).all() and np.isposinf(uprior[1]).all():
uprior = None
if np.isposinf(gprior[1]).all():
gprior = None
if np.isposinf(lprior[1]).all():
lprior = None
# create limetr object
self.lt = LimeTr(n,
k_beta,
k_gamma,
y,
x_fun,
x_fun_jac,
z_mat,
S=s,
C=c_fun,
JC=c_fun_jac,
c=c_vec,
H=h_fun,
JH=h_fun_jac,
h=h_vec,
uprior=uprior,
gprior=gprior,
lprior=lprior,
inlier_percentage=self.inlier_pct)
self.lt.fitModel(**fit_options)
self.lt.Z *= z_scale
if hasattr(self.lt, 'gprior'):
self.lt.gprior[:, self.lt.idx_gamma] /= z_scale**2
if hasattr(self.lt, 'uprior'):
self.lt.uprior[:, self.lt.idx_gamma] /= z_scale**2
if hasattr(self.lt, 'lprior'):
self.lt.lprior[:, self.lt.idx_gamma] /= z_scale**2
self.lt.gamma /= z_scale**2
self.beta_soln = self.lt.beta.copy()
self.gamma_soln = self.lt.gamma.copy()
self.w_soln = self.lt.w.copy()
self.u_soln = self.lt.estimateRE()
self.re_soln = {
study: self.u_soln[i]
for i, study in enumerate(self.data.studies)
}
def extract_re(self, study_id: np.ndarray) -> np.ndarray:
"""Extract the random effect for a given dataset.
"""
re = np.vstack([
self.re_soln[study]
if study in self.re_soln else np.zeros(self.num_z_vars)
for study in study_id
])
return re
def predict(self,
data: MRData,
predict_for_study: bool = False,
sort_by_data_id: bool = False) -> np.ndarray:
"""Create new prediction with existing solution.
Args:
data (MRData): MRData object contains the predict data.
predict_for_study (bool, optional):
If `True`, use the random effects information to prediction for specific
study. If the `study_id` in `data` do not contain in the fitting data, it
will assume the corresponding random effects equal to 0.
sort_by_data_id (bool, optional):
If `True`, will sort the final prediction as the order of the original
data frame that used to create the `data`. Default to False.
Returns:
np.ndarray: Predicted outcome array.
"""
assert data.has_covs(
self.cov_names
), "Prediction data do not have covariates used for fitting."
x_fun, _ = self.create_x_fun(data=data)
prediction = x_fun(self.beta_soln)
if predict_for_study:
z_mat = self.create_z_mat(data=data)
re = self.extract_re(data.study_id)
prediction += np.sum(z_mat * re, axis=1)
if sort_by_data_id:
prediction = prediction[np.argsort(data.data_id)]
return prediction
def sample_soln(self,
sample_size: int = 1,
sim_prior: bool = True,
sim_re: bool = True,
print_level: int = 0) -> Tuple[np.ndarray, np.ndarray]:
"""Sample solutions.
Args:
sample_size (int, optional): Number of samples.
sim_prior (bool, optional): If `True`, simulate priors.
sim_re (bool, optional): If `True`, simulate random effects.
print_level (int, optional):
Level detailed of optimization information printed out during sampling process.
If 0, no information will be printed out.
Return:
Tuple[np.ndarray, np.ndarray]:
Return beta samples and gamma samples.
"""
if self.lt is None:
raise ValueError('Please fit the model first.')
beta_soln_samples, gamma_soln_samples = \
self.lt.sampleSoln(self.lt,
sample_size=sample_size,
sim_prior=sim_prior,
sim_re=sim_re,
print_level=print_level)
return beta_soln_samples, gamma_soln_samples
def create_draws(self,
data: MRData,
beta_samples: np.ndarray,
gamma_samples: np.ndarray,
random_study: bool = True,
sort_by_study_id: bool = False) -> np.ndarray:
"""Create draws for the given data set.
Args:
data (MRData): MRData object contains predict data.
beta_samples (np.ndarray): Samples of beta.
gamma_samples (np.ndarray): Samples of gamma.
random_study (bool, optional):
If `True` the draws will include uncertainty from study heterogeneity.
sort_by_data_id (bool, optional):
If `True`, will sort the final prediction as the order of the original
data frame that used to create the `data`. Default to False.
Returns:
np.ndarray: Returns outcome sample matrix.
"""
sample_size = beta_samples.shape[0]
assert beta_samples.shape == (sample_size, self.num_x_vars)
assert gamma_samples.shape == (sample_size, self.num_z_vars)
x_fun, x_jac_fun = self.create_x_fun(data=data)
z_mat = self.create_z_mat(data=data)
y_samples = np.vstack(
[x_fun(beta_sample) for beta_sample in beta_samples])
if random_study:
u_samples = np.random.randn(
sample_size, self.num_z_vars) * np.sqrt(gamma_samples)
y_samples += u_samples.dot(z_mat.T)
else:
re = self.extract_re(data.study_id)
y_samples += np.sum(z_mat * re, axis=1)
if sort_by_study_id:
y_samples = y_samples[:, np.argsort(data.data_id)]
return y_samples.T
def fit_model(self, **fit_options):
"""Fitting the model through limetr.
Args:
x0 (np.ndarray): Initial guess for the optimization problem.
inner_print_level (int): If non-zero printing iteration information of the inner problem.
inner_max_iter (int): Maximum inner number of iterations.
inner_tol (float): Tolerance of the inner problem.
outer_verbose (bool): If `True` print out iteration information.
outer_max_iter (int): Maximum outer number of iterations.
outer_step_size (float): Step size of the outer problem.
outer_tol (float): Tolerance of the outer problem.
normalize_trimming_grad (bool): If `True`, normalize the gradient of the outer trimmign problem.
"""
# dimensions
n = self.data.study_sizes
k_beta = self.num_x_vars
k_gamma = self.num_z_vars
# data
y = self.data.obs
s = self.data.obs_se
# create x fun and z mat
x_fun, x_fun_jac = self.create_x_fun()
z_mat = self.create_z_mat()
# scale z_mat
z_scale = np.max(np.abs(z_mat), axis=0)
z_mat /= z_scale
# priors
c_mat, c_vec = self.create_c_mat()
h_mat, h_vec = self.create_h_mat()
c_fun, c_fun_jac = utils.mat_to_fun(c_mat)
h_fun, h_fun_jac = utils.mat_to_fun(h_mat)
uprior = self.create_uprior()
uprior[:, self.num_x_vars:self.num_vars] *= z_scale**2
gprior = self.create_gprior()
gprior[:, self.num_x_vars:self.num_vars] *= z_scale**2
lprior = self.create_lprior()
lprior[:, self.num_x_vars:self.num_vars] *= z_scale**2
if np.isneginf(uprior[0]).all() and np.isposinf(uprior[1]).all():
uprior = None
if np.isposinf(gprior[1]).all():
gprior = None
if np.isposinf(lprior[1]).all():
lprior = None
# create limetr object
self.lt = LimeTr(n,
k_beta,
k_gamma,
y,
x_fun,
x_fun_jac,
z_mat,
S=s,
C=c_fun,
JC=c_fun_jac,
c=c_vec,
H=h_fun,
JH=h_fun_jac,
h=h_vec,
uprior=uprior,
gprior=gprior,
lprior=lprior,
inlier_percentage=self.inlier_pct)
self.lt.fitModel(**fit_options)
self.lt.Z *= z_scale
if hasattr(self.lt, 'gprior'):
self.lt.gprior[:, self.lt.idx_gamma] /= z_scale**2
if hasattr(self.lt, 'uprior'):
self.lt.uprior[:, self.lt.idx_gamma] /= z_scale**2
if hasattr(self.lt, 'lprior'):
self.lt.lprior[:, self.lt.idx_gamma] /= z_scale**2
self.lt.gamma /= z_scale**2
self.beta_soln = self.lt.beta.copy()
self.gamma_soln = self.lt.gamma.copy()
self.w_soln = self.lt.w.copy()
self.u_soln = self.lt.estimateRE()
self.re_soln = {
study: self.u_soln[i]
for i, study in enumerate(self.data.studies)
}
def sampleGlobalWithLimeTr(self, sample_size=100, max_iter=300):
beta_samples, gamma_samples = LimeTr.sampleSoln(
self.model, sample_size=sample_size, max_iter=max_iter)
return beta_samples, gamma_samples
def optimize(self,
var=None,
S=None,
trim_percentage=0.0,
share_obs_std=True,
fit_fixed=True,
inner_print_level=5,
inner_max_iter=100,
inner_tol=1e-5,
inner_verbose=True,
inner_acceptable_tol=1e-4,
inner_nlp_scaling_min_value=1e-8,
outer_verbose=False,
outer_max_iter=1,
outer_step_size=1,
outer_tol=1e-6,
normalize_Z=False,
build_X=True,
random_seed=0):
"""
Run optimization routine via LimeTr.
Args:
var (numpy.ndarray | None, optional):
One-dimensional array that gives initialization for variables.
If None, the program will first run without random effects
to obtain a starting point.
S (numpy.ndarray | None, optional):
One-dimensional numpy array that gives standard deviation for
each measurement. The size of S should be the same as that of
measurements vector. If None standard deviation of measurement
will be treated as variables and optimized.
trim_percentage (float | 0.0, optional):
A float that gives percentage of datapoints to trim.
Default is 0, i.e. no trimming.
share_obs_std (boolean | True, optional):
A boolean that indicates whether the model should assume data
across studies share the same measurement standard deviation.
fit_fixed (boolean | True, optional):
A boolean that indicates whether to run a fit without random
effects first in order to obtain a good starting point.
inner_print_level (int | 5, optional):
``print_level`` for Ipopt.
inner_max_iter (int | 100, optional):
Maximum number of iterations for inner optimization.
inner_tol (float | 1e-5, optional):
Tolerance level for inner optimization.
inner_verbose (boolean | True, optional):
Verbose option for inner optimization.
inner_acceptable_tol (float | 1e-4, optional):
Acceptable tolerance level for inner optimization.
inner_nlp_scaling_min_value (float | 1e-8, optional):
Min scaling for objective function.
outer_verbose (boolean | False, optional):
Verbose option for outer optimization.
outer_max_iter (int | 1, optional):
Maximum number of iterations for outer optimization. When there
is no trimming, outer optimization is not needed, so the default
is set to be 1.
outer_step_size (float |1.0, optional):
Step size for outer optimization. Used in trimming.
outer_tol (float | 1e-6, optional):
Tolerance level for outer optimization.
normalize_Z (bool | False, optional):
Whether to normalize Z matrix before optimization.
build_X (bool | True, optional):
Whether to explicitly build and store X matrix.
random_seed (int | 0, optional):
random seed for choosing an initial point for optimization. If equals 0
the initial point is chosen to be a vector of 0.01.
"""
self.S = S
self.share_obs_std = share_obs_std
Z_norm = self.buildZ(normalize_Z)
k = self.k_beta + self.k_gamma
if S is None:
if share_obs_std:
k += 1
else:
k += len(self.grouping)
print('n_groups', self.n_groups)
print('k_beta', self.k_beta)
print('k_gamma', self.k_gamma)
print('total number of fixed effects variables', k)
if self.k_gamma == 0:
self.add_re = False
self.k_gamma = 1
k += 1
else:
self.add_re = True
C = []
start = self.k_beta
for ran in self.ran_list:
_, dims = ran
m = np.prod(dims[self.n_grouping_dims:])
c = np.zeros((m - 1, k))
for i in range(m - 1):
c[i, start + i] = 1
c[i, start + i + 1] = -1
C.append(c)
start += m
if len(C) > 0:
self.constraints = np.vstack(C)
assert self.constraints.shape[1] == k
else:
self.constraints = []
C = None
if len(self.constraints) > 0:
def C(var):
return self.constraints.dot(var)
JC = None
if len(self.constraints) > 0:
def JC(var):
return self.constraints
c = None
if len(self.constraints) > 0:
c = np.zeros((2, self.constraints.shape[0]))
self.uprior = np.array(
[[-np.inf] * self.k_beta + [1e-7] * self.k_gamma + [1e-7] *
(k - self.k_beta - self.k_gamma), [np.inf] * k])
if self.global_cov_bounds is not None:
if self.global_intercept:
self.uprior[:, 1:len(self.global_ids) +
1] = self.global_cov_bounds
else:
self.uprior[:, :len(self.global_ids)] = self.global_cov_bounds
self.gprior = None
if self.use_gprior:
assert len(self.ran_eff_gamma_sd) == self.k_gamma
self.gprior = np.array(
[[0] * k, [np.inf] * self.k_beta + self.ran_eff_gamma_sd +
[np.inf] * (k - self.k_beta - self.k_gamma)])
x0 = np.ones(k) * .01
if random_seed != 0:
np.random.seed(random_seed)
x0 = np.random.randn(k) * .01
if var is not None:
if self.add_re is True:
assert len(var) == k
x0 = var
else:
assert len(var) == self.k_beta
x0 = np.append(var, [1e-8])
assert len(x0) == k
if build_X:
self._buildX()
if fit_fixed or self.add_re is False:
uprior_fixed = copy.deepcopy(self.uprior)
uprior_fixed[:, self.k_beta:self.k_beta + self.k_gamma] = 1e-8
if S is None or trim_percentage >= 0.01:
model_fixed = LimeTr(self.grouping,
int(self.k_beta),
int(self.k_gamma),
self.Y,
self.X,
self.JX,
self.Z,
S=S,
C=C,
JC=JC,
c=c,
inlier_percentage=1. - trim_percentage,
share_obs_std=share_obs_std,
uprior=uprior_fixed)
model_fixed.optimize(
x0=x0,
print_level=inner_print_level,
max_iter=inner_max_iter,
tol=inner_tol,
acceptable_tol=inner_acceptable_tol,
nlp_scaling_min_value=inner_nlp_scaling_min_value)
x0 = model_fixed.soln
self.beta_fixed = model_fixed.beta
if self.add_re is False:
self.beta_soln = self.beta_fixed
self.delta_soln = model_fixed.delta
self.gamma_soln = model_fixed.gamma
self.w_soln = model_fixed.w
self.info = model_fixed.info['status_msg']
self.yfit_no_random = model_fixed.F(model_fixed.beta)
return
else:
self.beta_fixed = self._solveBeta(S)
x0 = np.append(self.beta_fixed, [1e-8] * self.k_gamma)
if self.add_re is False:
self.beta_soln = self.beta_fixed
self.yfit_no_random = self.Xm.dot(self.beta_fixed)
return
model = LimeTr(self.grouping,
int(self.k_beta),
int(self.k_gamma),
self.Y,
self.X,
self.JX,
self.Z,
S=S,
C=C,
JC=JC,
c=c,
inlier_percentage=1 - trim_percentage,
share_obs_std=share_obs_std,
uprior=self.uprior,
gprior=self.gprior)
model.fitModel(x0=x0,
inner_print_level=inner_print_level,
inner_max_iter=inner_max_iter,
inner_acceptable_tol=inner_acceptable_tol,
inner_nlp_scaling_min_value=inner_nlp_scaling_min_value,
inner_tol=inner_tol,
outer_verbose=outer_verbose,
outer_max_iter=outer_max_iter,
outer_step_size=outer_step_size,
outer_tol=outer_tol)
self.beta_soln = model.beta
self.gamma_soln = model.gamma
if normalize_Z:
self.gamma_soln /= Z_norm**2
self.delta_soln = model.delta
self.info = model.info
self.w_soln = model.w
self.u_soln = model.estimateRE()
self.solve_status = model.info['status']
self.solve_status_msg = model.info['status_msg']
self.yfit_no_random = model.F(model.beta)
self.yfit = []
Z_split = np.split(self.Z, self.n_groups)
yfit_no_random_split = np.split(self.yfit_no_random, self.n_groups)
for i in range(self.n_groups):
self.yfit.append(yfit_no_random_split[i] +
Z_split[i].dot(self.u_soln[i]))
self.yfit = np.concatenate(self.yfit)
self.model = model
if inner_verbose == True and self.solve_status != 0:
print(self.solve_status_msg)
def fit(self,
max_iter=100,
inlier_pct=1.0,
outer_max_iter=100,
outer_step_size=1.0):
"""Optimize the model parameters.
This is a interface to limetr.
Args:
max_iter (int, optional):
Maximum number of iterations.
inlier_pct (float, optional):
How much percentage of the data do you trust.
outer_max_iter (int, optional):
Outer maximum number of iterations.
outer_step_size (float, optional):
Step size of the trimming problem, the larger the step size the faster it will converge,
and the less quality of trimming it will guarantee.
"""
# dimensions for limetr
n = self.cwdata.study_sizes
if n.size == 0:
n = np.full(self.cwdata.num_obs, 1)
k_beta = self.num_vars
k_gamma = 1
y = self.cwdata.obs
s = self.cwdata.obs_se
x = self.design_mat
z = np.ones((self.cwdata.num_obs, 1))
uprior = np.hstack(
(self.prior_beta_uniform, self.prior_gamma_uniform[:, None]))
gprior = np.hstack(
(self.prior_beta_gaussian, self.prior_gamma_gaussian[:, None]))
if self.constraint_mat is None:
cfun = None
jcfun = None
cvec = None
else:
num_constraints = self.constraint_mat.shape[0]
cmat = np.hstack(
(self.constraint_mat, np.zeros((num_constraints, 1))))
cvec = np.array([[-np.inf] * num_constraints,
[0.0] * num_constraints])
def cfun(var):
return cmat.dot(var)
def jcfun(var):
return cmat
def fun(var):
return x.dot(var)
def jfun(beta):
return x
self.lt = LimeTr(n,
k_beta,
k_gamma,
y,
fun,
jfun,
z,
S=s,
gprior=gprior,
uprior=uprior,
C=cfun,
JC=jcfun,
c=cvec,
inlier_percentage=inlier_pct)
self.beta, self.gamma, self.w = self.lt.fitModel(
inner_print_level=5,
inner_max_iter=max_iter,
outer_max_iter=outer_max_iter,
outer_step_size=outer_step_size)
self.fixed_vars = {
var: self.beta[self.var_idx[var]]
for var in self.vars
}
if self.use_random_intercept:
u = self.lt.estimateRE()
self.random_vars = {
sid: u[i]
for i, sid in enumerate(self.cwdata.unique_study_id)
}
else:
self.random_vars = dict()
# compute the posterior distribution of beta
hessian = self.get_beta_hessian()
unconstrained_id = np.hstack([
np.arange(self.lt.k_beta)[self.var_idx[dorm]]
for dorm in self.cwdata.unique_dorms if dorm != self.gold_dorm
])
self.beta_sd = np.zeros(self.lt.k_beta)
self.beta_sd[unconstrained_id] = np.sqrt(
np.diag(np.linalg.inv(hessian)))
class CWModel:
"""Cross Walk model.
"""
def __init__(self,
cwdata,
obs_type='diff_log',
cov_models=None,
gold_dorm=None,
order_prior=None,
use_random_intercept=True,
prior_gamma_uniform=None,
prior_gamma_gaussian=None):
"""Constructor of CWModel.
Args:
cwdata (data.CWData):
Data for cross walk.
obs_type (str, optional):
Type of observation can only be chosen from `'diff_log'` and
`'diff_logit'`.
cov_models (list{crosswalk.CovModel}):
A list of covariate models for the definitions/methods
gold_dorm (str | None, optional):
Gold standard definition/method.
order_prior (list{list{str}} | None, optional):
Order priors between different definitions.
use_random_intercept (bool, optional):
If ``True``, use random intercept.
prior_gamma_uniform (Tuple[float, float], optional):
If not ``None``, use it as the bound of gamma.
prior_gamma_gaussian (Tuple[float, float], optional):
If not ``None``, use it as the gaussian prior of gamma.
"""
self.cwdata = cwdata
self.obs_type = obs_type
self.cov_models = utils.default_input(cov_models,
[CovModel('intercept')])
self.gold_dorm = utils.default_input(gold_dorm, cwdata.max_ref_dorm)
self.order_prior = order_prior
self.use_random_intercept = use_random_intercept
if self.cwdata.num_studies == 0 and self.use_random_intercept:
warnings.warn("Must have study_id to use random intercept."
" Reset use_random_intercept to False.")
self.use_random_intercept = False
# check input
self.check()
# create function for prediction
if self.obs_type == 'diff_log':
def obs_fun(x):
return np.log(x)
def obs_inv_fun(y):
return np.exp(y)
else:
def obs_fun(x):
return np.log(x / (1.0 - x))
def obs_inv_fun(y):
return 1.0 / (1.0 + np.exp(-y))
self.obs_fun = obs_fun
self.obs_inv_fun = obs_inv_fun
# variable names
self.vars = [dorm for dorm in self.cwdata.unique_dorms]
# dimensions
self.num_vars_per_dorm = sum(
[model.num_vars for model in self.cov_models])
self.num_vars = self.num_vars_per_dorm * self.cwdata.num_dorms
# indices for easy access the variables
var_sizes = np.array([self.num_vars_per_dorm] * self.cwdata.num_dorms)
var_idx = utils.sizes_to_indices(var_sizes)
self.var_idx = {var: var_idx[i] for i, var in enumerate(self.vars)}
# create design matrix
self.relation_mat = self.create_relation_mat()
self._check_relation_mat()
self.cov_mat = self.create_cov_mat()
self._assert_covs_independent()
self.design_mat = self.create_design_mat()
self._assert_rank_efficient()
self.constraint_mat = self.create_constraint_mat()
# gamma bounds
self.prior_gamma_uniform = np.array([
0.0, np.inf
]) if prior_gamma_uniform is None else np.array(prior_gamma_uniform)
if not self.use_random_intercept:
self.prior_gamma_uniform = np.zeros(2)
if self.prior_gamma_uniform[0] < 0.0:
warnings.warn(
"Lower bound of gamma has to be non-negative, reset it to zero."
)
self.prior_gamma_uniform[0] = 0.0
# gamma Gaussian prior
self.prior_gamma_gaussian = np.array([
0.0, np.inf
]) if prior_gamma_gaussian is None else np.array(prior_gamma_gaussian)
if not self.use_random_intercept:
self.prior_gamma_gaussian = np.array([0.0, np.inf])
# beta bounds
uprior = np.repeat(np.array([[-np.inf], [np.inf]]),
self.num_vars,
axis=1)
for i, cov_model in enumerate(self.cov_models):
for dorm, prior in cov_model.prior_beta_uniform.items():
uprior[:, self.var_idx[dorm][i]] = prior
uprior[:, self.var_idx[self.gold_dorm]] = 0.0
self.prior_beta_uniform = uprior
# beta Gaussian prior
gprior = np.repeat(np.array([[0.0], [np.inf]]), self.num_vars, axis=1)
for i, cov_model in enumerate(self.cov_models):
for dorm, prior in cov_model.prior_beta_gaussian.items():
gprior[:, self.var_idx[dorm][i]] = prior
gprior[:, self.var_idx[self.gold_dorm]] = np.array([[0.0], [np.inf]])
self.prior_beta_gaussian = gprior
# place holder for the solutions
self.beta = None
self.beta_sd = None
self.gamma = None
self.fixed_vars = None
self.random_vars = None
def check(self):
"""Check input type, dimension and values.
"""
assert isinstance(self.cwdata, data.CWData)
assert self.obs_type in ['diff_log', 'diff_logit'], \
"Unsupport observation type"
assert isinstance(self.cov_models, list)
assert all([isinstance(model, CovModel) for model in self.cov_models])
assert self.gold_dorm in self.cwdata.unique_dorms
assert self.order_prior is None or isinstance(self.order_prior, list)
def _assert_covs_independent(self):
"""Check if the covariates are independent.
"""
rank = np.linalg.matrix_rank(self.cov_mat)
if rank < self.cov_mat.shape[1]:
raise ValueError(
"Covariates are collinear, that is, some covariate column is a linear combination of "
"some of the other columns. Please check them carefully.")
def _assert_rank_efficient(self):
"""Check the rank of the design matrix.
"""
rank = np.linalg.matrix_rank(self.design_mat)
num_unknowns = self.num_vars_per_dorm * (self.cwdata.num_dorms - 1)
if rank < num_unknowns:
raise ValueError(
f"Not enough information in the data to recover parameters."
f"Number of effective data points is {rank} and number of unknowns is {num_unknowns}."
f"Please include more effective data or reduce the number of covariates."
)
def create_relation_mat(self, cwdata=None):
"""Creating relation matrix.
Args:
cwdata (data.CWData | None, optional):
Optional data set, if None, use `self.cwdata`.
Returns:
numpy.ndarray:
Returns relation matrix with 1 encode alternative definition
and -1 encode reference definition.
"""
cwdata = utils.default_input(cwdata, default=self.cwdata)
assert isinstance(cwdata, data.CWData)
relation_mat = np.zeros((cwdata.num_obs, cwdata.num_dorms))
for i, dorms in enumerate(cwdata.alt_dorms):
for dorm in dorms:
relation_mat[i, cwdata.dorm_idx[dorm]] += 1.0
for i, dorms in enumerate(cwdata.ref_dorms):
for dorm in dorms:
relation_mat[i, cwdata.dorm_idx[dorm]] -= 1.0
return relation_mat
def _check_relation_mat(self):
"""Check relation matrix, detect unused dorms.
"""
col_scales = np.max(np.abs(self.relation_mat), axis=0)
unused_dorms = [
self.cwdata.unique_dorms[i] for i, scale in enumerate(col_scales)
if scale == 0.0
]
if len(unused_dorms) != 0:
raise ValueError(
f"{unused_dorms} appears to be unused, most likely it is (they are) "
f"in both alt_dorms and ref_dorms at the same time for all its (their) "
f"appearance. Please remove {unused_dorms} from alt_dorms and ref_dorms."
)
def create_cov_mat(self, cwdata=None):
"""Create covariates matrix for definitions/methods model.
Args:
cwdata (data.CWData | None, optional):
Optional data set, if None, use `self.cwdata`.
Returns:
numpy.ndarray:
Returns covarites matrix.
"""
cwdata = utils.default_input(cwdata, default=self.cwdata)
assert isinstance(cwdata, data.CWData)
return np.hstack(
[model.create_design_mat(cwdata) for model in self.cov_models])
def create_design_mat(self, cwdata=None, relation_mat=None, cov_mat=None):
"""Create linear design matrix.
Args:
cwdata (data.CWData | None, optional):
Optional data set, if None, use `self.cwdata`.
relation_mat (numpy.ndarray | None, optional):
Optional relation matrix, if None, use `self.relation_mat`
cov_mat (numpy.ndarray | None, optional):
Optional covariates matrix, if None, use `self.cov_mat`
Returns:
numpy.ndarray:
Returns linear design matrix.
"""
cwdata = utils.default_input(cwdata, default=self.cwdata)
relation_mat = utils.default_input(relation_mat,
default=self.relation_mat)
cov_mat = utils.default_input(cov_mat, default=self.cov_mat)
mat = (relation_mat.ravel()[:, None] *
np.repeat(cov_mat, cwdata.num_dorms, axis=0)).reshape(
cwdata.num_obs, self.num_vars)
return mat
def create_constraint_mat(self):
"""Create constraint matrix.
Returns:
numpy.ndarray:
Return constraints matrix.
"""
mat = np.array([]).reshape(0, self.num_vars)
if self.order_prior is not None:
dorm_constraint_mat = []
cov_mat = self.cov_mat
min_cov_mat = np.min(cov_mat, axis=0)
max_cov_mat = np.max(cov_mat, axis=0)
if np.allclose(min_cov_mat, max_cov_mat):
design_mat = min_cov_mat[None, :]
else:
design_mat = np.vstack((min_cov_mat, max_cov_mat))
for p in self.order_prior:
sub_mat = np.zeros((design_mat.shape[0], self.num_vars))
sub_mat[:, self.var_idx[p[0]]] = design_mat
sub_mat[:, self.var_idx[p[1]]] = -design_mat
dorm_constraint_mat.append(sub_mat)
dorm_constraint_mat = np.vstack(dorm_constraint_mat)
mat = np.vstack((mat, dorm_constraint_mat))
if mat.size == 0:
return None
else:
return mat
def fit(self,
max_iter=100,
inlier_pct=1.0,
outer_max_iter=100,
outer_step_size=1.0):
"""Optimize the model parameters.
This is a interface to limetr.
Args:
max_iter (int, optional):
Maximum number of iterations.
inlier_pct (float, optional):
How much percentage of the data do you trust.
outer_max_iter (int, optional):
Outer maximum number of iterations.
outer_step_size (float, optional):
Step size of the trimming problem, the larger the step size the faster it will converge,
and the less quality of trimming it will guarantee.
"""
# dimensions for limetr
n = self.cwdata.study_sizes
if n.size == 0:
n = np.full(self.cwdata.num_obs, 1)
k_beta = self.num_vars
k_gamma = 1
y = self.cwdata.obs
s = self.cwdata.obs_se
x = self.design_mat
z = np.ones((self.cwdata.num_obs, 1))
uprior = np.hstack(
(self.prior_beta_uniform, self.prior_gamma_uniform[:, None]))
gprior = np.hstack(
(self.prior_beta_gaussian, self.prior_gamma_gaussian[:, None]))
if self.constraint_mat is None:
cfun = None
jcfun = None
cvec = None
else:
num_constraints = self.constraint_mat.shape[0]
cmat = np.hstack(
(self.constraint_mat, np.zeros((num_constraints, 1))))
cvec = np.array([[-np.inf] * num_constraints,
[0.0] * num_constraints])
def cfun(var):
return cmat.dot(var)
def jcfun(var):
return cmat
def fun(var):
return x.dot(var)
def jfun(beta):
return x
self.lt = LimeTr(n,
k_beta,
k_gamma,
y,
fun,
jfun,
z,
S=s,
gprior=gprior,
uprior=uprior,
C=cfun,
JC=jcfun,
c=cvec,
inlier_percentage=inlier_pct)
self.beta, self.gamma, self.w = self.lt.fitModel(
inner_print_level=5,
inner_max_iter=max_iter,
outer_max_iter=outer_max_iter,
outer_step_size=outer_step_size)
self.fixed_vars = {
var: self.beta[self.var_idx[var]]
for var in self.vars
}
if self.use_random_intercept:
u = self.lt.estimateRE()
self.random_vars = {
sid: u[i]
for i, sid in enumerate(self.cwdata.unique_study_id)
}
else:
self.random_vars = dict()
# compute the posterior distribution of beta
hessian = self.get_beta_hessian()
unconstrained_id = np.hstack([
np.arange(self.lt.k_beta)[self.var_idx[dorm]]
for dorm in self.cwdata.unique_dorms if dorm != self.gold_dorm
])
self.beta_sd = np.zeros(self.lt.k_beta)
self.beta_sd[unconstrained_id] = np.sqrt(
np.diag(np.linalg.inv(hessian)))
def get_beta_hessian(self) -> np.ndarray:
# compute the posterior distribution of beta
x = self.lt.JF(self.lt.beta) * np.sqrt(self.lt.w)[:, None]
z = self.lt.Z * np.sqrt(self.lt.w)[:, None]
v = limetr.utils.VarMat(self.lt.V**self.lt.w, z, self.lt.gamma,
self.lt.n)
if hasattr(self.lt, 'gprior'):
beta_gprior_sd = self.lt.gprior[:, self.lt.idx_beta][1]
else:
beta_gprior_sd = np.repeat(np.inf, self.lt.k_beta)
hessian = x.T.dot(v.invDot(x)) + np.diag(1.0 / beta_gprior_sd**2)
hessian = np.delete(hessian, self.var_idx[self.gold_dorm], axis=0)
hessian = np.delete(hessian, self.var_idx[self.gold_dorm], axis=1)
return hessian
def get_cov_names(self) -> List[str]:
# column of covariate name
cov_names = []
for model in self.cov_models:
if model.spline is None:
cov_names.append(model.cov_name)
else:
cov_names.extend([
f'{model.cov_name}_spline_{i}'
for i in range(model.num_vars)
])
return cov_names
def create_result_df(self) -> pd.DataFrame:
"""Create result data frame.
Returns:
pd.DataFrame: Data frame that contains the result.
"""
# column of dorms
dorms = np.repeat(self.cwdata.unique_dorms, self.num_vars_per_dorm)
cov_names = self.get_cov_names()
cov_names *= self.cwdata.num_dorms
# create data frame
df = pd.DataFrame({
'dorms': dorms,
'cov_names': cov_names,
'beta': self.beta,
'beta_sd': self.beta_sd,
})
if self.use_random_intercept:
gamma = np.hstack((self.lt.gamma, np.full(self.num_vars - 1,
np.nan)))
re = np.hstack(
(self.lt.u,
np.full((self.cwdata.num_studies, self.num_vars - 1),
np.nan)))
df['gamma'] = gamma
for i, study_id in enumerate(self.cwdata.unique_study_id):
df[study_id] = re[i]
return df
def save_result_df(self, folder: str, filename: str = 'result.csv'):
"""Save result.
Args:
folder (str): Path to the result folder.
filename (str): Name of the result. Default to `'result.csv'`.
"""
if not filename.endswith('.csv'):
filename += '.csv'
df = self.create_result_df()
df.to_csv(folder + '/' + filename, index=False)
def adjust_orig_vals(self,
df,
orig_dorms,
orig_vals_mean,
orig_vals_se,
study_id=None,
data_id=None,
ref_dorms=None):
"""Adjust alternative values.
Args:
df (pd.DataFrame):
Data frame of the alternative values that need to be adjusted.
orig_dorms (str):
Name of the column in `df` that contains the alternative
definitions or methods.
orig_vals_mean (str):
Name of the column in `df` that contains the alternative values.
orig_vals_se (str):
Name of the column in `df` that contains the standard error of
alternative values.
study_id (str | None, optional):
If not `None`, predict with the random effects.
data_id (str | None, optional):
If `None` create data_id by the integer sequence.
ref_dorms (str, optional):
Name of the column with reference dorms, if is ``None``, use the
gold_dorm as the reference dorm. Default to ``None``.
Returns:
pandas.DataFrame:
The adjusted values and standard deviations.
"""
df_copy = df.copy()
if ref_dorms is None:
ref_dorms = 'ref_dorms'
df_copy[ref_dorms] = np.array([self.gold_dorm] * df_copy.shape[0])
if 'intercept' not in df_copy.columns:
df_copy['intercept'] = np.ones(df_copy.shape[0])
new_cwdata = data.CWData(df_copy,
alt_dorms=orig_dorms,
ref_dorms=ref_dorms,
dorm_separator=self.cwdata.dorm_separator,
covs=list(self.cwdata.covs.columns),
data_id=data_id,
add_intercept=False)
# transfer data dorm structure to the new_cwdata
new_cwdata.copy_dorm_structure(self.cwdata)
# create new design matrix
new_relation_mat = self.create_relation_mat(cwdata=new_cwdata)
new_cov_mat = self.create_cov_mat(cwdata=new_cwdata)
new_design_mat = self.create_design_mat(cwdata=new_cwdata,
relation_mat=new_relation_mat,
cov_mat=new_cov_mat)
# calculate the random effects
if study_id is not None:
random_effects = np.array([
self.random_vars[sid][0] if sid in self.random_vars else 0.0
for sid in df[study_id]
])
else:
random_effects = np.zeros(df.shape[0])
random_effects[df[orig_dorms].values == self.gold_dorm] = 0.0
# compute the corresponding gold_dorm value
if self.obs_type == 'diff_log':
transformed_orig_vals_mean,\
transformed_orig_vals_se = utils.linear_to_log(
df[orig_vals_mean].values,
df[orig_vals_se].values
)
else:
transformed_orig_vals_mean, \
transformed_orig_vals_se = utils.linear_to_logit(
df[orig_vals_mean].values,
df[orig_vals_se].values
)
pred_diff_mean = new_design_mat.dot(self.beta)
pred_diff_sd = np.sqrt(
np.array([(new_design_mat[i]**2).dot(self.beta_sd**2)
if dorm != self.gold_dorm else 0.0
for i, dorm in enumerate(df[orig_dorms])]))
transformed_ref_vals_mean = transformed_orig_vals_mean - \
pred_diff_mean - random_effects
transformed_ref_vals_sd = np.sqrt(transformed_orig_vals_se**2 +
pred_diff_sd**2 + self.gamma[0]**2)
if self.obs_type == 'diff_log':
ref_vals_mean,\
ref_vals_sd = utils.log_to_linear(transformed_ref_vals_mean,
transformed_ref_vals_sd)
else:
ref_vals_mean,\
ref_vals_sd = utils.logit_to_linear(transformed_ref_vals_mean,
transformed_ref_vals_sd)
pred_df = pd.DataFrame({
'ref_vals_mean': ref_vals_mean,
'ref_vals_sd': ref_vals_sd,
'pred_diff_mean': pred_diff_mean,
'pred_diff_sd': pred_diff_sd,
'data_id': new_cwdata.data_id
})
return pred_df