def lmm_from_cache_file(self):
logging.info("Loading precomputation from {0}".format(self.cache_file))
lmm = LMM()
with np.load(self.cache_file) as data:
lmm.U = data['arr_0']
lmm.S = data['arr_1']
return lmm
def lmm_from_cache_file(self):
logging.info("Loading precomputation from {0}".format(self.cache_file))
lmm = LMM()
with np.load(self.cache_file) as data:
lmm.U = data['arr_0']
lmm.S = data['arr_1']
return lmm
def fill_in_cache_file(self):
self._run_once()
logging.info("filling in the cache_file and log_delta, as needed")
if self.G1_or_none is None:
self.G1val_or_none = None
else:
self.G1val_or_none = self.G1_or_none.read().standardize().val
# The S and U are always cached, in case they are needed for the cluster or for multi-threaded runs
if self.cache_file is None:
self.cache_file = os.path.join(self.__tempdirectory,
"cache_file.npz")
if os.path.exists(
self.cache_file
): # If there is already a cache file in the temp directory, it must be removed because it might be out-of-date
os.remove(self.cache_file)
lmm = None
if not os.path.exists(self.cache_file):
logging.info("Precomputing eigen")
lmm = LMM()
G0_standardized = self.G0.read().standardize()
lmm.setG(G0_standardized.val, self.G1val_or_none, a2=self.mixing)
logging.info("Saving precomputation to {0}".format(
self.cache_file))
pstutil.create_directory_if_necessary(self.cache_file)
np.savez(
self.cache_file, lmm.U, lmm.S
) #using np.savez instead of pickle because it seems to be faster to read and write
if self.external_log_delta is None:
if lmm is None:
lmm = self.lmm_from_cache_file()
logging.info("searching for internal delta")
lmm.setX(self.covar)
lmm.sety(self.pheno['vals'])
#log delta is used here. Might be better to use findH2, but if so will need to normalized G so that its K's diagonal would sum to iid_count
# As per the paper, we optimized delta with REML=True, but
# we will later optimize beta and find log likelihood with ML (REML=False)
result = lmm.find_log_delta(
REML=True,
sid_count=self.G0.sid_count,
min_log_delta=self.min_log_delta,
max_log_delta=self.max_log_delta
) #!!what about findA2H2? minH2=0.00001
self.external_log_delta = result['log_delta']
self.internal_delta = np.exp(
self.external_log_delta) * self.G0.sid_count
logging.info("internal_delta={0}".format(self.internal_delta))
logging.info("external_log_delta={0}".format(self.external_log_delta))
def train_null(self):
"""
train model under null hypothesis
"""
logging.info("training null model")
# use LMM
self.lmm = LMM()
self.lmm.setG(self.train_snps, self.train_pcs, a2=self.mixing)
self.lmm.setX(self.cov)
self.lmm.sety(self.phen)
logging.info("finding delta")
if self.delta is None:
result = self.lmm.findH2(REML=self.REML, minH2=0.00001 )
self.delta = 1.0/result['h2']-1.0
# UX = lmm_null.U.dot(test_snps)
self.res_null = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.ll_null = -self.res_null["nLL"]
def train_null(self):
"""
find delta on all snps
"""
logging.info("training null model")
# use LMM
self.lmm = LMM()
self.lmm.setG(self.G0, self.G1, a2=self.mixing)
self.lmm.setX(self.cov)
self.lmm.sety(self.phen)
logging.info("finding delta")
#result = self.lmm.find_log_delta(self, self.N)
#self.delta = np.exp(result['log_delta'])
if self.delta is None:
result = self.lmm.find_log_delta_chris()
self.delta = result['delta']
def RealVar(self, y, X):
lmmg = LMM()
m = np.shape(X)[1]
n = len(y)
lmmg.setG(X / math.sqrt(m))
lmmg.sety(y)
lmmg.setX(np.ones([n, 1]))
try:
dct = lmmg.findH2()
except:
dct = {}
dct['h2'] = .5
mn = sum(y) / float(n)
dct['sigma2'] = sum([(i - mn)**2 for i in y]) / float(n)
h2 = dct['h2']
s2 = dct['sigma2']
sg2 = h2 * s2
se2 = s2 - sg2
return [se2, sg2]
def RealVar(self,y,X):
lmmg=LMM()
m=np.shape(X)[1];
n=len(y);
lmmg.setG(X/math.sqrt(m))
lmmg.sety(y);
lmmg.setX(np.ones([n,1]))
try:
dct=lmmg.findH2();
except:
dct={};
dct['h2']=.5;
mn=sum(y)/float(n);
dct['sigma2']=sum([(i-mn)**2 for i in y])/float(n);
h2=dct['h2'];
s2=dct['sigma2'];
sg2=h2*s2;
se2=s2-sg2;
return [se2,sg2];
def fill_in_cache_file(self):
self._run_once()
logging.info("filling in the cache_file and log_delta, as needed")
if self.G1_or_none is None:
self.G1val_or_none = None
else:
self.G1val_or_none = self.G1_or_none.read().val
# The S and U are always cached, in case they are needed for the cluster or for multi-threaded runs
if self.cache_file is None:
self.cache_file = os.path.join(self.__tempdirectory, "cache_file.npz")
if os.path.exists(self.cache_file): # If there is already a cache file in the temp directory, it must be removed because it might be out-of-date
os.remove(self.cache_file)
lmm = None
if not os.path.exists(self.cache_file):
logging.info("Precomputing eigen")
lmm = LMM()
G0_standardized = self.G0.read().standardize()
lmm.setG(G0_standardized.val, self.G1val_or_none, a2=self.mixing)
logging.info("Saving precomputation to {0}".format(self.cache_file))
util.create_directory_if_necessary(self.cache_file)
np.savez(self.cache_file, lmm.U,lmm.S) #using np.savez instead of pickle because it seems to be faster to read and write
if self.external_log_delta is None:
if lmm is None:
lmm = self.lmm_from_cache_file()
logging.info("searching for internal delta")
lmm.setX(self.covar)
lmm.sety(self.pheno['vals'])
#log delta is used here. Might be better to use findH2, but if so will need to normalized G so that its K's diagonal would sum to iid_count
result = lmm.find_log_delta(REML=False, sid_count=self.G0.sid_count, min_log_delta=self.min_log_delta, max_log_delta=self.max_log_delta ) #!!what about findA2H2? minH2=0.00001
self.external_log_delta = result['log_delta']
self.internal_delta = np.exp(self.external_log_delta) * self.G0.sid_count
logging.info("internal_delta={0}".format(self.internal_delta))
logging.info("external_log_delta={0}".format(self.external_log_delta))
def train_null(self):
"""
train model under null hypothesis
"""
logging.info("training null model")
# use LMM
self.lmm = LMM()
self.lmm.setG(self.train_snps, self.train_pcs, a2=self.mixing)
self.lmm.setX(self.cov)
self.lmm.sety(self.phen)
logging.info("finding delta")
if self.delta is None:
result = self.lmm.findH2(REML=self.REML, minH2=0.00001 )
self.delta = 1.0/result['h2']-1.0
# UX = lmm_null.U.dot(test_snps)
self.res_null = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.ll_null = -self.res_null["nLL"]
def train_null(self):
"""
find delta on all snps
"""
logging.info("training null model")
# use LMM
self.lmm = LMM()
self.lmm.setG(self.G0, self.G1, a2=self.mixing)
self.lmm.setX(self.cov)
self.lmm.sety(self.phen)
logging.info("finding delta")
#result = self.lmm.find_log_delta(self, self.N)
#self.delta = np.exp(result['log_delta'])
if self.delta is None:
result = self.lmm.find_log_delta_chris()
self.delta = result['delta']
class GwasPrototype(object):
"""
class to perform genome-wide scan
"""
def __init__(self, train_snps, test_snps, phen, delta=None, cov=None, REML=False, train_pcs=None, mixing=0.0):
"""
set up GWAS object
"""
self.REML = REML
self.train_snps = train_snps
self.test_snps = test_snps
self.phen = phen
if delta is None:
self.delta=None
else:
self.delta = delta * train_snps.shape[1]
self.n_test = test_snps.shape[1]
self.n_ind = len(self.phen)
self.train_pcs = train_pcs
self.mixing = mixing
# add bias if no covariates are used
if cov is None:
self.cov = np.ones((self.n_ind, 1))
else:
self.cov = cov
self.n_cov = self.cov.shape[1]
self.lmm = None
self.res_null = None
self.res_alt = []
self.ll_null = None
self.ll_alt = np.zeros(self.n_test)
self.p_values = np.zeros(self.n_test)
self.sorted_p_values = np.zeros(self.n_test)
# merge covariates and test snps
self.X = np.hstack((self.cov, self.test_snps))
def precompute_UX(self, X):
'''
precompute UX for all snps to be tested
--------------------------------------------------------------------------
Input:
X : [N*D] 2-dimensional array of covariates
--------------------------------------------------------------------------
'''
logging.info("precomputing UX")
self.UX = self.lmm.U.T.dot(X)
self.k = self.lmm.S.shape[0]
self.N = self.lmm.X.shape[0]
if (self.k<self.N):
self.UUX = X - self.lmm.U.dot(self.UX)
logging.info("done.")
def train_null(self):
"""
train model under null hypothesis
"""
logging.info("training null model")
# use LMM
self.lmm = LMM()
self.lmm.setG(self.train_snps, self.train_pcs, a2=self.mixing)
self.lmm.setX(self.cov)
self.lmm.sety(self.phen)
logging.info("finding delta")
if self.delta is None:
result = self.lmm.findH2(REML=self.REML, minH2=0.00001 )
self.delta = 1.0/result['h2']-1.0
# UX = lmm_null.U.dot(test_snps)
self.res_null = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.ll_null = -self.res_null["nLL"]
def set_current_UX(self, idx):
"""
set the current UX to pre-trained LMM
"""
si = idx + self.n_cov
self.lmm.X = np.hstack((self.X[:,0:self.n_cov], self.X[:,si:si+1]))
self.lmm.UX = np.hstack((self.UX[:,0:self.n_cov], self.UX[:,si:si+1]))
if (self.k<self.N):
self.lmm.UUX = np.hstack((self.UUX[:,0:self.n_cov], self.UUX[:,si:si+1]))
def train_alt(self):
"""
train alternative model
"""
assert self.lmm != None
self.precompute_UX(self.X)
for idx in xrange(self.n_test):
self.set_current_UX(idx)
res = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.res_alt.append(res)
self.ll_alt[idx] = -res["nLL"]
if idx % 1000 == 0:
logging.info("processing snp {0}".format(idx))
def compute_p_values(self):
"""
given trained null and alt models, compute p-values
"""
# from C++ (?)
#real df = rank_beta[ snp ] - ((real)1.0 * rank_beta_0[ snp ]) ;
#pvals[ snp ] = PvalFromLikelihoodRatioTest( LL[ snp ] - LL_0[ snp ], ((real)0.5 * df) );
degrees_of_freedom = 1
assert len(self.res_alt) == self.n_test
for idx in xrange(self.n_test):
test_statistic = self.ll_alt[idx] - self.ll_null
self.p_values[idx] = stats.chi2.sf(2.0 * test_statistic, degrees_of_freedom)
self.p_idx = np.argsort(self.p_values)
self.sorted_p_values = self.p_values[self.p_idx]
def plot_result(self):
"""
plot results
"""
import pylab
pylab.semilogy(self.p_values)
pylab.show()
dummy = [self.res_alt[idx]["nLL"] for idx in xrange(self.n_test)]
pylab.hist(dummy, bins=100)
pylab.title("neg likelihood")
pylab.show()
pylab.hist(self.p_values, bins=100)
pylab.title("p-values")
pylab.show()
def run_gwas(self):
"""
invoke all steps in the right order
"""
self.train_null()
self.train_alt()
self.compute_p_values()
class WindowingGwas(object):
"""
class to perform genome-wide scan with single-snp windowing
"""
def __init__(self,
G0,
phen,
delta=None,
cov=None,
REML=False,
G1=None,
mixing=0.0):
"""
set up GWAS object
"""
self.REML = REML
self.G0 = G0
self.test_snps = G0
self.phen = phen
if delta is None:
self.delta = None
else:
self.delta = delta * G0.shape[1]
self.n_test = self.test_snps.shape[1]
self.n_ind = len(self.phen)
self.G1 = G1
self.mixing = mixing
# add bias if no covariates are used
if cov is None:
self.cov = np.ones((self.n_ind, 1))
else:
self.cov = cov
self.n_cov = self.cov.shape[1]
self.lmm = None
self.res_null = None
self.res_alt = []
self.ll_null = np.zeros(self.n_test)
self.ll_alt = np.zeros(self.n_test)
self.p_values = np.zeros(self.n_test)
self.sorted_p_values = np.zeros(self.n_test)
# merge covariates and test snps
self.X = np.hstack((self.cov, self.test_snps))
self.N = self.X.shape[0]
def precompute_UX(self, X):
'''
precompute UX for all snps to be tested
--------------------------------------------------------------------------
Input:
X : [N*D] 2-dimensional array of covariates
--------------------------------------------------------------------------
'''
logging.info("precomputing UX")
self.UX = self.lmm.U.T.dot(X)
self.k = self.lmm.S.shape[0]
self.N = self.lmm.X.shape[0]
if (self.k < self.N):
self.UUX = X - self.lmm.U.dot(self.UX)
logging.info("done.")
def train_null(self):
"""
find delta on all snps
"""
logging.info("training null model")
# use LMM
self.lmm = LMM()
self.lmm.setG(self.G0, self.G1, a2=self.mixing)
self.lmm.setX(self.cov)
self.lmm.sety(self.phen)
logging.info("finding delta")
#result = self.lmm.find_log_delta(self, self.N)
#self.delta = np.exp(result['log_delta'])
if self.delta is None:
result = self.lmm.find_log_delta_chris()
self.delta = result['delta']
def set_current_UX(self, idx):
"""
set the current UX to pre-trained LMM
"""
si = idx + self.n_cov
self.lmm.X = np.hstack((self.X[:, 0:self.n_cov], self.X[:, si:si + 1]))
self.lmm.UX = np.hstack((self.UX[:, 0:self.n_cov], self.UX[:,
si:si + 1]))
if (self.k < self.N):
self.lmm.UUX = np.hstack(
(self.UUX[:, 0:self.n_cov], self.UUX[:, si:si + 1]))
def set_null_UX(self):
"""
reset UX to covariates only
"""
self.lmm.X = self.X[:, 0:self.n_cov]
self.lmm.UX = self.UX[:, 0:self.n_cov]
if (self.k < self.N):
self.lmm.UUX = self.UUX[:, 0:self.n_cov]
def train_windowing(self):
"""
train null and alternative model
"""
assert self.lmm != None
self.precompute_UX(self.X)
for idx in range(self.n_test):
#TODO: this can be generalized to bigger window
self.lmm.set_exclude_idx([idx])
# null model
self.set_null_UX()
res = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.ll_null[idx] = -res["nLL"]
# alternative model
self.set_current_UX(idx)
res = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.res_alt.append(res)
self.ll_alt[idx] = -res["nLL"]
if idx % 1000 == 0:
logging.warning("processing snp {0}".format(idx))
def compute_p_values(self):
"""
given trained null and alt models, compute p-values
"""
degrees_of_freedom = 1
assert len(self.res_alt) == self.n_test
for idx in range(self.n_test):
test_statistic = self.ll_alt[idx] - self.ll_null[idx]
self.p_values[idx] = stats.chi2.sf(2.0 * test_statistic,
degrees_of_freedom)
self.p_idx = np.argsort(self.p_values)
self.sorted_p_values = self.p_values[self.p_idx]
return self.p_values
def plot_result(self):
"""
plot results
"""
import pylab
pylab.semilogy(self.p_values)
pylab.show()
dummy = [self.res_alt[idx]["nLL"] for idx in range(self.n_test)]
pylab.hist(dummy, bins=100)
pylab.title("neg likelihood")
pylab.show()
pylab.hist(self.p_values, bins=100)
pylab.title("p-values")
pylab.show()
def run_gwas(self):
"""
invoke all steps in the right order
"""
self.train_null()
self.train_windowing()
return self.compute_p_values()
class GwasPrototype(object):
"""
class to perform genome-wide scan
"""
def __init__(self, train_snps, test_snps, phen, delta=None, cov=None, REML=False, train_pcs=None, mixing=0.0):
"""
set up GWAS object
"""
self.REML = REML
self.train_snps = train_snps
self.test_snps = test_snps
self.phen = phen
if delta is None:
self.delta=None
else:
self.delta = delta * train_snps.shape[1]
self.n_test = test_snps.shape[1]
self.n_ind = len(self.phen)
self.train_pcs = train_pcs
self.mixing = mixing
# add bias if no covariates are used
if cov is None:
self.cov = np.ones((self.n_ind, 1))
else:
self.cov = cov
self.n_cov = self.cov.shape[1]
self.lmm = None
self.res_null = None
self.res_alt = []
self.ll_null = None
self.ll_alt = np.zeros(self.n_test)
self.p_values = np.zeros(self.n_test)
self.sorted_p_values = np.zeros(self.n_test)
# merge covariates and test snps
self.X = np.hstack((self.cov, self.test_snps))
def precompute_UX(self, X):
'''
precompute UX for all snps to be tested
--------------------------------------------------------------------------
Input:
X : [N*D] 2-dimensional array of covariates
--------------------------------------------------------------------------
'''
logging.info("precomputing UX")
self.UX = self.lmm.U.T.dot(X)
self.k = self.lmm.S.shape[0]
self.N = self.lmm.X.shape[0]
if (self.k<self.N):
self.UUX = X - self.lmm.U.dot(self.UX)
logging.info("done.")
def train_null(self):
"""
train model under null hypothesis
"""
logging.info("training null model")
# use LMM
self.lmm = LMM()
self.lmm.setG(self.train_snps, self.train_pcs, a2=self.mixing)
self.lmm.setX(self.cov)
self.lmm.sety(self.phen)
logging.info("finding delta")
if self.delta is None:
result = self.lmm.findH2(REML=self.REML, minH2=0.00001 )
self.delta = 1.0/result['h2']-1.0
# UX = lmm_null.U.dot(test_snps)
self.res_null = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.ll_null = -self.res_null["nLL"]
def set_current_UX(self, idx):
"""
set the current UX to pre-trained LMM
"""
si = idx + self.n_cov
self.lmm.X = np.hstack((self.X[:,0:self.n_cov], self.X[:,si:si+1]))
self.lmm.UX = np.hstack((self.UX[:,0:self.n_cov], self.UX[:,si:si+1]))
if (self.k<self.N):
self.lmm.UUX = np.hstack((self.UUX[:,0:self.n_cov], self.UUX[:,si:si+1]))
def train_alt(self):
"""
train alternative model
"""
assert self.lmm != None
self.precompute_UX(self.X)
for idx in xrange(self.n_test):
self.set_current_UX(idx)
res = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.res_alt.append(res)
self.ll_alt[idx] = -res["nLL"]
if idx % 1000 == 0:
logging.info("processing snp {0}".format(idx))
def compute_p_values(self):
"""
given trained null and alt models, compute p-values
"""
# from C++ (?)
#real df = rank_beta[ snp ] - ((real)1.0 * rank_beta_0[ snp ]) ;
#pvals[ snp ] = PvalFromLikelihoodRatioTest( LL[ snp ] - LL_0[ snp ], ((real)0.5 * df) );
degrees_of_freedom = 1
assert len(self.res_alt) == self.n_test
for idx in xrange(self.n_test):
test_statistic = self.ll_alt[idx] - self.ll_null
self.p_values[idx] = stats.chi2.sf(2.0 * test_statistic, degrees_of_freedom)
self.p_idx = np.argsort(self.p_values)
self.sorted_p_values = self.p_values[self.p_idx]
def plot_result(self):
"""
plot results
"""
import pylab
pylab.semilogy(self.p_values)
pylab.show()
dummy = [self.res_alt[idx]["nLL"] for idx in xrange(self.n_test)]
pylab.hist(dummy, bins=100)
pylab.title("neg likelihood")
pylab.show()
pylab.hist(self.p_values, bins=100)
pylab.title("p-values")
pylab.show()
def run_gwas(self):
"""
invoke all steps in the right order
"""
self.train_null()
self.train_alt()
self.compute_p_values()
def run_select(self, G0, G_bg, y, cov=None):
"""set up two kernel feature selection
Parameters
----------
G0 : numpy array of shape (num_ind, num_snps)
Data matrix from which foreground snps will be selected
G0_bg : numpy array of shape (num_ind, num_snps)
Data matrix containing background snps on which will be conditioned
y : numpy vector of shape (num_ind, )
Vector of phenotypes
cov : numpy array of shape (num_ind, num_covariates) or None
Covariates to be used as fixed effects
Returns
-------
best_k, feat_idx, best_mix, best_delta: tuple(int, np.array(int), float, float)
best_k is the best number of SNPs selected,
feat_idx is a np.array of integers denoting the indices of these snps,
best_mix is the best mixing coefficient between foreground and background kernel,
best_delta is the best regularization coefficient
"""
num_ind = len(y)
if cov is None:
cov = np.ones((num_ind, 1))
else:
logging.info("normalizing covariates")
cov = cov.copy()
cov = 1. / np.sqrt((cov**2).sum() / float(cov.shape[0])) * cov
cov.flags.writeable = False
# normalize to diag(K) = N
norm_factor = 1. / np.sqrt((G_bg**2).sum() / float(G_bg.shape[0]))
# we copy in case G and G_bg are pointing to the same object
G_bg = norm_factor * G_bg
K_bg_full = G_bg.dot(G_bg.T)
K_bg_full.flags.writeable = False
# some asserts
np.testing.assert_almost_equal(sum(np.diag(K_bg_full)), G_bg.shape[0])
if self.debug:
norm_factor_check = 1. / np.sqrt(G_bg.shape[1])
np.testing.assert_array_almost_equal(norm_factor,
norm_factor_check,
decimal=1)
for kfold_idx, (train_idx, test_idx) in enumerate(
KFold(num_ind,
n_folds=self.n_folds,
random_state=self.random_state,
shuffle=True)):
t0 = time.time()
logging.info("running fold: %i" % kfold_idx)
y_train = y.take(train_idx, axis=0)
y_test = y.take(test_idx, axis=0)
G0_train = G0.take(train_idx, axis=0)
G0_test = G0.take(test_idx, axis=0)
G_bg_train = G_bg.take(train_idx, axis=0)
G_bg_test = G_bg.take(test_idx, axis=0)
cov_train = cov.take(train_idx, axis=0)
cov_test = cov.take(test_idx, axis=0)
# write protect data
y_train.flags.writeable = False
y_test.flags.writeable = False
G0_train.flags.writeable = False
G0_test.flags.writeable = False
G_bg_train.flags.writeable = False
G_bg_test.flags.writeable = False
cov_train.flags.writeable = False
cov_test.flags.writeable = False
# precompute background kernel
K_bg_train = K_bg_full.take(train_idx, axis=0).take(train_idx,
axis=1)
K_bg_train.flags.writeable = False
if self.measure != "mse":
K_bg_test = K_bg_full.take(test_idx, axis=0).take(test_idx,
axis=1)
K_bg_test.flags.writeable = False
# rank features
if self.order_by_lmm:
logging.info("using linear mixed model to rank features")
t0 = time.time()
gwas = FastGwas(G_bg_train,
G0_train,
y_train,
delta=None,
train_pcs=None,
mixing=0.0,
cov=cov_train)
gwas.run_gwas()
_pval = gwas.p_values
logging.info("time taken: %s" % (str(time.time() - t0)))
else:
logging.info("using linear regression to rank features")
_F, _pval = lin_reg.f_regression_block(
lin_reg.f_regression_cov_alt,
G0_train,
y_train,
blocksize=10000,
C=cov_train)
feat_idx = np.argsort(_pval)
for k_idx, max_k in enumerate(self.grid_k):
feat_idx_subset = feat_idx[0:max_k]
G_fs_train = G0_train.take(feat_idx_subset, axis=1)
G_fs_test = G0_test.take(feat_idx_subset, axis=1)
# normalize to sum(diag)=N
norm_factor = 1. / np.sqrt(
(G_fs_train**2).sum() / float(G_fs_train.shape[0]))
G_fs_train *= norm_factor
G_fs_test *= norm_factor
G_fs_train.flags.writeable = False
G_fs_test.flags.writeable = False
# asserts
if self.debug:
norm_factor_check = 1.0 / np.sqrt(max_k)
np.testing.assert_array_almost_equal(norm_factor,
norm_factor_check,
decimal=1)
np.testing.assert_almost_equal(
sum(np.diag(G_fs_train.dot(G_fs_train.T))),
G_fs_train.shape[0])
logging.info("k: %i" % (max_k))
# use LMM
from fastlmm.inference.lmm_cov import LMM as fastLMM
if G_bg_train.shape[1] <= G_bg_train.shape[0]:
lmm = fastLMM(X=cov_train,
Y=y_train[:, np.newaxis],
G=G_bg_train)
else:
lmm = fastLMM(X=cov_train,
Y=y_train[:, np.newaxis],
K=K_bg_train)
W = G_fs_train.copy()
UGup, UUGup = lmm.rotate(W)
i_up = np.zeros((G_fs_train.shape[1]), dtype=np.bool)
i_G1 = np.ones((G_fs_train.shape[1]), dtype=np.bool)
t0 = time.time()
res = lmm.findH2_2K(nGridH2=10,
minH2=0.0,
maxH2=0.99999,
i_up=i_up,
i_G1=i_G1,
UW=UGup,
UUW=UUGup)
logging.info("time taken for k=%i: %s" %
(max_k, str(time.time() - t0)))
# recover a2 from alternate parameterization
a2 = res["h2_1"] / float(res["h2"] + res["h2_1"])
h2 = res["h2"] + res["h2_1"]
delta = (1 - h2) / h2
#res_cov = res
# do final prediction using lmm.py
from fastlmm.inference import LMM
lmm = LMM(forcefullrank=False)
lmm.setG(G0=G_bg_train, G1=G_fs_train, a2=a2)
lmm.setX(cov_train)
lmm.sety(y_train)
# we take an additional step to estimate betas on covariates (not given from new model)
res = lmm.nLLeval(delta=delta, REML=True)
# predict on test set
lmm.setTestData(Xstar=cov_test,
G0star=G_bg_test,
G1star=G_fs_test)
out = lmm.predictMean(beta=res["beta"], delta=delta)
mse = mean_squared_error(y_test, out)
logging.info("mse: %f" % (mse))
self.mse[kfold_idx, k_idx] = mse
self.mixes[kfold_idx, k_idx] = a2
self.deltas[kfold_idx, k_idx] = delta
if self.measure != "mse":
K_test_test = a2 * G_fs_test.dot(
G_fs_test.T) + (1.0 - a2) * K_bg_test
ll = lmm.nLLeval_test(y_test,
res["beta"],
sigma2=res["sigma2"],
delta=delta,
Kstar_star=K_test_test,
robust=True)
if self.debug:
ll2 = lmm.nLLeval_test(y_test,
res["beta"],
sigma2=res["sigma2"],
delta=delta,
Kstar_star=None,
robust=True)
np.testing.assert_almost_equal(ll, ll2, decimal=4)
logging.info("ll: %f" % (ll))
self.ll[kfold_idx, k_idx] = ll
logging.info("time taken for fold: %s" % str(time.time() - t0))
best_k, best_mix, best_delta = self.select_best_k()
logging.info("best_k: %i, best_mix: %f, best_delta: %f" %
(best_k, best_mix, best_delta))
# final scan
if self.order_by_lmm:
logging.info("final scan using LMM")
gwas = FastGwas(G_bg,
G0,
y,
delta=None,
train_pcs=None,
mixing=0.0,
cov=cov)
gwas.run_gwas()
_pval = gwas.p_values
feat_idx = np.argsort(_pval)[0:best_k]
else:
logging.info("final scan using LR")
_F, _pval = lin_reg.f_regression_block(
lin_reg.f_regression_cov_alt, G0, y, C=cov, blocksize=10000)
logging.info("number of snps selected: %i" % (best_k))
return best_k, feat_idx, best_mix, best_delta
class WindowingGwas(object):
"""
class to perform genome-wide scan with single-snp windowing
"""
def __init__(self, G0, phen, delta=None, cov=None, REML=False, G1=None, mixing=0.0):
"""
set up GWAS object
"""
self.REML = REML
self.G0 = G0
self.test_snps = G0
self.phen = phen
if delta is None:
self.delta=None
else:
self.delta = delta * G0.shape[1]
self.n_test = self.test_snps.shape[1]
self.n_ind = len(self.phen)
self.G1 = G1
self.mixing = mixing
# add bias if no covariates are used
if cov is None:
self.cov = np.ones((self.n_ind, 1))
else:
self.cov = cov
self.n_cov = self.cov.shape[1]
self.lmm = None
self.res_null = None
self.res_alt = []
self.ll_null = np.zeros(self.n_test)
self.ll_alt = np.zeros(self.n_test)
self.p_values = np.zeros(self.n_test)
self.sorted_p_values = np.zeros(self.n_test)
# merge covariates and test snps
self.X = np.hstack((self.cov, self.test_snps))
self.N = self.X.shape[0]
def precompute_UX(self, X):
'''
precompute UX for all snps to be tested
--------------------------------------------------------------------------
Input:
X : [N*D] 2-dimensional array of covariates
--------------------------------------------------------------------------
'''
logging.info("precomputing UX")
self.UX = self.lmm.U.T.dot(X)
self.k = self.lmm.S.shape[0]
self.N = self.lmm.X.shape[0]
if (self.k<self.N):
self.UUX = X - self.lmm.U.dot(self.UX)
logging.info("done.")
def train_null(self):
"""
find delta on all snps
"""
logging.info("training null model")
# use LMM
self.lmm = LMM()
self.lmm.setG(self.G0, self.G1, a2=self.mixing)
self.lmm.setX(self.cov)
self.lmm.sety(self.phen)
logging.info("finding delta")
#result = self.lmm.find_log_delta(self, self.N)
#self.delta = np.exp(result['log_delta'])
if self.delta is None:
result = self.lmm.find_log_delta_chris()
self.delta = result['delta']
def set_current_UX(self, idx):
"""
set the current UX to pre-trained LMM
"""
si = idx + self.n_cov
self.lmm.X = np.hstack((self.X[:,0:self.n_cov], self.X[:,si:si+1]))
self.lmm.UX = np.hstack((self.UX[:,0:self.n_cov], self.UX[:,si:si+1]))
if (self.k<self.N):
self.lmm.UUX = np.hstack((self.UUX[:,0:self.n_cov], self.UUX[:,si:si+1]))
def set_null_UX(self):
"""
reset UX to covariates only
"""
self.lmm.X = self.X[:,0:self.n_cov]
self.lmm.UX = self.UX[:,0:self.n_cov]
if (self.k<self.N):
self.lmm.UUX = self.UUX[:,0:self.n_cov]
def train_windowing(self):
"""
train null and alternative model
"""
assert self.lmm != None
self.precompute_UX(self.X)
for idx in xrange(self.n_test):
#TODO: this can be generalized to bigger window
self.lmm.set_exclude_idx([idx])
# null model
self.set_null_UX()
res = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.ll_null[idx] = -res["nLL"]
# alternative model
self.set_current_UX(idx)
res = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.res_alt.append(res)
self.ll_alt[idx] = -res["nLL"]
if idx % 1000 == 0:
logging.warning("processing snp {0}".format(idx))
def compute_p_values(self):
"""
given trained null and alt models, compute p-values
"""
degrees_of_freedom = 1
assert len(self.res_alt) == self.n_test
for idx in xrange(self.n_test):
test_statistic = self.ll_alt[idx] - self.ll_null[idx]
self.p_values[idx] = stats.chi2.sf(2.0 * test_statistic, degrees_of_freedom)
self.p_idx = np.argsort(self.p_values)
self.sorted_p_values = self.p_values[self.p_idx]
return self.p_values
def plot_result(self):
"""
plot results
"""
import pylab
pylab.semilogy(self.p_values)
pylab.show()
dummy = [self.res_alt[idx]["nLL"] for idx in xrange(self.n_test)]
pylab.hist(dummy, bins=100)
pylab.title("neg likelihood")
pylab.show()
pylab.hist(self.p_values, bins=100)
pylab.title("p-values")
pylab.show()
def run_gwas(self):
"""
invoke all steps in the right order
"""
self.train_null()
self.train_windowing()
return self.compute_p_values()
def run_select(self, G0, G_bg, y, cov=None):
"""set up two kernel feature selection
Parameters
----------
G0 : numpy array of shape (num_ind, num_snps)
Data matrix from which foreground snps will be selected
G0_bg : numpy array of shape (num_ind, num_snps)
Data matrix containing background snps on which will be conditioned
y : numpy vector of shape (num_ind, )
Vector of phenotypes
cov : numpy array of shape (num_ind, num_covariates) or None
Covariates to be used as fixed effects
Returns
-------
best_k, feat_idx, best_mix, best_delta: tuple(int, np.array(int), float, float)
best_k is the best number of SNPs selected,
feat_idx is a np.array of integers denoting the indices of these snps,
best_mix is the best mixing coefficient between foreground and background kernel,
best_delta is the best regularization coefficient
"""
num_ind = len(y)
if cov is None:
cov = np.ones((num_ind,1))
else:
logging.info("normalizing covariates")
cov = cov.copy()
cov = 1./np.sqrt((cov**2).sum() / float(cov.shape[0])) * cov
cov.flags.writeable = False
# normalize to diag(K) = N
norm_factor = 1./np.sqrt((G_bg**2).sum() / float(G_bg.shape[0]))
# we copy in case G and G_bg are pointing to the same object
G_bg = norm_factor * G_bg
K_bg_full = G_bg.dot(G_bg.T)
K_bg_full.flags.writeable = False
# some asserts
np.testing.assert_almost_equal(sum(np.diag(K_bg_full)), G_bg.shape[0])
if self.debug:
norm_factor_check = 1./np.sqrt(G_bg.shape[1])
np.testing.assert_array_almost_equal(norm_factor, norm_factor_check, decimal=1)
for kfold_idx, (train_idx, test_idx) in enumerate(KFold(num_ind, n_folds=self.n_folds, random_state=self.random_state, shuffle=True)):
t0 = time.time()
logging.info("running fold: %i" % kfold_idx)
y_train = y.take(train_idx, axis=0)
y_test = y.take(test_idx, axis=0)
G0_train = G0.take(train_idx, axis=0)
G0_test = G0.take(test_idx, axis=0)
G_bg_train = G_bg.take(train_idx, axis=0)
G_bg_test = G_bg.take(test_idx, axis=0)
cov_train = cov.take(train_idx, axis=0)
cov_test = cov.take(test_idx, axis=0)
# write protect data
y_train.flags.writeable = False
y_test.flags.writeable = False
G0_train.flags.writeable = False
G0_test.flags.writeable = False
G_bg_train.flags.writeable = False
G_bg_test.flags.writeable = False
cov_train.flags.writeable = False
cov_test.flags.writeable = False
# precompute background kernel
K_bg_train = K_bg_full.take(train_idx, axis=0).take(train_idx, axis=1)
K_bg_train.flags.writeable = False
if self.measure != "mse":
K_bg_test = K_bg_full.take(test_idx, axis=0).take(test_idx, axis=1)
K_bg_test.flags.writeable = False
# rank features
if self.order_by_lmm:
logging.info("using linear mixed model to rank features")
t0 = time.time()
gwas = FastGwas(G_bg_train, G0_train, y_train, delta=None, train_pcs=None, mixing=0.0, cov=cov_train)
gwas.run_gwas()
_pval = gwas.p_values
logging.info("time taken: %s" % (str(time.time()-t0)))
else:
logging.info("using linear regression to rank features")
_F,_pval = lin_reg.f_regression_block(lin_reg.f_regression_cov_alt, G0_train, y_train, blocksize=10000, C=cov_train)
feat_idx = np.argsort(_pval)
for k_idx, max_k in enumerate(self.grid_k):
feat_idx_subset = feat_idx[0:max_k]
G_fs_train = G0_train.take(feat_idx_subset, axis=1)
G_fs_test = G0_test.take(feat_idx_subset, axis=1)
# normalize to sum(diag)=N
norm_factor = 1./np.sqrt((G_fs_train**2).sum() / float(G_fs_train.shape[0]))
G_fs_train *= norm_factor
G_fs_test *= norm_factor
G_fs_train.flags.writeable = False
G_fs_test.flags.writeable = False
# asserts
if self.debug:
norm_factor_check = 1.0 / np.sqrt(max_k)
np.testing.assert_array_almost_equal(norm_factor, norm_factor_check, decimal=1)
np.testing.assert_almost_equal(sum(np.diag(G_fs_train.dot(G_fs_train.T))), G_fs_train.shape[0])
logging.info("k: %i" % (max_k))
# use LMM
from fastlmm.inference.lmm_cov import LMM as fastLMM
if G_bg_train.shape[1] <= G_bg_train.shape[0]:
lmm = fastLMM(X=cov_train, Y=y_train[:,np.newaxis], G=G_bg_train)
else:
lmm = fastLMM(X=cov_train, Y=y_train[:,np.newaxis], K=K_bg_train)
W = G_fs_train.copy()
UGup,UUGup = lmm.rotate(W)
i_up = np.zeros((G_fs_train.shape[1]), dtype=np.bool)
i_G1 = np.ones((G_fs_train.shape[1]), dtype=np.bool)
t0 = time.time()
res = lmm.findH2_2K(nGridH2=10, minH2=0.0, maxH2=0.99999, i_up=i_up, i_G1=i_G1, UW=UGup, UUW=UUGup)
logging.info("time taken for k=%i: %s" % (max_k, str(time.time()-t0)))
# recover a2 from alternate parameterization
a2 = res["h2_1"] / float(res["h2"] + res["h2_1"])
h2 = res["h2"] + res["h2_1"]
delta = (1-h2) / h2
#res_cov = res
# do final prediction using lmm.py
from fastlmm.inference import LMM
lmm = LMM(forcefullrank=False)
lmm.setG(G0=G_bg_train, G1=G_fs_train, a2=a2)
lmm.setX(cov_train)
lmm.sety(y_train)
# we take an additional step to estimate betas on covariates (not given from new model)
res = lmm.nLLeval(delta=delta, REML=True)
# predict on test set
lmm.setTestData(Xstar=cov_test, G0star=G_bg_test, G1star=G_fs_test)
out = lmm.predictMean(beta=res["beta"], delta=delta)
mse = mean_squared_error(y_test, out)
logging.info("mse: %f" % (mse))
self.mse[kfold_idx, k_idx] = mse
self.mixes[kfold_idx, k_idx] = a2
self.deltas[kfold_idx, k_idx] = delta
if self.measure != "mse":
K_test_test = a2 * G_fs_test.dot(G_fs_test.T) + (1.0-a2) * K_bg_test
ll = lmm.nLLeval_test(y_test, res["beta"], sigma2=res["sigma2"], delta=delta, Kstar_star=K_test_test, robust=True)
if self.debug:
ll2 = lmm.nLLeval_test(y_test, res["beta"], sigma2=res["sigma2"], delta=delta, Kstar_star=None, robust=True)
np.testing.assert_almost_equal(ll, ll2, decimal=4)
logging.info("ll: %f" % (ll))
self.ll[kfold_idx, k_idx] = ll
logging.info("time taken for fold: %s" % str(time.time()-t0))
best_k, best_mix, best_delta = self.select_best_k()
logging.info("best_k: %i, best_mix: %f, best_delta: %f" % (best_k, best_mix, best_delta))
# final scan
if self.order_by_lmm:
logging.info("final scan using LMM")
gwas = FastGwas(G_bg, G0, y, delta=None, train_pcs=None, mixing=0.0, cov=cov)
gwas.run_gwas()
_pval = gwas.p_values
feat_idx = np.argsort(_pval)[0:best_k]
else:
logging.info("final scan using LR")
_F,_pval = lin_reg.f_regression_block(lin_reg.f_regression_cov_alt, G0, y, C=cov, blocksize=10000)
logging.info("number of snps selected: %i" % (best_k))
return best_k, feat_idx, best_mix, best_delta