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run_laplace.py
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import numpy as np
import scipy.linalg as la
import sys
import time
import pandas as pd
import laplace_cython
import scipy.optimize as optimize
import scipy.stats as stats
import scipy.special
np.set_printoptions(precision=4, linewidth=200)
def symmetrize(X): return X + X.T - np.diag(X.diagonal())
def approx_hessian(fun_g, w0, args, rr=1e-3):
H = np.eye(w0.shape[0])
for i in xrange(len(w0)):
v = H[:,i]
try:
_, g2 = fun_g(w0-rr*v, *args)
_, g1 = fun_g(w0+rr*v, *args)
except:
g1 = optimize.approx_fprime(w0-rr*v, fun_g, 1e-8, *args)
g2 = optimize.approx_fprime(w0+rr*v, fun_g, 1e-8, *args)
H[:,i] = (g1 - g2) / (2*rr)
return H
class EWAS_Laplace():
def __init__(self):
self.optIter = 0
self.optimization = False
self.verbose = False
pass
def ll_binom_laplace(self, hyp, *varargin):
if (np.max(np.abs(hyp[:2])) > 5): return np.inf, np.ones(len(hyp)) + np.inf
try:
nlZ = laplace_cython.laplace_nlZ(hyp, *varargin)
except ValueError, e:
print '#optimization failed with ValueError!'
print '#message:', e
print '#hyp:', hyp
nlZ = np.inf, np.ones(len(hyp)) + np.inf
try: returnGrad = (len(nlZ) > 1)
except: returnGrad=False
if returnGrad:
nlZ, grad = nlZ
if (self.verbose and self.optimization):
if (self.optIter % 10 == 0):
t1 = time.time()
print 'll_binom_laplace optimization iteration %d nlZ: %0.4f time: %0.2f seconds'%(self.optIter, nlZ, t1-self.iter_t0)
self.iter_t0 = t1
self.optIter += 1
if returnGrad: return nlZ, grad
else: return nlZ
def optim_ll_binom_laplace(self, hyp0, opt='gpstuff', *opt_args):
self.optIter = 0
self.optimization = True
self.iter_t0 = time.time()
hyp_opt = optimize.minimize(self.ll_binom_laplace, hyp0, args=opt_args, jac=True, method=opt)#, options={'gtol':1e-5, 'ftol':1e-5})#, bounds=[(-5,2) for p in hyp0])
self.optimization = False
if self.verbose:
print 'final nlZ: %0.4f'%(hyp_opt.fun)
print 'final params:', hyp_opt.x
print
try:
return hyp_opt.fun, hyp_opt.x, hyp_opt.hess_inv
except:
return hyp_opt.fun, hyp_opt.x, None
def testBeta(self, params0_null, params0_alt, kernels, covars_null, covars_alt, y, r, covars_null_fixed, covars_alt_fixed, verbose=True, opt='gpstuff', test='wald', returnF=False, returnGrad=True, inv_tol=-1.0, num_simu=0, ZC_direct=True):
old_verbose = self.verbose
self.verbose = verbose
t0_beta = time.time()
opt_covars = True
params0_alt_orig = params0_alt.copy()
params0_null_orig = params0_null.copy()
opt_alt = False
try:
beta0_alt = solve_binom(y, r, covars_alt_fixed, return_ll=False)
params0_alt[-covars_alt.shape[1]:] = beta0_alt[:covars_alt.shape[1]]
opt_alt = True
except: pass
opt_null = False
if ((test != 'wald') or not opt_alt or (not opt_covars)):
try:
beta0_null = solve_binom(y, r, covars_null_fixed, return_ll=False)
params0_null[-covars_null.shape[1]:] = beta0_null[:covars_null.shape[1]]
opt_null = True
except: opt_covars=True
if (opt_null and (not opt_covars)):
m0 = covars_null.dot(beta0_null)
opt_args_null = (kernels, np.empty((y.shape[0],0)), m0, y, r, True, returnGrad, False, False, np.zeros(y.shape[0]), inv_tol, num_simu, False, ZC_direct)
opt_args_alt = (kernels, covars_alt[:,-1:], m0, y, r, True, returnGrad, False, False, np.zeros(y.shape[0]), inv_tol, num_simu, False, ZC_direct)
params0_null = params0_null[:2]
params0_alt = params0_alt[[0,1,-1]]
else:
m0 = np.zeros(y.shape[0])
opt_args_null = (kernels, covars_null, m0, y, r, True, returnGrad, False, False, np.zeros(y.shape[0]), inv_tol, num_simu, False, ZC_direct)
opt_args_alt = (kernels, covars_alt, m0, y, r, True, returnGrad, False, False, np.zeros(y.shape[0]), inv_tol, num_simu, False, ZC_direct)
nlZ_null = np.inf
if ((test != 'wald') or not opt_alt):
try: nlZ_null, params_opt_null, hess_inv_null = self.optim_ll_binom_laplace(params0_null, opt, *opt_args_null)
except: return np.nan, np.nan
if (test != 'score'):
params0_alt2 = params0_alt.copy()
if not opt_alt:
if returnF: params0_alt2 = params_opt_null.copy()
else: params0_alt2[:-1] = params_opt_null
try:
nlZ_alt, params_opt_alt, hess_inv_alt = self.optim_ll_binom_laplace(params0_alt2, opt, *opt_args_alt)
if np.isclose(nlZ_alt, 0):
params0_alt2 = params0_alt_orig.copy()
nlZ_alt, params_opt_alt, hess_inv_alt = self.optim_ll_binom_laplace(params0_alt2, opt, *opt_args_alt)
except:
opt_args_null=list(opt_args_null); opt_args_null[12] = True; opt_args_null = tuple(opt_args_null)
opt_args_alt=list(opt_args_alt); opt_args_alt[12] = True; opt_args_alt = tuple(opt_args_alt)
try:
nlZ_alt, params_opt_alt, hess_inv_alt = self.optim_ll_binom_laplace(params0_alt2, opt, *opt_args_alt)
if np.isclose(nlZ_alt, 0):
params0_alt2 = params0_alt_orig.copy()
nlZ_alt, params_opt_alt, hess_inv_alt = self.optim_ll_binom_laplace(params0_alt2, opt, *opt_args_alt)
except:
return np.nan, np.nan
#find numerical problems
if (test=='wald' and np.any(np.abs(params_opt_alt) > 400)):
try: nlZ_null, params_opt_null, hess_inv_null = self.optim_ll_binom_laplace(params0_null, opt, *opt_args_null)
except:
opt_args_null=list(opt_args_null); opt_args_null[12] = True; opt_args_null = tuple(opt_args_null)
opt_args_alt=list(opt_args_alt); opt_args_alt[12] = True; opt_args_alt = tuple(opt_args_alt)
try: nlZ_null, params_opt_null, hess_inv_null = self.optim_ll_binom_laplace(params0_null, opt, *opt_args_null)
except: return np.nan, np.nan
if returnF: params0_alt2 = params_opt_null.copy()
else: params0_alt2[:-1] = params_opt_null
try: nlZ_alt, params_opt_alt, hess_inv_alt = self.optim_ll_binom_laplace(params0_alt2, opt, *opt_args_alt)
except:
opt_args_null=list(opt_args_null); opt_args_null[12] = True; opt_args_null = tuple(opt_args_null)
opt_args_alt=list(opt_args_alt); opt_args_alt[12] = True; opt_args_alt = tuple(opt_args_alt)
try: nlZ_alt, params_opt_alt, hess_inv_alt = self.optim_ll_binom_laplace(params0_alt2, opt, *opt_args_alt)
except: return np.nan, np.nan
if (np.any(np.abs(params_opt_alt) > 400)): return np.nan, np.nan
#hack for L-BFGS-B
if (test != 'score' and not returnF):
try:
try:
nlZ_null2, _ = self.ll_binom_laplace(params_opt_alt[:-1], *opt_args_null)
if (nlZ_null2 < nlZ_null):
nlZ_null=nlZ_null2
params_opt_null = params_opt_alt[:-1]
except: pass
if (nlZ_alt > nlZ_null):
params0_alt2[:-1] = params_opt_null
params0_alt2[-1]=0
try: nlZ_alt2, params_opt_alt2, hess_inv_alt2 = self.optim_ll_binom_laplace(params0_alt2, opt, *opt_args_alt)
except:
opt_args_null=list(opt_args_null); opt_args_null[12] = True; opt_args_null = tuple(opt_args_null)
opt_args_alt=list(opt_args_alt); opt_args_alt[12] = True; opt_args_alt = tuple(opt_args_alt)
try: nlZ_alt2, params_opt_alt2, hess_inv_alt2 = self.optim_ll_binom_laplace(params0_alt2, opt, *opt_args_alt)
except: return np.nan, np.nan
if (nlZ_alt2 < nlZ_alt and nlZ_alt2>0):
nlZ_alt=nlZ_alt2
params_opt_alt = params_opt_alt2
hess_inv_alt = hess_inv_alt2
if (test != 'wald'):
nlZ_null2, _ = self.ll_binom_laplace(params_opt_alt2[:-1], *opt_args_null)
if (nlZ_null2 < nlZ_null):
nlZ_null=nlZ_null2
params_opt_null = params_opt_alt2[:-1]
except: raise
if (test == 'score'):
params0_final = params0_alt.copy()
params0_final[:-1] = params_opt_null
params0_final[-1]=0
nlZ_null_final, grad_opt_alt = self.ll_binom_laplace(params0_final, *opt_args_alt)
self.verbose = old_verbose
if (test == 'wald'):
if returnF:
opt_args_alt = list(opt_args_alt)
opt_args_alt[-2] = True
opt_args_alt = tuple(opt_args_alt)
f = laplace_cython.laplace_nlZ(params_opt_alt, *opt_args_alt)
return f, None
try:
#H = approx_hessian(self.ll_binom_laplace, params_opt_alt, opt_args_alt)
if (False and hess_inv_alt is not None):
invH_last = hess_inv_alt.todense()[-1,-1]
else:
H = approx_hessian(laplace_cython.laplace_nlZ, params_opt_alt, opt_args_alt)
H_symm = (H+H.T)/2.0
sH, UH = la.eigh(H_symm)
i_pos = (sH > 1e-10)
assert np.any(i_pos)
invH_last = np.sum(UH[-1,i_pos]**2 / sH[i_pos])
wald_stat = params_opt_alt[-1]**2 / invH_last
return wald_stat, None
except:
return np.nan, None
elif (test == 'score'):
H = approx_hessian(self.ll_binom_laplace, params0_final, opt_args_alt)
H_symm = (H+H.T)/2.0
sH, UH = la.eigh(H_symm)
i_pos = (sH > 1e-10)
invH_last = np.sum(UH[-1,i_pos]**2 / sH[i_pos])
score_stat = grad_opt_alt[-1]**2 / invH_last
return score_stat, None
elif (test == 'lr'):
return 2*(nlZ_null - nlZ_alt), None
else:
raise Exception('unknown test')
def readMacauTest(mcounts_file, counts_file, kernel_file, predictor_file, covars_file=None, correctK=True, kernel2=None):
#read methelated counts file
df_mcounts = pd.read_csv(mcounts_file, sep='\t', comment='#', header=0).dropna(axis=1, how='all')
yMat = df_mcounts[df_mcounts.columns[1:]].values.astype(np.int)
snpNames_y = df_mcounts[df_mcounts.columns[0]].values
#read total counts file
df_rcounts = pd.read_csv(counts_file, sep='\t', comment='#', header=0).dropna(axis=1, how='all')
rMat = df_rcounts[df_rcounts.columns[1:]].values.astype(np.int)
snpNames_r = df_rcounts[df_rcounts.columns[0]].values
assert np.all(snpNames_y == snpNames_r)
#remove illegal positions
bad = np.where(rMat < yMat)
# if (len(bad[0]) > 0):
# print '#removing the following illegal sites:',
# for s in snpNames_r[bad[0]]: print s,
# print
is_good = np.ones(len(snpNames_r), dtype=np.bool)
is_good[bad[0]] = False
snpNames_r = snpNames_r[is_good]
snpNames_y = snpNames_y[is_good]
yMat = yMat[is_good, :]
rMat = rMat[is_good, :]
#load kernels
K = np.loadtxt(kernel_file)
if (kernel2 is not None): K2 = np.loadtxt(kernel2)
#make K a positive-definite matrix
if correctK:
print 'kernel is not positive definite...'
d = np.diag(K).copy()
factor = 1e-8
s = la.eigh(K, eigvals_only=True, eigvals=(0,0), check_finite=False)
while (s[0] <= 0):
np.fill_diagonal(K, d*(1+factor))
factor*=2
s = la.eigh(K, eigvals_only=True, eigvals=(0,0), check_finite=False)
if (factor>1e-8): print 'inflated the diagonal of K by %0.5e'%(1+factor)
K /= np.mean(np.diag(K))
#np.savetxt('../example/relatedness_n50_fixed.txt', K, delimiter='\t',fmt='%0.4f'); sys.exit(0)
#load predictor
covToTest = np.loadtxt(predictor_file, dtype=np.float)
#load covariates
covars=None
if (covars_file is not None):
covars = np.loadtxt(covars_file)
covars_std = covars.std(axis=0, ddof=1)
is_const = (covars_std == 0)
if (np.all(is_const)): covars=None
else:
covars = covars[:, ~is_const]
covars -= covars.mean(axis=0)
covars /= covars_std[~is_const]
if (kernel2 is None): return K, yMat, rMat, covToTest, covars, snpNames_y
else: return (K, K2), yMat, rMat, covToTest, covars, snpNames_y
def solve_binom(y, r, X, return_ll=False):
#compute beta with IRLS
prev_beta = np.zeros(X.shape[1])
dlp_f = np.empty(y.shape[0])
d2lp_f = np.empty(y.shape[0])
dummy = np.empty(y.shape[0])
beta = prev_beta
prev_ll = np.inf
ll = 0
tol = 1e-6
iter=0
while (np.abs(ll-prev_ll) > tol):
iter+=1
f = X.dot(beta)
lp = laplace_cython.likBinomLaplace(y, f, r, dlp_f, d2lp_f, dummy)
d2lp_f = -d2lp_f
dlp_beta = dlp_f.dot(X)
d2lp_beta = -(X.T*d2lp_f).dot(X)
L = la.cho_factor(d2lp_beta, overwrite_a=True, check_finite=False)
beta = prev_beta + la.cho_solve(L, dlp_beta)
prev_beta = beta
prev_ll = ll
ll = lp
if return_ll: return beta, ll
return beta
def nll_bb2(bb_rho, covars, y, r, returnBeta=False):
tol1 = 1e-6
mudiff=1.0
n_iter=0
max_iter=50
fixed_effects = np.zeros(covars.shape[1])
while (mudiff>tol1 and n_iter<max_iter):
n_iter+=1
Xbeta = covars.dot(fixed_effects)
mu = r * (1 - 1.0 / (np.exp(Xbeta) + 1))
M_sqr = mu*(1-mu/r)*(1+(r-1)*bb_rho) #equivalent to Gamma from the Carat paper
M_sqr[M_sqr<1e-12] = 1e-12
D = (mu * (1-mu/r))[:, np.newaxis] * covars
M_sqr_inv = 1.0/M_sqr
smallM = (M_sqr<=1e-12)
M_sqr_inv[smallM] = 1e12
temp = D.T * M_sqr_inv
DT_invOmega_D = temp.dot(D)
DT_invOmega_yc = temp.dot(y-mu)
L = la.cho_factor(DT_invOmega_D, overwrite_a=True, check_finite=False)
fixed_effects += la.cho_solve(L, DT_invOmega_yc, overwrite_b=True, check_finite=False)
Xbeta_new = covars.dot(fixed_effects)
mu_new = r * (1 - 1.0 / (np.exp(Xbeta_new) + 1))
mudiff = np.abs(mu-mu_new).sum()
if returnBeta: return fixed_effects
sum_ab = (1-bb_rho) / bb_rho
mu_p = 1.0 / (1 + np.exp(-covars.dot(fixed_effects)))
alpha = mu_p * sum_ab
beta = sum_ab - alpha
ll = np.sum(scipy.special.betaln(y + alpha, r - y + beta) - scipy.special.betaln(alpha, beta))
if (np.isnan(ll)): return np.inf
return -ll
def perform_ewas_fixed_bb_lr(mcounts, counts, kernel, predictor, covars, verbose=False, out_file=None):
K, yMat, rMat, covToTest, covars, snpNames = readMacauTest(mcounts, counts, kernel, predictor, covars, correctK=False)
covars_null = np.ones((yMat.shape[1],1))
if (covars is not None): covars_null = np.concatenate((covars_null, covars), axis=1)
covars_alt = np.concatenate((covars_null, np.row_stack(covToTest)), axis=1)
ewas_laplace = EWAS_Laplace()
use_dispersion = True
chi2 = stats.chi2(1)
U = np.eye(K.shape[0])
s = np.ones(K.shape[0])
beta0_null = np.zeros(covars_null.shape[1])
beta0_alt = np.zeros(covars_alt.shape[1])
#print header
out_file_h = open(out_file, 'w')
out_file_h.write('%s\t%s\t%s\t%s\n'%('index', 'id', 'test_stat', 'P-value'))
test_stats = np.zeros(len(snpNames))
t0_ewas = time.time()
for i in xrange(len(snpNames)):
snpName = snpNames[i]
r_i = rMat[i,:]
y_i = yMat[i,:]
#exclude individuals with no data
if (np.sum(r_i>0) < 3): continue
y_i = y_i[r_i>0]
covars_null_i = covars_null[r_i>0,:]
covars_alt_i = covars_alt[r_i>0,:]
U_i = U[r_i>0,:]
r_i = r_i[r_i>0]
try:
nll_null = optimize.minimize_scalar(nll_bb2, args=(covars_null_i, y_i, r_i), method='bounded', bounds=(0,1)).fun
nll_alt = optimize.minimize_scalar(nll_bb2, args=(covars_alt_i, y_i, r_i), method='bounded', bounds=(0,1)).fun
test_stats[i] = 2*(nll_null - nll_alt)
except:
test_stats[i] = np.nan
out_file_h.write('%d\t%s\t%0.4f\t%0.5e\n'%(i+1, snpName, test_stats[i], chi2.sf(test_stats[i])))
out_file_h.close()
print
print '#total EWAS time: %0.2f minutes'%((time.time()-t0_ewas) / 60.0)
def perform_ewas_laplace(mcounts, counts, kernel, predictor, covars, verbose=False, kernel2=None, out_file=None):
K, yMat, rMat, covToTest, covars, snpNames = readMacauTest(mcounts, counts, kernel, predictor, covars, correctK=False, kernel2=kernel2)
if (kernel2 is not None): K, K2 = K
returnGrad = True
opt = 'L-BFGS-B'
test = 'wald'
inv_tol = -1 #1e-5
num_simu = 0
#create kernels
num_kernels = 2
if (kernel2 is not None): num_kernels+=1
kernel_params = np.ones(num_kernels) * np.log(0.5)
kernels = np.empty((num_kernels, K.shape[0], K.shape[1]))
kernels[0,:,:] = K
if (kernel2 is not None): kernels[1,:,:] = K2
kernels[-1,:,:] = np.eye(K.shape[0])
test_stats = np.zeros(len(snpNames))
covars_null = np.ones((yMat.shape[1],1))
if (covars is not None): covars_null = np.concatenate((covars_null, covars), axis=1)
covars_alt = np.concatenate((covars_null, np.row_stack(covToTest)), axis=1)
num_pcs = 0
s,U = la.eigh(K)
ind = np.argsort(s)[::-1]
s = s[ind]
U = U[:, ind]
U = U[:, s>0]
s = s[s>0]
covars_null_fixed = np.concatenate((covars_null, U[:, :num_pcs]), axis=1)
covars_alt_fixed = np.concatenate((covars_alt, U[:, :num_pcs]), axis=1)
ewas_laplace = EWAS_Laplace()
params0_null = np.concatenate((kernel_params, np.zeros(covars_null.shape[1])))
params0_alt = np.concatenate((kernel_params, np.zeros(covars_alt.shape[1])))
out_file_h = open(out_file, 'w')
out_file_h.write('%s\t%s\t%s\t%s\t%s\n'%('index', 'id', 'test_stat', 'P-value', 'time'))
chi2 = stats.chi2(1)
t0_ewas = time.time()
for i in xrange(len(snpNames)):
snpName = snpNames[i]
r_i = rMat[i,:]
y_i = yMat[i,:]
if (np.sum(r_i>0) < 3): continue
is_good = (r_i>0)
y_i = y_i[is_good]
covars_null_i = np.asfortranarray(covars_null[is_good, :])
covars_alt_i = np.asfortranarray(covars_alt[is_good, :])
covars_null_fixed_i = covars_null_fixed[is_good, :]
covars_alt_fixed_i = covars_alt_fixed[is_good, :]
kernels_i = kernels[np.ix_(np.ones(num_kernels, dtype=np.bool), is_good, is_good)]
r_i = r_i[is_good]
if (np.all(y_i==r_i)): continue
t0_site = time.time()
test_stats[i], test_info = ewas_laplace.testBeta(params0_null=params0_null, params0_alt=params0_alt, kernels=kernels_i, covars_null=covars_null_i, covars_alt=covars_alt_i, y=y_i, r=r_i, verbose=verbose, opt=opt, covars_null_fixed=covars_null_fixed_i, covars_alt_fixed=covars_alt_fixed_i, test=test, returnGrad=returnGrad, inv_tol=inv_tol, num_simu=num_simu, ZC_direct=False)
pvalue = chi2.sf(test_stats[i])
if (pvalue < 1e-6): #because of some strange bug...
test_stats[i], test_info = ewas_laplace.testBeta(params0_null=params0_null, params0_alt=params0_alt, kernels=kernels_i, covars_null=covars_null_i, covars_alt=covars_alt_i, y=y_i, r=r_i, verbose=verbose, opt=opt, covars_null_fixed=covars_null_fixed_i, covars_alt_fixed=covars_alt_fixed_i, test=test, returnGrad=returnGrad, inv_tol=inv_tol, num_simu=num_simu, ZC_direct=True)
pvalue = chi2.sf(test_stats[i])
if (pvalue < 1e-16): test_stats[i], pvalue = np.nan, np.nan
out_file_h.write('%d\t%s\t%0.4f\t%0.5e\t%0.2f\n'%(i+1, snpName, test_stats[i], pvalue, time.time()-t0_site))
out_file_h.close()
print
print '#total EWAS time: %0.2f minutes'%((time.time()-t0_ewas) / 60.0)
if __name__ == '__main__':
import argparse
parser = argparse.ArgumentParser()
parser.add_argument('--mcounts', metavar='mcounts', default=None, required=True, help='mcounts file')
parser.add_argument('--counts', metavar='counts', default=None, required=True, help='counts file')
parser.add_argument('--kernel', metavar='kernel', default=None, required=True, help='kernel file')
parser.add_argument('--kernel2', metavar='kernel2', default=None, help='kernel2 file')
parser.add_argument('--predictor', metavar='predictor', default=None, required=True, help='predictor file')
parser.add_argument('--covars', metavar='covars', default=None, help='covariates file')
parser.add_argument('--verbose', metavar='verbose', type=int, default=0, help='verbosity level')
parser.add_argument('--test', metavar='test', default='malax')
parser.add_argument('--out', metavar='out', required=True, help='output file')
args = parser.parse_args()
if (args.test == 'malax'):
perform_ewas_laplace(args.mcounts, args.counts, args.kernel, args.predictor, args.covars, args.verbose>0, kernel2=args.kernel2, out_file=args.out)
elif (args.test == 'bb'):
perform_ewas_fixed_bb_lr(args.mcounts, args.counts, args.kernel, args.predictor, args.covars, args.verbose>0, out_file=args.out)
else:
raise Exception('unknown test')