def _initMean(self, Y, F=None, tol=1e-6):
"""
initialize the mean term
Args:
F: sample design of the fixed effect
"""
if F is not None:
R = LA.qr(F, mode='r')[0][:F.shape[1], :]
I = (abs(R.diagonal()) > tol)
if SP.any(~I):
warnings.warn(
'cols ' + str(SP.where(~I)[0]) +
' have been removed because linearly dependent on the others'
)
self.F = F[:, I]
else:
self.F = None
#dimensions
self.N, self.P = Y.shape
#get F and Y
self.Y = Y
# build mean
self.mean = mean(Y)
if F is not None:
A = SP.eye(self.P)
self.mean.addFixedEffect(F=self.F, A=A)
def fitPairwiseModel(Y,XX=None,S_XX=None,U_XX=None,verbose=False):
N,P = Y.shape
""" initilizes parameters """
RV = fitSingleTraitModel(Y,XX=XX,S_XX=S_XX,U_XX=U_XX,verbose=verbose)
Cg = covariance.freeform(2)
Cn = covariance.freeform(2)
gp = gp2kronSum(mean(Y[:,0:2]),Cg,Cn,XX=XX,S_XX=S_XX,U_XX=U_XX)
conv2 = SP.ones((P,P),dtype=bool)
rho_g = SP.ones((P,P))
rho_n = SP.ones((P,P))
for p1 in range(P):
for p2 in range(p1):
if verbose:
print '.. fitting correlation (%d,%d)'%(p1,p2)
gp.setY(Y[:,[p1,p2]])
Cg_params0 = SP.array([SP.sqrt(RV['varST'][p1,0]),1e-6*SP.randn(),SP.sqrt(RV['varST'][p2,0])])
Cn_params0 = SP.array([SP.sqrt(RV['varST'][p1,1]),1e-6*SP.randn(),SP.sqrt(RV['varST'][p2,1])])
params0 = {'Cg':Cg_params0,'Cn':Cn_params0}
conv2[p1,p2],info = OPT.opt_hyper(gp,params0,factr=1e3)
rho_g[p1,p2] = Cg.K()[0,1]/SP.sqrt(Cg.K().diagonal().prod())
rho_n[p1,p2] = Cn.K()[0,1]/SP.sqrt(Cn.K().diagonal().prod())
conv2[p2,p1] = conv2[p1,p2]; rho_g[p2,p1] = rho_g[p1,p2]; rho_n[p2,p1] = rho_n[p1,p2]
RV['Cg0'] = rho_g*SP.dot(SP.sqrt(RV['varST'][:,0:1]),SP.sqrt(RV['varST'][:,0:1].T))
RV['Cn0'] = rho_n*SP.dot(SP.sqrt(RV['varST'][:,1:2]),SP.sqrt(RV['varST'][:,1:2].T))
RV['conv2'] = conv2
#3. regularizes covariance matrices
offset_g = abs(SP.minimum(LA.eigh(RV['Cg0'])[0].min(),0))+1e-4
offset_n = abs(SP.minimum(LA.eigh(RV['Cn0'])[0].min(),0))+1e-4
RV['Cg0_reg'] = RV['Cg0']+offset_g*SP.eye(P)
RV['Cn0_reg'] = RV['Cn0']+offset_n*SP.eye(P)
RV['params0_Cg']=LA.cholesky(RV['Cg0_reg'])[SP.tril_indices(P)]
RV['params0_Cn']=LA.cholesky(RV['Cn0_reg'])[SP.tril_indices(P)]
return RV
def fitPairwiseModel(Y, XX=None, S_XX=None, U_XX=None, verbose=False):
N, P = Y.shape
""" initilizes parameters """
RV = fitSingleTraitModel(Y, XX=XX, S_XX=S_XX, U_XX=U_XX, verbose=verbose)
Cg = covariance.freeform(2)
Cn = covariance.freeform(2)
gp = gp2kronSum(mean(Y[:, 0:2]), Cg, Cn, XX=XX, S_XX=S_XX, U_XX=U_XX)
conv2 = SP.ones((P, P), dtype=bool)
rho_g = SP.ones((P, P))
rho_n = SP.ones((P, P))
for p1 in range(P):
for p2 in range(p1):
if verbose:
print '.. fitting correlation (%d,%d)' % (p1, p2)
gp.setY(Y[:, [p1, p2]])
Cg_params0 = SP.array([
SP.sqrt(RV['varST'][p1, 0]), 1e-6 * SP.randn(),
SP.sqrt(RV['varST'][p2, 0])
])
Cn_params0 = SP.array([
SP.sqrt(RV['varST'][p1, 1]), 1e-6 * SP.randn(),
SP.sqrt(RV['varST'][p2, 1])
])
params0 = {'Cg': Cg_params0, 'Cn': Cn_params0}
conv2[p1, p2], info = OPT.opt_hyper(gp, params0, factr=1e3)
rho_g[p1, p2] = Cg.K()[0, 1] / SP.sqrt(Cg.K().diagonal().prod())
rho_n[p1, p2] = Cn.K()[0, 1] / SP.sqrt(Cn.K().diagonal().prod())
conv2[p2, p1] = conv2[p1, p2]
rho_g[p2, p1] = rho_g[p1, p2]
rho_n[p2, p1] = rho_n[p1, p2]
RV['Cg0'] = rho_g * SP.dot(SP.sqrt(RV['varST'][:, 0:1]),
SP.sqrt(RV['varST'][:, 0:1].T))
RV['Cn0'] = rho_n * SP.dot(SP.sqrt(RV['varST'][:, 1:2]),
SP.sqrt(RV['varST'][:, 1:2].T))
RV['conv2'] = conv2
#3. regularizes covariance matrices
offset_g = abs(SP.minimum(LA.eigh(RV['Cg0'])[0].min(), 0)) + 1e-4
offset_n = abs(SP.minimum(LA.eigh(RV['Cn0'])[0].min(), 0)) + 1e-4
RV['Cg0_reg'] = RV['Cg0'] + offset_g * SP.eye(P)
RV['Cn0_reg'] = RV['Cn0'] + offset_n * SP.eye(P)
RV['params0_Cg'] = LA.cholesky(RV['Cg0_reg'])[SP.tril_indices(P)]
RV['params0_Cn'] = LA.cholesky(RV['Cn0_reg'])[SP.tril_indices(P)]
return RV
def fitSingleTraitModel(Y,XX=None,S_XX=None,U_XX=None,verbose=False):
""" fit single trait model """
N,P = Y.shape
RV = {}
Cg = covariance.lowrank(1)
Cn = covariance.lowrank(1)
gp = gp2kronSum(mean(Y[:,0:1]),Cg,Cn,XX=XX,S_XX=S_XX,U_XX=U_XX)
params0 = {'Cg':SP.sqrt(0.5)*SP.ones(1),'Cn':SP.sqrt(0.5)*SP.ones(1)}
var = SP.zeros((P,2))
conv1 = SP.zeros(P,dtype=bool)
for p in range(P):
if verbose:
print '.. fitting variance trait %d'%p
gp.setY(Y[:,p:p+1])
conv1[p],info = OPT.opt_hyper(gp,params0,factr=1e3)
var[p,0] = Cg.K()[0,0]
var[p,1] = Cn.K()[0,0]
RV['conv1'] = conv1
RV['varST'] = var
return RV
def _initMean(self,Y,F=None,tol=1e-6):
"""
initialize the mean term
Args:
F: sample design of the fixed effect
"""
if F is not None:
R = LA.qr(F,mode='r')[0][:F.shape[1],:]
I = (abs(R.diagonal())>tol)
if SP.any(~I):
warnings.warn('cols '+str(SP.where(~I)[0])+' have been removed because linearly dependent on the others')
self.F = F[:,I]
else:
self.F = None
#dimensions
self.N,self.P = Y.shape
#get F and Y
self.Y=Y
# build mean
self.mean = mean(Y)
if F is not None:
A = SP.eye(self.P)
self.mean.addFixedEffect(F=self.F,A=A)
def fitSingleTraitModel(Y, XX=None, S_XX=None, U_XX=None, verbose=False):
""" fit single trait model """
N, P = Y.shape
RV = {}
Cg = covariance.lowrank(1)
Cn = covariance.lowrank(1)
gp = gp2kronSum(mean(Y[:, 0:1]), Cg, Cn, XX=XX, S_XX=S_XX, U_XX=U_XX)
params0 = {
'Cg': SP.sqrt(0.5) * SP.ones(1),
'Cn': SP.sqrt(0.5) * SP.ones(1)
}
var = SP.zeros((P, 2))
conv1 = SP.zeros(P, dtype=bool)
for p in range(P):
if verbose:
print '.. fitting variance trait %d' % p
gp.setY(Y[:, p:p + 1])
conv1[p], info = OPT.opt_hyper(gp, params0, factr=1e3)
var[p, 0] = Cg.K()[0, 0]
var[p, 1] = Cn.K()[0, 0]
RV['conv1'] = conv1
RV['varST'] = var
return RV
Xr*= SP.sqrt(N/(Xr**2).sum())
# define mean term
mu = mean(Y)
# add first fixed effect
F = 1.*(SP.rand(N,2)<0.2); A = SP.eye(P)
# add second fixed effect
F2 = 1.*(SP.rand(N,3)<0.2); A2 = SP.ones((1,P))
mu.addFixedEffect(F=F,A=A)
mu.addFixedEffect(F=F2,A=A2)
if mtSet_present:
mu1 = MEAN.mean(Y)
mu1.addFixedEffect(F=F,A=A)
mu1.addFixedEffect(F=F2,A=A2)
# define covariance matrices
Cg = freeform(P)
Cn = freeform(P)
Cg1 = freeform(P)
Cn1 = freeform(P)
ipdb.set_trace()
if 1:
# compare with mtSet implementation
params = {}
Xr*= SP.sqrt(N/(Xr**2).sum())
# define mean term
mu = mean(Y)
# add first fixed effect
F = 1.*(SP.rand(N,2)<0.2); A = SP.eye(P)
# add second fixed effect
F2 = 1.*(SP.rand(N,3)<0.2); A2 = SP.ones((1,P))
mu.addFixedEffect(F=F,A=A)
mu.addFixedEffect(F=F2,A=A2)
if mtSet_present:
mu1 = MEAN.mean(Y)
mu1.addFixedEffect(F=F,A=A)
mu1.addFixedEffect(F=F2,A=A2)
# define covariance matrices
Cg = freeform(P)
Cn = freeform(P)
Cg1 = freeform(P)
Cn1 = freeform(P)
ipdb.set_trace()
if 1:
# compare with mtSet implementation
params = {}
if not os.path.exists(out_file) or 'recalc' in sys.argv:
Ns = sp.array([100,150,200,300,500,800,1200,1600,2000,3000,4000,5000])
n_rips = 5
t = sp.zeros((Ns.shape[0], n_rips))
t0 = sp.zeros((Ns.shape[0], n_rips))
r = sp.zeros((Ns.shape[0], n_rips))
for ni, n in enumerate(Ns):
for ri in range(n_rips):
print '.. %d individuals - rip %d' % (n, ri)
print ' .. generating data'
Y, S, U, G = gen_data(N=n, P=P)
# define GPs
gp = GP3KronSumLR(Y = Y, Cg = Cg, Cn = Cn, S_R = S, U_R = U, G = G, rank = 1)
gp0 = gp3ks0(mean(Y), covariance.freeform(P), covariance.freeform(P), S_XX=S, U_XX=U, rank=1)
gp0.set_Xr(G)
gp._reset_profiler()
if 1:
gp.covar.setRandomParams()
else:
n_params = gp.covar.Cr.getNumberParams()
n_params+= gp.covar.Cg.getNumberParams()
n_params+= gp.covar.Cn.getNumberParams()
params1 = {'covar': sp.randn(n_params)}
gp.setParams(params1)
params = {}
params['Cr'] = gp.covar.Cr.getParams().copy()
params['Cg'] = gp.covar.Cg.getParams().copy()
params['Cn'] = gp.covar.Cn.getParams().copy()
# generate data
h2 = 0.3
N = 2000; P = 4; S = 1000
X = 1.*(SP.rand(N,S)<0.2)
beta = SP.randn(S,P)
Yg = SP.dot(X,beta); Yg*=SP.sqrt(h2/Yg.var(0).mean())
Yn = SP.randn(N,P); Yn*=SP.sqrt((1-h2)/Yn.var(0).mean())
Y = Yg+Yn; Y-=Y.mean(0); Y/=Y.std(0)
XX = SP.dot(X,X.T)
XX/= XX.diagonal().mean()
Xr = 1.*(SP.rand(N,10)<0.2)
Xr*= SP.sqrt(N/(Xr**2).sum())
# define mean term
mean = MEAN.mean(Y)
# add first fixed effect
F = 1.*(SP.rand(N,2)<0.2); A = SP.eye(P)
mean.addFixedEffect(F=F,A=A)
# add first fixed effect
F = 1.*(SP.rand(N,3)<0.2); A = SP.ones((1,P))
mean.addFixedEffect(F=F,A=A)
# define covariance matrices
Cg = limix.CFreeFormCF(P)
Cn = limix.CFreeFormCF(P)
if 0:
# generate parameters
params = {}
params['Cg'] = SP.randn(int(0.5*P*(P+1)))
if not os.path.exists(out_file) or 'recalc' in sys.argv:
Ns = sp.array(
[100, 150, 200, 300, 500, 800, 1200, 1600, 2000, 3000, 4000, 5000])
n_rips = 5
t = sp.zeros((Ns.shape[0], n_rips))
t0 = sp.zeros((Ns.shape[0], n_rips))
r = sp.zeros((Ns.shape[0], n_rips))
for ni, n in enumerate(Ns):
for ri in range(n_rips):
print '.. %d individuals - rip %d' % (n, ri)
print ' .. generating data'
Y, S, U, G = gen_data(N=n, P=P)
# define GPs
gp = GP3KronSumLR(Y=Y, Cg=Cg, Cn=Cn, S_R=S, U_R=U, G=G, rank=1)
gp0 = gp3ks0(mean(Y),
covariance.freeform(P),
covariance.freeform(P),
S_XX=S,
U_XX=U,
rank=1)
gp0.set_Xr(G)
gp._reset_profiler()
if 1:
gp.covar.setRandomParams()
else:
n_params = gp.covar.Cr.getNumberParams()
n_params += gp.covar.Cg.getNumberParams()
n_params += gp.covar.Cn.getNumberParams()
params1 = {'covar': sp.randn(n_params)}
