def setUp(self):
np.random.seed(1)
# generate data
N = 400
s_x = 0.05
s_y = 0.1
X = (sp.linspace(0,2,N)+s_x*sp.randn(N))[:,sp.newaxis]
Y = sp.sin(X)+s_y*sp.randn(N,1)
Y-= Y.mean(0)
Y/= Y.std(0)
Xstar = sp.linspace(0,2,1000)[:,sp.newaxis]
# define mean term
F = 1.*(sp.rand(N,2)<0.2)
mean = lin_mean(Y,F)
# define covariance matrices
covar1 = SQExpCov(X,Xstar=Xstar)
covar2 = FixedCov(sp.eye(N))
covar = SumCov(covar1,covar2)
# define gp
self._gp = GP(covar=covar,mean=mean)
def setUp(self):
np.random.seed(1)
# generate data
N = 400
s_x = 0.05
s_y = 0.1
X = (sp.linspace(0, 2, N) + s_x * sp.randn(N))[:, sp.newaxis]
Y = sp.sin(X) + s_y * sp.randn(N, 1)
Y -= Y.mean(0)
Y /= Y.std(0)
Xstar = sp.linspace(0, 2, 1000)[:, sp.newaxis]
# define mean term
F = 1.0 * (sp.rand(N, 2) < 0.2)
mean = lin_mean(Y, F)
# define covariance matrices
covar1 = SQExpCov(X, Xstar=Xstar)
covar2 = FixedCov(sp.eye(N))
covar = SumCov(covar1, covar2)
# define gp
self._gp = GP(covar=covar, mean=mean)
def setUp(self):
np.random.seed(1)
N = 400
s_x = 0.05
s_y = 0.1
X = (np.linspace(0, 2, N) + s_x * np.random.randn(N))[:, np.newaxis]
Y = np.sin(X) + s_y * np.random.randn(N, 1)
#pl.plot(x,y,'x')
# define mean term
F = 1. * (np.random.rand(N, 2) < 0.2)
mean = lin_mean(Y, F)
# define covariance matrices
covar1 = sqexp(X)
covar2 = fixed(np.eye(N))
covar = sumcov(covar1, covar2)
def setUp(self):
np.random.seed(1)
N = 400
s_x = 0.05
s_y = 0.1
X = (np.linspace(0, 2, N) + s_x * np.random.randn(N))[:, np.newaxis]
Y = np.sin(X) + s_y * np.random.randn(N, 1)
# pl.plot(x,y,'x')
# define mean term
F = 1.0 * (np.random.rand(N, 2) < 0.2)
mean = lin_mean(Y, F)
# define covariance matrices
covar1 = sqexp(X)
covar2 = fixed(np.eye(N))
covar = sumcov(covar1, covar2)
def VD(self, DGE, IGE, IEE, cageEffect):
""" defines covariance for variance decomposition."""
#defines mean
mean = lin_mean(self.pheno,self.covs)
#define cagemate assignment - required for SGE, SEE, and cage effects. Z is N focal x N_cm and has 0s in cells Z_i,i (i.e. an animal is not its own cage mate)
same_cage = 1. * (self.cage==self.cage_cm)
diff_inds = 1. * (self.sampleID[:,sp.newaxis]!=self.sampleID_cm)
Z = same_cage * diff_inds
#define the overall genetic covariance matrix
if DGE or IGE:
#scales kinship (DGE component) to sample variance 1
sf_K = covar_rescaling_factor(self.kinship)
self.kinship *= sf_K
#now create and scale SGE and DGE/SGE covariance components
if IGE:
#first SGE component: ZKcmZ' in this code (ZKZ' in paper)
_ZKcmZ = sp.dot(Z,sp.dot(self.kinship_cm,Z.T))
sf_ZKcmZ = covar_rescaling_factor(_ZKcmZ)
self.kinship_cm *= sf_ZKcmZ
#second DGE/SGE covariance:
self.kinship_cross *= sp.sqrt(sf_K * sf_ZKcmZ)
if DGE and not IGE:
self._genoCov = FixedCov(self.kinship)
elif IGE and not DGE:
self._genoCov = FixedCov(_ZKcmZ)
elif DGE and IGE:
self._genoCov = DirIndirCov(self.kinship,Z,kinship_cm=self.kinship_cm,kinship_cross=self.kinship_cross)
else:
self._genoCov = None
#define the overall environmental covariance matrix
#there is always DEE
#env naturally has sample variance 1 so no need to scale it
if IEE:
#_ZZ = ZIcmZ'
_ZZ = sp.dot(Z,Z.T)
sf_ZZ = covar_rescaling_factor(_ZZ)
self.env_cm *= sf_ZZ
self.env_cross *= sp.sqrt(1 * sf_ZZ)
self._envCov = DirIndirCov(self.env,Z,kinship_cm=self.env_cm,kinship_cross=self.env_cross)
else:
self._envCov = FixedCov(self.env)
##define cage effect covariance matrix
if cageEffect:
N = self.pheno.shape[0]
uCage = sp.unique(self.cage)
#W, the cage design matrix, is N x n_cages (where N is number of focal animals)
W = sp.zeros((N,uCage.shape[0]))
for cv_i, cv in enumerate(uCage):
W[:,cv_i] = 1.*(self.cage[:,0]==cv)
#WW, the cage effect covariance matrix, is N x N and has 1s in cells WW_i,i
WW = sp.dot(W,W.T)
#this is equivalent to getting covar_rescaling_factor first and then multiplying, as done for other matrices above
WW = covar_rescale(WW)
self._cageCov = FixedCov(WW)
else:
self._cageCov = None
# define overall covariance matrix as sum of genetic, environmental and cage covariance matrices
if self._genoCov is None:
if self._cageCov is None:
self.covar = SumCov(self._envCov)
else:
self.covar = SumCov(self._envCov,self._cageCov)
else:
if self._cageCov is None:
self.covar = SumCov(self._genoCov,self._envCov)
else:
self.covar = SumCov(self._genoCov,self._envCov,self._cageCov)
## define gp
self._gp = GP(covar=self.covar,mean=mean)
sp.random.seed(1)
if __name__ == "__main__":
# generate data
N = 400
X = sp.linspace(0,2,N)[:,sp.newaxis]
v_noise = 0.01
Y = sp.sin(X) + sp.sqrt(v_noise) * sp.randn(N, 1)
# for out-of-sample preditions
Xstar = sp.linspace(0,2,1000)[:,sp.newaxis]
# define mean term
W = 1. * (sp.rand(N, 2) < 0.2)
mean = lin_mean(Y, W)
# define covariance matrices
sqexp = SQExpCov(X, Xstar = Xstar)
noise = FixedCov(sp.eye(N))
covar = SumCov(sqexp, noise)
# define gp
gp = GP(covar=covar,mean=mean)
# initialize params
sqexp.scale = 1e-4
sqexp.length = 1
noise.scale = Y.var()
# optimize
gp.optimize(calc_ste=True)
# predict out-of-sample