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MU_LMM.py
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MU_LMM.py
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###########
##Implements the MU matrix class for
##PrivLMM (see manuscript)
###################
import numpy as np;
from MU_Mat import MU_Mat;
from MU_Mat import MU_Mem;
import math;
from numpy.linalg import inv
import math;
from numpy.random import permutation as perm
import os;
from pysnptools.util import intersect_apply;
from pysnptools.snpreader import Bed;
from pysnptools.snpreader import Pheno;
from os.path import isfile;
from numpy.random import laplace as Lap;
from fastlmm.inference import LMM;
class MU_LMM(MU_Mem):
##
##Implementation of calc MU matrix for PrivLMM
##
def calcMU(self,par=[]):
se2=-1;
sg2=-1;
if isinstance(par,tuple):
se2=float(par[0]);
sg2=float(par[1])
if se2<0:
num=par[0];
epsilon=par[1];
if len(par)>2:
self.VarCalc=par[2];
else:
self.VarCalc=FastLMM();
print "Calculate variance"
[se2,sg2]=self.estVar(num,epsilon)
self.se2=se2;
self.sg2=sg2;
n=len(self.X);
m=len(self.X[0])
print "Taking inverse!"
Kinv=inv(np.eye(n)*se2+sg2/float(m)*np.dot(self.X,(self.X).T))
print "Calc Top"
self.MU=np.dot(self.X.T,Kinv);
print "Calc Bottom"
bot=np.asarray([math.sqrt(np.dot(self.X[:,i],self.MU[i])) for i in range(0,m)])
print "Divide through!!"
self.MU=self.MU/bot[:,np.newaxis]
print "Center!"
mn=np.mean(self.MU,axis=1);
print len(mn);
print np.sum(Kinv);
#self.MU=np.dot(self.MU,(np.eye(n)-np.ones((n,n)))/np.sum(Kinv) );
self.MU=self.MU-mn[:,np.newaxis];
print "Done!";
##
##estimates the variance of y
##
def estVarY(self,y,epsilon):
vr=np.var(y);
n=len(y);
return vr+Lap(0,3/float(epsilon*n))
##
##Divide data!
##
def divideData(self,filename,num=5,mph=3,delet=True):
print "Estimating heritability using "+str(num)+" components"
direct="TEMP"
sFil=Bed(filename);
yFil=Pheno(filename+".fam");
n=sFil.iid_count
reOrd=perm(n);
yFil=yFil[reOrd,:];
sFil=sFil[reOrd,:];
y=yFil.read().val[:,3];
div=[int(math.ceil( i*n/float(num) )) for i in range(0,num+1)];
varEsts=[];
for i in range(0,num):
print "For component "+str(i);
sFilTemp=self.BED[div[i]:div[i+1],:];
Xtemp=sFilTemp.read().standardize().val;
ytemp=y[div[i]:div[i+1]];
varEsts.append(self.VarCalc.RealVar(ytemp,Xtemp));
return varEsts;
##
##Estimate Variance in \epsilon-DP way!
##
def estVar(self,num,epsilon):
filename=self.BED.filename;
y=Pheno(filename+".fam").read().val[:,3];
varEsts=self.divideData(filename,num=num);
if epsilon<0:
return varEsts[0];
e1=.1*epsilon;
e2=.45*epsilon;
e3=.45*epsilon;
vary=self.estVarY(y,e1);
se2=sum([v[1] for v in varEsts])/float(num)+Lap(0.0,vary/(e2*float(num)));
if se2<0:
se2=0;
if se2>vary:
se2=vary;
sg2=sum([v[0] for v in varEsts])/float(num)+Lap(0.0,vary/(e3*float(num)));
if sg2<0:
sg2=.01*vary;
if sg2>vary:
sg2=vary;
return [sg2,se2];
##
##Class used to estimate variance
##
class VarEstimator:
def realVar(self,y,X):
raise NotImplementedError("Not implemented!");
from fastlmm.inference import LMM;
##
##Uases FASTLMM
##
class FastLMM():
##
##uses REML to estimate variance components
##
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];