/
mleem.py
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/
mleem.py
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'''
Defining the core EM MLE approach
'''
import re
import sys
import scipy
from scipy.stats import nbinom
from scipy.stats import norm
import random
import math
import numpy as np
import numpy.linalg as linalg
import copy
from mageck_nest.mleclassdef import *
from mageck_nest.mledesignmat import *
import logging
def getloglikelihood2(kmat,mu_estimate,alpha,sumup=False,log=True):
'''
Get the log likelihood estimation of NB, using the current estimation of beta
'''
if kmat.shape[0] != mu_estimate.shape[0]:
raise ValueError('Count table dimension is not the same as mu vector dimension.')
alpha=np.matrix(alpha).reshape(mu_estimate.shape[0],mu_estimate.shape[1])
kmat_r=np.round(kmat)
mu_sq=np.multiply(mu_estimate,mu_estimate)
var_vec=mu_estimate+np.multiply(alpha, mu_sq)
nb_p=np.divide(mu_estimate,var_vec)
nb_r=np.divide(mu_sq,var_vec-mu_estimate)
if log:
logp=nbinom.logpmf(kmat_r,nb_r,nb_p)
else:
logp=nbinom.pmf(kmat,nb_r,nb_p)
if np.isnan(np.sum(logp)):
#raise ValueError('nan values for log likelihood!')
logp=np.where(np.isnan(logp),0,logp)
if sumup:
return np.sum(logp)
else:
return logp
def getloglikelihood3(kmat,mu_estimate,alpha,sumup=False,log=True):
'''
Get the log likelihood estimation of NB, using the current estimation of beta
'''
if kmat.shape[0] != mu_estimate.shape[0]:
raise ValueError('Count table dimension is not the same as mu vector dimension.')
alpha=np.matrix(alpha).reshape(mu_estimate.shape[0],mu_estimate.shape[1])
kmat_r=np.round(kmat)
mu_sq=np.multiply(mu_estimate,mu_estimate)
var_vec=mu_estimate+np.multiply(alpha, mu_sq)
nb_p=np.divide(mu_estimate,var_vec)
nb_r=np.divide(mu_sq,var_vec-mu_estimate)
p=nbinom.cdf(kmat,nb_r,nb_p)
p=np.where(p<0.5,p,1-p)
if log:
#logp=nbinom.logcdf(kmat_r,nb_r,nb_p)
logp=np.log(p)
else:
logp=p
#logp=nbinom.cdf(kmat,nb_r,nb_p)
#
if np.isnan(np.sum(logp)):
#raise ValueError('nan values for log likelihood!')
logp=np.where(np.isnan(logp),0,logp)
if sumup:
return np.sum(logp)
else:
return logp
def iteratenbem(sk,debug=True,estimateeff=False,updateeff=True,plot=False,PPI_prior=False,alpha_val=0.01,meanvarmodel=None,restart=True,removeoutliers=False,size_factor=None,beta1_prior_var=None):
# parameters
n_max_init=1000
diff_cutoff=1e-9
n=(sk.nb_count.shape[1])
nallsample=sk.design_mat.shape[0]
nsample=sk.design_mat.shape[0]-1 # the number of samples excluding the 1st base sample
nbeta1=sk.design_mat.shape[1]-1 # the number of betas excluding the 1st beta (baseline beta)
logll_list=[] # log likelihood
if DesignMatCache.has_record(n) == False:
DesignMatCache.save_record(sk.design_mat,n)
if DesignMatCache.has_record(n) == True:
(basesampleid,design_mat,extdesign_mat,extdesignmat_residule)=DesignMatCache.get_record(n)
else:
raise ValueError('There is no corresponding record in DesignMatCache.')
extdesign_mat=extdesign_mat[:(sk.nb_count.shape[0])*(sk.nb_count.shape[1]),]
sk.extended_design_mat=extdesign_mat
if PPI_prior==False:
if beta1_prior_var!=None:
beta1_prior_inverse_variance=[1/i for i in beta1_prior_var]
else:
beta1_prior_inverse_variance=[0]*nbeta1
else:
beta1_prior_inverse_variance=[1/i for i in sk.prior_variance]
beta_prior_mean=np.matrix([0]*n+sk.prior_mean)
beta_prior_mean=beta_prior_mean.reshape(n+len(sk.prior_mean),1)
beta_prior_inverse_variance=[0]*n+beta1_prior_inverse_variance
if size_factor==None:
size_vec=np.ones(n*(nallsample))
else:
if len(size_factor) != nallsample:
raise ValueError('The provided size factor length does not equal to the number of samples.')
size_vec=np.repeat(size_factor,n)
size_mat=np.matrix(size_vec.reshape([nallsample,n]))
size_vec=np.matrix(size_vec).getT()
datak_mat_0=sk.nb_count
datak=datak_mat_0.reshape(datak_mat_0.shape[0]*datak_mat_0.shape[1],1)
sk.sgrna_kvalue=datak
normalized_k=[]
inverse_size_f=[1/i for i in size_factor]
sg_k=[x[0] for x in sk.sgrna_kvalue.tolist()]
for i in range(len(sk.sgrnaid)):
normalized_k_mean=np.mean(np.multiply(inverse_size_f,[sg_k[i+k*n] for k in range(nallsample)]))
normalized_k.append([normalized_k_mean])
normalized_k=normalized_k*nallsample
normalized_datak=np.matrix(normalized_k).reshape(datak_mat_0.shape[0]*datak_mat_0.shape[1],1)
# prepare for the dispersion estimation
if meanvarmodel == None:
alpha_dispersion=alpha_val
alpha_dispersion_mat=alpha_val
else:
alpha_dispersion_mat=np.matrix(meanvarmodel.get_glm_dispersion(normalized_datak,returnalpha=True))
alpha_dispersion=alpha_dispersion_mat.getA1()
stored_alpha_dispersion=copy.copy(alpha_dispersion)
baseline_sample_matrix=np.log(sk.nb_count[basesampleid,:])-np.log(size_mat[basesampleid,:])
if restart==True or len(sk.beta_estimate)==0:
beta_vec1=np.mean(baseline_sample_matrix,axis=0)
beta_vec2=np.log(sk.nb_count[1:,:])-np.log(size_mat[1:,:])-beta_vec1
beta1_meanval=np.mean(beta_vec2,axis=1)
beta1_es_mat=linalg.inv(design_mat.getT()*design_mat+alpha_val*np.matrix(np.identity(design_mat.shape[1])))*design_mat.getT()*(beta1_meanval)
beta_init_mat=np.vstack((beta_vec1.getT(),beta1_es_mat))
else:
beta_init_mat=np.matrix([[x] for x in sk.beta_estimate])
if removeoutliers==False:
eff_list=[1]*n # a list of size nsgRNA
sk.eff_estimate=eff_list
if removeoutliers==True:
eff_list=sk.eff_estimate
eff_index=[i for i,j in enumerate(eff_list+[1]*nbeta1) if j==1]
converting_matrix=np.identity(sk.nb_count.shape[0]*sk.nb_count.shape[1])
efficieent_grna_index=[i for i,x in enumerate(eff_list*nallsample) if x==1]
converting_matrix=converting_matrix[np.ix_(efficieent_grna_index,)]
full_datak=copy.copy(datak)
full_extdesign_mat=copy.copy(extdesign_mat)
full_size_vec=copy.copy(size_vec)
full_beta_init_mat=copy.copy(beta_init_mat)
full_beta_prior_inverse_variance=copy.copy(beta_prior_inverse_variance)
if PPI_prior==True:
full_beta_prior_mean=copy.copy(beta_prior_mean)
beta_prior_mean=beta_prior_mean[eff_index,:]
beta_prior_inverse_variance=[beta_prior_inverse_variance[i] for i in eff_index]
beta_init_mat=beta_init_mat[eff_index,:]
datak=converting_matrix*datak
extdesign_mat=(converting_matrix*extdesign_mat)[:,eff_index]
size_vec=converting_matrix*size_vec
alpha_dispersion=[alpha_dispersion[i] for i in range(len(alpha_dispersion)) if eff_list[i%len(eff_list)]==1]
n_iter=1
beta1_se_mat=None
beta1_new=None
while(True):
if PPI_prior==False:
logmu_estimate=extdesign_mat*beta_init_mat # (nsample*nsgrna)*1 matrix
mu_estimate=(np.multiply(np.exp(logmu_estimate),size_vec))
sgrna_residule=(datak-mu_estimate)
else:
# beta=beta_prior + beta_sec
# mu=mu_prior * mu_sec
# alpha_sec=alpha+(1/mu)-(1/mu_sec)
# K~N_B(mu,alpha)
# K_sec(==K/mu_prior)~N_B(mu_sec,alpha_sec)
if n_iter==1:
beta_init_mat=beta_init_mat-beta_prior_mean
logmu_prior_estimate=extdesign_mat*beta_prior_mean
mu_prior_estimate=np.exp(logmu_prior_estimate)
logmu_estimate=extdesign_mat*beta_init_mat
mu_estimate=(np.multiply(np.exp(logmu_estimate),size_vec))
sgrna_residule=((datak/mu_prior_estimate)-mu_estimate)
mu_prior_list=[i[0] for i in mu_prior_estimate.tolist()]
mu_sec_list=[i[0] for i in mu_estimate.tolist()]
mu_list=[mu_prior_list[i]*mu_sec_list[i] for i in range(len(mu_prior_list))]
inverse_mu_sec_list=[(1/(i+10**(-10))) for i in mu_sec_list]
inverse_mu_list=[1/(i+10**(-10)) for i in mu_list]
alpha_sec_dispersion=[stored_alpha_dispersion[i]+inverse_mu_list[i]-inverse_mu_sec_list[i] for i in range(len(mu_list))]
alpha_sec_dispersion_mat=(np.matrix(alpha_sec_dispersion)).reshape(len(alpha_sec_dispersion),1)
alpha_dispersion=alpha_sec_dispersion
z_estimate=sgrna_residule/mu_estimate + logmu_estimate
w_list=mu_estimate.getA1()
w_list_ele=1.0/((1.0/w_list)+alpha_dispersion)
w_matrix=np.diag(w_list_ele)
xwx_mat=extdesign_mat.getT()*w_matrix*extdesign_mat+np.diag(beta_prior_inverse_variance)
xwx_inv=linalg.inv(xwx_mat)
beta_new=xwx_inv*extdesign_mat.getT()*w_matrix*z_estimate
beta_diff=beta_new-beta_init_mat
if np.isnan(np.sum(beta_new)):
break
else:
beta_init_mat=beta_new
n_iter+=1
diffval=np.sum(beta_diff.getA1()[len([i for i in eff_list if i==1]):]**2)
absval=np.sum(beta_new.getA1()[len([i for i in eff_list if i==1]):]**2)
if abs(absval)<1e-9:
absval=1.0
difffrac=diffval/absval
if n_iter>3:
if difffrac<diff_cutoff or n_iter>n_max_init:
break
if PPI_prior==True:
beta_init_mat=beta_init_mat+beta_prior_mean
logmu_estimate=extdesign_mat*beta_init_mat
mu_estimate=(np.multiply(np.exp(logmu_estimate),size_vec))
sgrna_residule=(datak-mu_estimate)
if removeoutliers==False:
alpha_dispersion=stored_alpha_dispersion
else:
alpha_dispersion=[stored_alpha_dispersion[i] for i in range(len(stored_alpha_dispersion)) if eff_list[i%len(eff_list)]==1]
w_list_ele=1.0/((1.0/mu_estimate.getA1())+alpha_dispersion)
w_matrix=np.diag(w_list_ele)
xwx_mat=extdesign_mat.getT()*w_matrix*extdesign_mat+np.diag(beta_prior_inverse_variance)
xwx_inv=linalg.inv(xwx_mat)
hat_matrix=np.sqrt(w_matrix)*extdesign_mat*xwx_inv*extdesign_mat.getT()*np.sqrt(w_matrix)
v=extdesign_mat.shape[0]-(2*hat_matrix-hat_matrix*hat_matrix.getT()).trace()
temp=((sgrna_residule/mu_estimate).getT()*(sgrna_residule/mu_estimate))/(v)
beta1_se_mat=xwx_inv*extdesign_mat.getT()*w_matrix*w_matrix*extdesign_mat*xwx_inv
#beta1_se_mat=xwx_inv*extdesign_mat.getT()*w_matrix*extdesign_mat*xwx_inv
beta_se_val=(temp.getA1()[0]**(0.5))*np.sqrt(np.diag(beta1_se_mat))
if removeoutliers==True:
beta_new_zscore_list=(beta_init_mat.getA1()/beta_se_val)[len([i for i in eff_list if i==1]):]
else:
beta_new_zscore_list=(beta_init_mat.getA1()/beta_se_val)[n:]
beta_new_pval=norm.sf(np.abs(beta_new_zscore_list))*2
if removeoutliers==True:
eff_index=[[i,j] for i,j in enumerate(eff_index)]
for k in eff_index:
full_beta_init_mat[k[1]]=beta_init_mat[k[0]]
sk.beta_estimate=full_beta_init_mat.getA1()
logmu_estimate=full_extdesign_mat*full_beta_init_mat
mu_estimate=(np.multiply(np.exp(logmu_estimate),full_size_vec))
else:
sk.beta_estimate=beta_init_mat.getA1()
logmu_estimate=extdesign_mat*beta_init_mat
mu_estimate=(np.multiply(np.exp(logmu_estimate),size_vec))
#sk.beta_estimate=beta_init_mat.getA1()
if removeoutliers==True:
sk.beta_se_val=beta_se_val[len([i for i in eff_list if i==1]):]
else:
sk.beta_se_val=beta_se_val[len([i for i in eff_list if i==1]):]
sk.beta_pval=beta_new_pval
sk.beta_zscore=beta_new_zscore_list
#sk.beta_pval_pos=norm.sf(beta_new_zscore_list)
#sk.beta_pval_neg=norm.cdf(beta_new_zscore_list)
sk.mu_estimate=mu_estimate
sk.dispersion_estimate=stored_alpha_dispersion
if meanvarmodel != None:
sk.loglikelihood=getloglikelihood3(sk.sgrna_kvalue,sk.mu_estimate,stored_alpha_dispersion,sumup=False,log=True)