def sample_motif_ar_tilted(matrix, mu, Ne, N):
nu = Ne - 1
L = len(matrix)
ep_min, ep_max, L = sum(map(min, matrix)), sum(map(max,
matrix)), len(matrix)
site_sigma = site_sigma_from_matrix(matrix)
density = lambda ep: (1 / (1 + exp(ep - mu)))**(Ne - 1) * dnorm(
ep, 0, site_sigma) * (ep_min <= ep <= ep_max)
d_density = lambda ep: ep / site_sigma**2 + nu / (1 + exp(mu - ep))
phat = lambda ep: (1 / (1 + exp(ep - mu)))**(Ne - 1)
mode = bisect_interval(d_density, -100, 100)
if mode < ep_min:
mode = ep_min + 1 # don't want mode right on the nose of ep_min for sampling purposes, so offset it a bit
dmode = density(mode)
# calculate mean epsilon via rejection sampling
motif = []
def mean_ep(lamb):
psfm = psfm_from_matrix(matrix, lamb=lamb)
return sum([
ep * p for (mat_row, psfm_row) in zip(matrix, psfm)
for (ep, p) in zip(mat_row, psfm_row)
])
lamb = bisect_interval(lambda l: mean_ep(l) - mode, -20, 20)
tilted_psfm = psfm_from_matrix(matrix, lamb=lamb)
log_tilted_psfm = [map(log, row) for row in tilted_psfm]
while len(motif) < N:
site = random_site(L)
ep = score_seq(matrix, site)
if random.random() < phat(ep) / pmode:
motif.append(site)
return motif
def sample_motif_ar_tilted(matrix, mu, Ne, N):
nu = Ne - 1
L = len(matrix)
ep_min, ep_max, L = sum(map(min,matrix)), sum(map(max,matrix)), len(matrix)
site_sigma = site_sigma_from_matrix(matrix)
density = lambda ep:(1/(1+exp(ep-mu)))**(Ne-1) * dnorm(ep,0,site_sigma)*(ep_min <= ep <= ep_max)
d_density = lambda ep:ep/site_sigma**2 + nu/(1+exp(mu-ep))
phat = lambda ep:(1/(1+exp(ep-mu)))**(Ne-1)
mode = bisect_interval(d_density, -100, 100)
if mode < ep_min:
mode = ep_min + 1 # don't want mode right on the nose of ep_min for sampling purposes, so offset it a bit
dmode = density(mode)
# calculate mean epsilon via rejection sampling
motif = []
def mean_ep(lamb):
psfm = psfm_from_matrix(matrix, lamb=lamb)
return sum([ep * p for (mat_row, psfm_row) in zip(matrix, psfm)
for (ep, p) in zip(mat_row, psfm_row)])
lamb = bisect_interval(lambda l:mean_ep(l) - mode, -20, 20)
tilted_psfm = psfm_from_matrix(matrix, lamb=lamb)
log_tilted_psfm = [map(log,row) for row in tilted_psfm]
while len(motif) < N:
site = random_site(L)
ep = score_seq(matrix, site)
if random.random() < phat(ep)/pmode:
motif.append(site)
return motif
def marginal(i, j):
red_matrix = [row for jp, row in enumerate(matrix) if not j == jp]
red_site_mu = site_mu_from_matrix(red_matrix)
red_site_sigma = site_sigma_from_matrix(red_matrix)
ep = matrix[i][j]
nom = integrate.quad(lambda ep_rest:f(ep + ep_rest)*dnorm(ep_rest, red_site_mu, red_site_sigma),
ep_min, ep_max)
denom = integrate.quad(lambda ep_rest:f(ep_rest)*dnorm(ep_rest, site_mu, site_sigma), ep_min, ep_max)
def remarginalize(matrix, mu, Ne):
def phat(site):
ep = score_seq(matix, site)
return 1/(1+exp(ep-mu))**(Ne-1)
def f(ep):
return 1/(1+exp(ep-mu))**(Ne-1)
site_mu = site_mu_from_matrix(matrix)
site_sigma = site_sigma_from_matrix(matrix)
ep_min = sum(map(argmin, matrix))
ep_max = sum(map(argmax, matrix))
def marginal(i, j):
red_matrix = [row for jp, row in enumerate(matrix) if not j == jp]
red_site_mu = site_mu_from_matrix(red_matrix)
red_site_sigma = site_sigma_from_matrix(red_matrix)
ep = matrix[i][j]
nom = integrate.quad(lambda ep_rest:f(ep + ep_rest)*dnorm(ep_rest, red_site_mu, red_site_sigma),
ep_min, ep_max)
denom = integrate.quad(lambda ep_rest:f(ep_rest)*dnorm(ep_rest, site_mu, site_sigma), ep_min, ep_max)
def predict_ic(matrix, mu, Ne, N=100):
nu = Ne - 1
ep_min, ep_max, L = sum(map(min, matrix)), sum(map(max,
matrix)), len(matrix)
site_sigma = site_sigma_from_matrix(matrix)
density = lambda ep: (1 / (1 + exp(ep - mu)))**(Ne - 1) * dnorm(
ep, 0, site_sigma) * (ep_min <= ep <= ep_max)
d_density = lambda ep: ep / site_sigma**2 + nu / (1 + exp(mu - ep))
mode = bisect_interval(d_density, -100, 100)
if mode < ep_min:
mode = ep_min
dmode = density(mode)
# calculate mean epsilon via rejection sampling
eps = []
while len(eps) < N:
ep = random.random() * (ep_max - ep_min) + ep_min
if random.random() < density(ep) / dmode:
eps.append(ep)
#return eps
des_mean_ep = mean(eps)
des_mean_ep_analytic = integrate.quad(lambda ep: ep * density(ep), ep_min,
ep_max)
# print "des_means:", des_mean_ep, des_mean_ep_analytic
# print "min ep: %s max_ep: %s des_mean_ep: %s" % (ep_min, ep_max, des_mean_ep)
def mean_ep(lamb):
try:
psfm = psfm_from_matrix(matrix, lamb=lamb)
return sum([
ep * p for (mat_row, psfm_row) in zip(matrix, psfm)
for (ep, p) in zip(mat_row, psfm_row)
])
except:
print matrix, lamb
raise Exception
try:
lamb = bisect_interval(lambda l: mean_ep(l) - des_mean_ep, -20, 20)
except:
print matrix, mu, Ne
raise Exception
tilted_psfm = psfm_from_matrix(matrix, lamb)
return sum([2 - h(col) for col in tilted_psfm])
def predict_ic(matrix, mu, Ne, N=100):
nu = Ne - 1
ep_min, ep_max, L = sum(map(min,matrix)), sum(map(max,matrix)), len(matrix)
site_sigma = site_sigma_from_matrix(matrix)
density = lambda ep:(1/(1+exp(ep-mu)))**(Ne-1) * dnorm(ep,0,site_sigma)*(ep_min <= ep <= ep_max)
d_density = lambda ep:ep/site_sigma**2 + nu/(1+exp(mu-ep))
mode = bisect_interval(d_density, -100, 100)
if mode < ep_min:
mode = ep_min
dmode = density(mode)
# calculate mean epsilon via rejection sampling
eps = []
while len(eps) < N:
ep = random.random() * (ep_max - ep_min) + ep_min
if random.random() < density(ep)/dmode:
eps.append(ep)
#return eps
des_mean_ep = mean(eps)
des_mean_ep_analytic = integrate.quad(lambda ep:ep*density(ep), ep_min, ep_max)
# print "des_means:", des_mean_ep, des_mean_ep_analytic
# print "min ep: %s max_ep: %s des_mean_ep: %s" % (ep_min, ep_max, des_mean_ep)
def mean_ep(lamb):
try:
psfm = psfm_from_matrix(matrix, lamb=lamb)
return sum([ep * p for (mat_row, psfm_row) in zip(matrix, psfm)
for (ep, p) in zip(mat_row, psfm_row)])
except:
print matrix, lamb
raise Exception
try:
lamb = bisect_interval(lambda l:mean_ep(l) - des_mean_ep, -20, 20)
except:
print matrix, mu, Ne
raise Exception
tilted_psfm = psfm_from_matrix(matrix, lamb)
return sum([2 - h(col) for col in tilted_psfm])