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 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
def rejection_sample_site((matrix, mu, Ne)):
psfm = psfm_from_matrix(matrix)
log_psfm = [[log(p) for p in row] for row in psfm]
log_psfm_prob = lambda site:score_seq(log_psfm, site)
log_M = -sum(map(max,psfm))
sites = [sample_from_psfm(psfm) for _ in xrange(trials)]
log_fs = [log_fhat((matrix, mu, Ne), [site]) for site in sites]
log_qs = [log_psfm_prob(site) for site in sites]
ars = [exp(log_f - (log_q + log_M)) for log_f, log_q in zip(log_fs, log_qs)]
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
def rejection_sample_site((matrix, mu, Ne)):
psfm = psfm_from_matrix(matrix)
log_psfm = [[log(p) for p in row] for row in psfm]
log_psfm_prob = lambda site: score_seq(log_psfm, site)
log_M = -sum(map(max, psfm))
sites = [sample_from_psfm(psfm) for _ in xrange(trials)]
log_fs = [log_fhat((matrix, mu, Ne), [site]) for site in sites]
log_qs = [log_psfm_prob(site) for site in sites]
ars = [
exp(log_f - (log_q + log_M)) for log_f, log_q in zip(log_fs, log_qs)
]
def sample_site_imh(matrix, mu, Ne, lamb, iterations=None):
nu = Ne - 1
L = len(matrix)
if iterations is None:
iterations = 10*L
log_phat = lambda site:-nu*log(1+exp(score_seq(matrix,site)-mu))
tilted_psfm = psfm_from_matrix(matrix, lamb=lamb)
log_tilted_psfm = [map(log,row) for row in tilted_psfm]
def prop(_):
return sample_from_psfm(tilted_psfm)
def log_dprop(xp, _):
return score_seq(log_tilted_psfm, xp)
return mh(log_phat, proposal=prop, dprop=log_dprop, x0=prop(None), use_log=True)[-1]
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 sample_site_imh(matrix, mu, Ne, lamb, iterations=None):
nu = Ne - 1
L = len(matrix)
if iterations is None:
iterations = 10 * L
log_phat = lambda site: -nu * log(1 + exp(score_seq(matrix, site) - mu))
tilted_psfm = psfm_from_matrix(matrix, lamb=lamb)
log_tilted_psfm = [map(log, row) for row in tilted_psfm]
def prop(_):
return sample_from_psfm(tilted_psfm)
def log_dprop(xp, _):
return score_seq(log_tilted_psfm, xp)
return mh(log_phat,
proposal=prop,
dprop=log_dprop,
x0=prop(None),
use_log=True)[-1]
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 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)
])
def f(lamb):
psfm = psfm_from_matrix(matrix, lamb)
return sum([
sum(ep * p for ep, p in zip(eps, ps))
for eps, ps in zip(matrix, psfm)
]) - des_ep
def log_Z_hack((matrix, mu, Ne), N):
L = len(matrix)
mat_mu = sum(map(mean, matrix))
mat_sigma = sqrt(sum(map(lambda xs: variance(xs, correct=False), matrix)))
log_perc_below_threshold = norm.logcdf(mu - log((Ne - 1)), mat_mu,
mat_sigma)
log_Zs = L * log(4) + log_perc_below_threshold
ans_ref = ((N * L * log(4)) + log_perc_below_threshold)
ans = N * log_Zs
return ans
def log_ZS_importance((matrix, mu, Ne), trials=1000):
L = len(matrix)
psfm = psfm_from_matrix(matrix)
log_psfm = [[log(p) for p in row] for row in psfm]
log_psfm_prob = lambda site: score_seq(log_psfm, site)
sites = [sample_from_psfm(psfm) for _ in xrange(trials)]
mean_ZS = mean(
exp(
log_fhat((matrix, mu, Ne), [site]) + log(1.0 / 4**L) -
log_psfm_prob(site)) for site in sites)
ZS = 4**L * mean_ZS
return log(ZS)
def log_ZS_importance_ref((matrix, mu, Ne), trials=1000):
L = len(matrix)
psfm = [[0.25] * 4 for _ in range(L)]
log_psfm = [[log(p) for p in row] for row in psfm]
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)])
def f(lamb):
psfm = psfm_from_matrix(matrix, lamb)
return sum([sum(ep*p for ep,p in zip(eps, ps)) for eps, ps in zip(matrix, psfm)]) - des_ep
log_ZS = log_ZS_hack((matrix, mu, Ne), N)
return N * log_ZS
def log_Z_hack((matrix, mu, Ne), N):
L = len(matrix)
mat_mu = sum(map(mean,matrix))
mat_sigma = sqrt(sum(map(lambda xs:variance(xs,correct=False), matrix)))
log_perc_below_threshold = norm.logcdf(mu - log((Ne-1)), mat_mu, mat_sigma)
log_Zs = L * log(4) + log_perc_below_threshold
ans_ref = ((N*L * log(4)) + log_perc_below_threshold)
ans = N * log_Zs
return ans
def log_ZS_importance((matrix, mu, Ne), trials=1000):
L = len(matrix)
psfm = psfm_from_matrix(matrix)
log_psfm = [[log(p) for p in row] for row in psfm]
log_psfm_prob = lambda site:score_seq(log_psfm, site)
sites = [sample_from_psfm(psfm) for _ in xrange(trials)]
mean_ZS = mean(exp(log_fhat((matrix, mu, Ne), [site]) + log(1.0/4**L) - log_psfm_prob(site))
for site in sites)
ZS = 4**L * mean_ZS
return log(ZS)
def log_ZS_importance_ref((matrix, mu, Ne), trials=1000):
L = len(matrix)
psfm = [[0.25]*4 for _ in range(L)]
log_psfm = [[log(p) for p in row] for row in psfm]
log_psfm_prob = lambda site:score_seq(log_psfm, site)
sites = [sample_from_psfm(psfm) for _ in xrange(trials)]
mean_ZS = mean(exp(log_fhat((matrix, mu, Ne), [site]) + log(1.0/4**L) - log_psfm_prob(site))