def estremo_gibbs(iterations=50000,
verbose=False,
every=1000,
sigma=1,
mu=-10,
Ne=5):
nu = Ne - 1
L = 10
N = 20
code, motif = (sample_code(L=10,
sigma=1), random_motif(length=L, num_sites=N))
def log_f((code, motif)):
eps = map(lambda x: -log(x), pw_prob_sites(motif, code))
return sum(nu * log(1 / (1 + exp(ep - mu))) for ep in eps)
chain = [(code, motif[:])]
print log_f((code, motif))
for iteration in trange(iterations):
for i in range(N):
site = motif[i]
for j in range(L):
b = site[j]
log_ps = []
bps = [bp for bp in "ACGT" if not bp == b]
for bp in bps:
site_p = subst(site, bp, j)
log_ps.append(log_f((code, [site_p])))
log_ps = [p - min(log_ps) for p in log_ps]
bp = inverse_cdf_sample(bps,
map(exp, log_ps),
normalized=False)
motif[i] = subst(site, bp, j)
for k in range(L - 1):
for b1 in "ACGT":
for b2 in "ACGT":
dws = [random.gauss(0, 0.1) for _ in range(10)]
code_ps = [[d.copy() for d in code] for _ in range(10)]
for code_p, dw in zip(code_ps, dws):
code_p[k][b1, b2] += dw
log_ps = [log_f((code_p, motif)) for code_p in code_ps]
log_ps = [p - min(log_ps) for p in log_ps]
code_p = inverse_cdf_sample(code_ps,
map(exp, log_ps),
normalized=False)
code = code_p
print log_f((code, motif))
chain.append((code, motif[:]))
return chain
x0 = (sample_code(L=10, sigma=1), random_motif(length=10, num_sites=20))
chain = mh(log_f,
prop,
x0,
use_log=True,
iterations=iterations,
verbose=verbose,
every=every)
return chain
def experiment3(trials=10):
mu = -10
Ne = 5
L = 10
sigma = 1
codes = [sample_code(L, sigma) for i in range(trials)]
pssms = [sample_matrix(L, sigma) for i in range(trials)]
sites = [random_site(L) for i in xrange(10000)]
apw_site_sigmas = [
sd([score(code, site) for site in sites]) for code in codes
]
linear_site_sigmas = [
sd([score_seq(pssm, site) for site in sites]) for pssm in pssms
]
def apw_phat(code, site):
ep = score(code, site)
return 1 / (1 + exp(ep - mu))**(Ne - 1)
def apw_occ(code, site):
ep = score(code, site)
return 1 / (1 + exp(ep - mu))
def linear_phat(pssm, site):
ep = score_seq(pssm, site)
return 1 / (1 + exp(ep - mu))**(Ne - 1)
def linear_occ(pssm, site):
ep = score_seq(pssm, site)
return 1 / (1 + exp(ep - mu))
apw_mean_fits = [
exp(
mean(
map(
log10,
mh(lambda s: apw_phat(code, s),
proposal=mutate_site,
x0=random_site(L),
capture_state=lambda s: apw_occ(code, s))[1:])))
for code in tqdm(codes)
]
linear_mean_fits = [
exp(
mean(
map(
log10,
mh(lambda s: linear_phat(pssm, s),
proposal=mutate_site,
x0=random_site(L),
capture_state=lambda s: linear_occ(pssm, s))[1:])))
for pssm in tqdm(pssms)
]
plt.scatter(apw_site_sigmas, apw_mean_fits, label='apw')
plt.scatter(linear_site_sigmas,
linear_mean_fits,
color='g',
label='linear')
plt.semilogy()
plt.legend(loc='lower right')
def experiment2_():
L = 10
sigma = 1
code = sample_code(L, 1)
mu = -10
Ne = 2
sites = [random_site(L) for i in xrange(10000)]
apw_eps = [score(code, site) for site in sites]
site_sigma = sd(apw_eps)
pssm = sample_matrix(L, sqrt(site_sigma**2 / L))
#linear_eps = [score_seq(pssm, site) for site in sites]
def apw_phat(site):
ep = score(code, site)
return 1 / (1 + exp(ep - mu))**(Ne - 1)
def linear_phat(site):
ep = score_seq(pssm, site)
return 1 / (1 + exp(ep - mu))**(Ne - 1)
def sample_apw_site():
return mh(apw_phat, proposal=mutate_site, x0=random_site(L))
apw_chain = mh(apw_phat, proposal=mutate_site, x0=random_site(L))
linear_chain = mh(linear_phat, proposal=mutate_site, x0=random_site(L))
apw_fits = map(apw_phat, apw_chain)
linear_fits = map(linear_phat, linear_chain)
return apw_fits, linear_fits
def degradation_experiment():
"""Determine whether linear or pairwise models are more resistant to degradation"""
L = 10
N = 50
Ne = 5
nu = Ne - 1
sigma = 1
mu = -10
matrix = sample_matrix(L, sigma)
code = sample_code(L, sigma)
li_motif = sample_motif_cftp(matrix, mu, Ne, N)
pw_motif = sample_pw_motif_mh(code, N, Ne, mu, iterations=100000)[-1]
def li_log_fitness(motif):
eps = [score_seq(matrix, site) for site in motif]
return sum(-nu * log((1 + exp(ep - mu))) for ep in eps)
def pw_log_fitness(motif):
eps = map(lambda x: -log(x), pw_prob_sites(motif, code))
return sum(log(1 / (1 + exp(ep - mu))**nu) for ep in eps)
li_base_fit = li_log_fitness(li_motif)
li_mut_fits = [li_log_fitness(mutate_motif(li_motif)) for i in range(100)]
pw_base_fit = pw_log_fitness(pw_motif)
pw_mut_fits = [pw_log_fitness(mutate_motif(pw_motif)) for i in range(100)]
def sanity_check():
pw_motifs = [(lambda code: [pw_sample_site(code)
for i in range(100)])(sample_code(10, 1))
for _ in range(100)]
li_motifs = maxent_motifs(100, 10, 10, 100)
cv_experiment(pw_motifs)
cv_experiment(li_motifs)
def experiment3(trials=10):
mu = -10
Ne = 5
L = 10
sigma = 1
codes = [sample_code(L, sigma) for i in range(trials)]
pssms = [sample_matrix(L, sigma) for i in range(trials)]
sites = [random_site(L) for i in xrange(10000)]
apw_site_sigmas = [sd([score(code,site) for site in sites]) for code in codes]
linear_site_sigmas = [sd([score_seq(pssm,site) for site in sites]) for pssm in pssms]
def apw_phat(code, site):
ep = score(code, site)
return 1/(1+exp(ep-mu))**(Ne-1)
def apw_occ(code, site):
ep = score(code, site)
return 1/(1+exp(ep-mu))
def linear_phat(pssm, site):
ep = score_seq(pssm, site)
return 1/(1+exp(ep-mu))**(Ne-1)
def linear_occ(pssm, site):
ep = score_seq(pssm, site)
return 1/(1+exp(ep-mu))
apw_mean_fits = [exp(mean(map(log10, mh(lambda s:apw_phat(code, s), proposal=mutate_site, x0=random_site(L),
capture_state = lambda s:apw_occ(code, s))[1:])))
for code in tqdm(codes)]
linear_mean_fits = [exp(mean(map(log10, mh(lambda s:linear_phat(pssm, s), proposal=mutate_site, x0=random_site(L),
capture_state = lambda s:linear_occ(pssm, s))[1:])))
for pssm in tqdm(pssms)]
plt.scatter(apw_site_sigmas, apw_mean_fits, label='apw')
plt.scatter(linear_site_sigmas, linear_mean_fits, color='g',label='linear')
plt.semilogy()
plt.legend(loc='lower right')
def apw_fit(sigma, mu, Ne):
code = sample_code(L, sigma)
def apw_phat(site):
ep = score(code, site)
return 1/(1+exp(ep-mu))**(Ne-1)
chain = mh(lambda s:apw_phat(s), proposal=mutate_site, x0=random_site(L),
capture_state = lambda s:apw_occ(code, mu, s))[25000:]
return mean(chain)
def apw_fit(sigma, mu, Ne):
code = sample_code(L, sigma)
def apw_phat(site):
ep = score(code, site)
return 1 / (1 + exp(ep - mu))**(Ne - 1)
chain = mh(lambda s: apw_phat(s),
proposal=mutate_site,
x0=random_site(L),
capture_state=lambda s: apw_occ(code, mu, s))[25000:]
return mean(chain)
def experiment1_():
L = 10
sigma = 1
code = sample_code(L, 1)
mu = -10
Ne = 2
pssm = linearize(code)
def apw_phat(site):
ep = score(code, site)
return 1/(1+exp(ep-mu))**(Ne-1)
def linear_phat(site):
ep = score_seq(pssm, site)
return 1/(1+exp(ep-mu))**(Ne-1)
def sample_apw_site():
return mh(apw_phat, proposal=mutate_site, x0=random_site(L))
apw_chain = mh(apw_phat, proposal=mutate_site, x0=random_site(L))
linear_chain = mh(linear_phat, proposal=mutate_site, x0=random_site(L))
apw_fits = map(apw_phat, apw_chain)
linear_fits = map(linear_phat, linear_chain)
return apw_fits, linear_fits
def experiment1_():
L = 10
sigma = 1
code = sample_code(L, 1)
mu = -10
Ne = 2
pssm = linearize(code)
def apw_phat(site):
ep = score(code, site)
return 1 / (1 + exp(ep - mu))**(Ne - 1)
def linear_phat(site):
ep = score_seq(pssm, site)
return 1 / (1 + exp(ep - mu))**(Ne - 1)
def sample_apw_site():
return mh(apw_phat, proposal=mutate_site, x0=random_site(L))
apw_chain = mh(apw_phat, proposal=mutate_site, x0=random_site(L))
linear_chain = mh(linear_phat, proposal=mutate_site, x0=random_site(L))
apw_fits = map(apw_phat, apw_chain)
linear_fits = map(linear_phat, linear_chain)
return apw_fits, linear_fits
def estremo(iterations=50000, verbose=False, every=1, sigma=1, mu=-10, Ne=5):
nu = Ne - 1
def log_f((code, motif)):
eps = map(lambda x: -log(x), pw_prob_sites(motif, code))
return sum(nu * log(1 / (1 + exp(ep - mu))) for ep in eps)
def prop((code, motif)):
code_p = [d.copy() for d in code]
i = random.randrange(len(code))
b1, b2 = random.choice("ACGT"), random.choice("ACGT")
code_p[i][(b1, b2)] += random.gauss(0, sigma)
motif_p = mutate_motif(motif)
return (code_p, motif_p)
x0 = (sample_code(L=10, sigma=1), random_motif(length=10, num_sites=20))
chain = mh(log_f,
prop,
x0,
use_log=True,
iterations=iterations,
verbose=verbose,
every=every)
return chain
def experiment2_():
L = 10
sigma = 1
code = sample_code(L, 1)
mu = -10
Ne = 2
sites = [random_site(L) for i in xrange(10000)]
apw_eps = [score(code, site) for site in sites]
site_sigma = sd(apw_eps)
pssm = sample_matrix(L, sqrt(site_sigma**2/L))
#linear_eps = [score_seq(pssm, site) for site in sites]
def apw_phat(site):
ep = score(code, site)
return 1/(1+exp(ep-mu))**(Ne-1)
def linear_phat(site):
ep = score_seq(pssm, site)
return 1/(1+exp(ep-mu))**(Ne-1)
def sample_apw_site():
return mh(apw_phat, proposal=mutate_site, x0=random_site(L))
apw_chain = mh(apw_phat, proposal=mutate_site, x0=random_site(L))
linear_chain = mh(linear_phat, proposal=mutate_site, x0=random_site(L))
apw_fits = map(apw_phat, apw_chain)
linear_fits = map(linear_phat, linear_chain)
return apw_fits, linear_fits