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 validation_plot(L=10, N=50, ref_trials=1000):
check_points = np.linspace(0, 10, 10)
#ics_ref = sorted([motif_ic(random_motif(L, N)) for i in range(ref_trials)])
ics_ref = sorted([
motif_ic(random_motif(L, N), correct=True) for i in trange(ref_trials)
])
plt.plot(ics_ref,
1 - np.linspace(0, 1, len(ics_ref)),
label="Empirical Complementary CDF",
marker='o',
linestyle='')
plt.plot(
check_points,
[exp(ic_log_pvalue(N, L, ic, method="MC")) for ic in check_points],
label="Importance Sampling Estimate")
plt.plot(
check_points,
[exp(ic_log_pvalue(N, L, ic, method="UB")) for ic in check_points],
label="Analytic Upper Bound")
plt.plot(check_points, [
exp(ic_log_pvalue(N, L, ic, method="analytic")) for ic in check_points
],
label="Analytic P-value")
plt.semilogy()
plt.legend()
plt.xlabel("Information Content (bits)")
plt.ylabel("P-value")
plt.xlim(0, 1.2)
plt.show()
def log_ZM_empirical_ref3(theta, N,trials=1000):
L = len(theta[0])
lfhs = [log_fhat(theta, random_motif(L, 1)) for _ in xrange(trials)]
log_avg = logsum(lfhs) - log(trials)
log_ZS = L*log(4) + log_avg
log_ZM = N * log_ZS
return log_ZM
def log_ZM_empirical_ref3(theta, N, trials=1000):
L = len(theta[0])
lfhs = [log_fhat(theta, random_motif(L, 1)) for _ in xrange(trials)]
log_avg = logsum(lfhs) - log(trials)
log_ZS = L * log(4) + log_avg
log_ZM = N * log_ZS
return log_ZM
def best_ic_motif(L,n,trials):
best_ic = 0
for i in trange(trials):
motif = random_motif(L,n)
cur_ic = motif_ic(motif,correct=False)
if cur_ic > best_ic:
best_motif = motif
return best_motif
def match_ic_mi(N,
L,
des_ic,
des_mi,
iterations=50000,
take_stock=None,
eta=0.01,
alpha=1,
beta=0):
if take_stock is None:
take_stock = int((N * L) * log(N * L))
x = random_motif(L, N)
xs = [None] * iterations
ics = [0.0] * iterations
mis = [0.0] * iterations
alphas = [0.0] * iterations
betas = [0.0] * iterations
ic = motif_ic(x)
mi = total_motif_mi(x)
accepts = 0
for i in xrange(iterations):
# if i == iterations/2:
# eta *= 0.1
xp = mutate_motif(x)
icp = motif_ic(xp)
mip = total_motif_mi(xp)
log_y = (alpha * ic + beta * mi)
log_yp = (alpha * icp + beta * mip)
if log(random.random()) < log_yp - log_y:
accepts += 1
x = xp
ic = icp
mi = mip
ics[i] = (ic)
mis[i] = (mi)
xs[i] = (x)
#print sum(site.count("A") for site in x)
alphas[i] = (alpha)
betas[i] = (beta)
if i > 0 and i % take_stock == 0:
if i < iterations / 10:
mean_ic = mean(ics[i - take_stock:i])
mean_mi = mean(mis[i - take_stock:i])
alpha += eta * (des_ic - mean_ic) * exp(
-i / (10 * float(iterations)))
beta += eta * (des_mi - mean_mi) * exp(
-i / (10 * float(iterations)))
else:
mean_ic = mean(ics[i - take_stock:i])
mean_mi = mean(mis[i - take_stock:i])
alpha = poly1d(polyfit(ics[:i], alphas[:i], 1))(des_ic)
beta = poly1d(polyfit(mis[:i], betas[:i], 1))(des_mi)
fmt_string = (
"mean ic: % 1.2f, mean mi: % 1.2f, alpha: % 1.2f, beta: % 1.2f"
% (mean_ic, mean_mi, alpha, beta))
print i, "AR:", accepts / (i + 1.0), fmt_string
return xs, ics, mis, alphas, betas
def sample_pw_motif_mh(code, N, Ne, mu, iterations=50000):
nu = Ne - 1
def log_f(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)
prop = mutate_motif
L = len(code) + 1
x0 = random_motif(L, N)
return mh(log_f, prop, x0, cache=True, use_log=True, iterations=iterations)
def sella_hirsch_mh_sampling(n=16,L=16,G=1000,N=100,sigma=1,iterations=50000):
Zb = compute_Zb(n,L,sigma,G)
nu = N-1
def fitness(motif):
eps = [sigma*sum(b!="A" for b in site) for site in motif]
fg = sum(exp(-sigma*ep) for ep in eps)
return fg/(fg + Zb)
def log_p(motif):
return (nu * log(fitness(motif)))
def proposal(motif):
p = 4.0/(n*L)
return mutate_motif_p(motif,p)
x0 = random_motif(n,L)
chain = mh(log_p,proposal,x0,use_log=True,iterations=iterations)
return chain
def validation_plot(L=10, N=50, ref_trials=1000):
check_points = np.linspace(0,10,10)
#ics_ref = sorted([motif_ic(random_motif(L, N)) for i in range(ref_trials)])
ics_ref = sorted([motif_ic(random_motif(L, N), correct=True) for i in trange(ref_trials)])
plt.plot(ics_ref, 1 - np.linspace(0,1,len(ics_ref)),label="Empirical Complementary CDF", marker='o',linestyle='')
plt.plot(check_points, [exp(ic_log_pvalue(N, L, ic, method="MC")) for ic in check_points],
label="Importance Sampling Estimate")
plt.plot(check_points, [exp(ic_log_pvalue(N, L, ic, method="UB")) for ic in check_points],
label="Analytic Upper Bound")
plt.plot(check_points, [exp(ic_log_pvalue(N, L, ic, method="analytic")) for ic in check_points],
label="Analytic P-value")
plt.semilogy()
plt.legend()
plt.xlabel("Information Content (bits)")
plt.ylabel("P-value")
plt.xlim(0,1.2)
plt.show()
def sella_hirsch_mh_penalize_mu(Ne=5,
n=16,
L=16,
G=5 * 10**6,
sigma=1,
alpha=0.01,
init="random",
matrix=None,
x0=None,
iterations=50000,
p=None):
print "p:", p
if matrix is None:
matrix = sample_matrix(L, sigma)
if x0 is None:
if init == "random":
x0 = (random_motif(L, n), random.gauss(0, 1))
elif init == "ringer":
x0 = (ringer_motif(matrix, n), random.gauss(0, 1))
elif init == "anti_ringer":
x0 = (anti_ringer_motif(matrix, n), random.gauss(0, 1))
else:
x0 = init
if p is None:
p = 1.0 / (n * L)
nu = Ne - 1
def log_f((motif, mu)):
return nu * log_fitness_penalize_mu(matrix, motif, mu, alpha)
def prop((motif, mu)):
motif_p = mutate_motif_p(motif,
p) # probability of mutation per basepair
mu_p = mu + random.gauss(0, 0.1)
return motif_p, mu_p
chain = mh(log_f, prop, x0, use_log=True, iterations=iterations)
return matrix, chain
def sella_hirsch_mh(Ne=5,
n=16,
L=16,
sigma=1,
mu=0,
init="random",
matrix=None,
x0=None,
iterations=50000,
p=None):
print "p:", p
if matrix is None:
matrix = sample_matrix(L, sigma)
else:
L = len(matrix)
if x0 is None:
if init == "random":
x0 = random_motif(L, n)
elif init == "ringer":
x0 = ringer_motif(matrix, n)
elif init == "anti_ringer":
x0 = anti_ringer_motif(matrix, n)
else:
x0 = init
if p is None:
p = 1.0 / (n * L)
nu = Ne - 1
def log_f(motif):
return nu * log_fitness(matrix, motif, mu)
def prop(motif):
motif_p = mutate_motif_p(motif,
p) # probability of mutation per basepair
return motif_p
chain = mh(log_f, prop, x0, use_log=True, iterations=iterations)
return matrix, chain
def sella_hirsch_mh_sampling(n=16,
L=16,
G=1000,
N=100,
sigma=1,
iterations=50000):
Zb = compute_Zb(n, L, sigma, G)
nu = N - 1
def fitness(motif):
eps = [sigma * sum(b != "A" for b in site) for site in motif]
fg = sum(exp(-sigma * ep) for ep in eps)
return fg / (fg + Zb)
def log_p(motif):
return (nu * log(fitness(motif)))
def proposal(motif):
p = 4.0 / (n * L)
return mutate_motif_p(motif, p)
x0 = random_motif(n, L)
chain = mh(log_p, proposal, x0, use_log=True, iterations=iterations)
return chain
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 random_genotype(n, L, linear_sigma, pairwise_sigma, copies):
motif = random_motif(L, n)
pwm = sample_matrix(L, linear_sigma)
pairwise_weights = [[[random.gauss(0, pairwise_sigma) for i in range(4)]
for j in range(4)] for k in range(L - 1)]
return motif, copies, (pwm, pairwise_weights)
def log_ZM_empirical_ref2(theta, N, trials=1000):
L = len(theta[0])
lfhs = [log_fhat(theta, random_motif(L, N)) for _ in xrange(trials)]
return N*L * log(4) + logsum(lfhs) - log(trials)
def log_ZM_empirical_ref2(theta, N, trials=1000):
L = len(theta[0])
lfhs = [log_fhat(theta, random_motif(L, N)) for _ in xrange(trials)]
return N * L * log(4) + logsum(lfhs) - log(trials)
def motif_mh(L,n,desired_ic):
x0 = random_motif(L,n)
def logf(motif,mu):
return (mu*motif_ic(motif,correct=False))
return mh()
def init_species():
return random_motif(n, L)
def init_species():
return random_motif(n,L)