def excess_mi_experiment(filename=None):
"""Do artificial motifs with linear BEMs show the same patterns of excess MI as biological motifs? (Yes)"""
n = 10
L = 10
G = 1000
desired_ic = 10
replicates = 1000
ics = np.array(
[mean_ic_from_eps(eps, n, L) for eps in enumerate_eps(n, L)])
def mean_ic(N):
ps = sella_hirsch_predictions(n, L, G, N)
return ics.dot(ps)
Ne = secant_interval(lambda N: mean_ic(N) - desired_ic,
0,
2000,
tolerance=0.1,
verbose=True) # ~= 1525
ps = sella_hirsch_predictions(n, L, G, Ne)
sh_sampler = inverse_cdf_sampler(list(enumerate_eps(n, L)), ps)
sh_motifs = [
sample_motif_from_mismatches(sh_sampler(), L)
for i in trange(replicates)
]
sh_mean_ic = mean(map(
motif_ic, sh_motifs)) # may undershoot desired due to approximation
maxent_motifs = maxent_sample_motifs_with_ic(n, L, sh_mean_ic, replicates)
plt.suptitle(
"Motif Statistics for Match/Mismatch Model vs. MaxEnt Ensembles (n=10,L=10,G=1000)"
)
all_boxplot_comparisons([sh_motifs, maxent_motifs],
labels=["M/MM", "MaxEnt"],
plot_titles="IC Gini MI".split(),
filename=filename)
def uniform_motifs_accept_reject(n,
L,
desired_ic,
num_motifs,
epsilon=0.1,
beta=None,
verbose=False):
if beta is None:
correction_per_col = 3 / (2 * log(2) * n)
desired_ic_for_beta = desired_ic + L * correction_per_col
beta = find_beta_for_mean_motif_ic(n,
L,
desired_ic_for_beta,
verbose=verbose)
ps = count_ps_from_beta(n, beta)
count_sampler = inverse_cdf_sampler(enumerate_counts(n), ps)
return [
uniform_motif_accept_reject(n,
L,
desired_ic,
epsilon=epsilon,
beta=beta,
ps=ps,
count_sampler=count_sampler,
verbose=verbose)
for i in trange(num_motifs)
]
def uniform_motif_accept_reject(n,
L,
desired_ic,
epsilon=0.1,
beta=None,
ps=None,
count_sampler=None,
verbose=False):
print "uniform motif accept reject:", n, L, desired_ic, beta
correction_per_col = 3 / (2 * log(2) * n)
desired_ic_for_beta = desired_ic + L * correction_per_col
if desired_ic_for_beta == 2 * L: # if we reach the upper limit, things break down
cols = [sample_col_from_count((0, 0, 0, n)) for _ in range(L)]
motif_p = map(lambda site: "".join(site), transpose(cols))
return motif_p
if beta is None:
beta = find_beta_for_mean_motif_ic(n, L, desired_ic_for_beta)
if verbose:
print "beta:", beta
if ps is None:
ps = count_ps_from_beta(n, beta)
if count_sampler is None:
count_sampler = inverse_cdf_sampler(enumerate_counts(n), ps)
def rQ_raw():
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count) for count in counts]
motif_p = map(lambda site: "".join(site), transpose(cols))
return motif_p
def rQ():
return sample_until(lambda M: inrange(M, desired_ic, epsilon),
rQ_raw,
1,
progress_bar=False)[0]
def dQhat(motif):
return exp(beta * motif_ic(motif))
Imin = desired_ic - epsilon
Imax = desired_ic + epsilon
log_M = -beta * Imin
if verbose: print "Imin, Imax, log_M:", Imin, Imax, log_M
def dQ(motif):
return exp(beta * motif_ic(motif) + log_M)
def AR(motif):
return 1.0 / dQ(motif)
#M = exp(-beta*(desired_ic - epsilon)) # which ic? +/- correction
trials = 0
while True:
trials += 1
motif = rQ()
r = random.random()
if r < AR(motif):
return motif
if verbose and trials % 100 == 0:
print trials, AR(motif)
def maxent_motifs_with_ic(n,
L,
desired_ic,
num_motifs,
tolerance=10**-10,
beta=None,
verbose=False):
if beta is None:
correction_per_col = 3 / (2 * log(2) * n)
desired_ic += L * correction_per_col
beta = find_beta_for_mean_motif_ic(n,
L,
desired_ic,
tolerance=tolerance,
verbose=verbose)
if verbose:
print "beta:", beta
ps = count_ps_from_beta(n, beta)
count_sampler = inverse_cdf_sampler(enumerate_counts(n), ps)
def sample():
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count) for count in counts]
return map(lambda site: "".join(site), transpose(cols))
return [sample() for _ in trange(num_motifs)]
def uniform_motif_with_ic_imh_ref(n,
L,
desired_ic,
epsilon=0.1,
iterations=None,
verbose=False,
num_chains=8):
correction_per_col = 3 / (2 * log(2) * n)
desired_ic_for_beta = desired_ic + L * correction_per_col
beta = find_beta_for_mean_motif_ic(n, L, desired_ic_for_beta)
ps = count_ps_from_beta(n, beta)
count_sampler = inverse_cdf_sampler(enumerate_counts(n), ps)
def Q(motif):
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count) for count in counts]
motif_p = map(lambda site: "".join(site), transpose(cols))
return motif_p
def log_dQ(motif_p, motif):
return (beta * motif_ic(motif_p))
def log_f(motif):
in_range = abs(motif_ic(motif) - desired_ic) < epsilon
return 0 if in_range else -10.0**100
if iterations:
x0 = sample_until(lambda x: log_f(x) > -1, lambda: Q(None), 1)[0]
chain = mh(log_f,
proposal=Q,
dprop=log_dQ,
x0=x0,
iterations=iterations,
use_log=True,
verbose=False)
return chain
else: #use gelman rubin criterion
x0s = sample_until(lambda x: log_f(x) > -1, lambda: Q(None),
num_chains)
iterations = 100
converged = False
chains = [[] for _ in range(num_chains)]
while not converged:
for chain, x0 in zip(chains, x0s):
chain.extend(
mh(log_f,
proposal=Q,
dprop=log_dQ,
x0=x0,
iterations=iterations,
use_log=True,
verbose=False))
ic_chains = mmap(motif_ic, chains)
R_hat, neff = gelman_rubin(ic_chains)
if R_hat < 1.1:
return chains
else:
x0s = [chain[-1] for chain in chains]
iterations *= 2
def uniform_motif_with_ic_imh(n,
L,
desired_ic,
epsilon=0.1,
iterations=None,
verbose=False,
beta=None,
num_chains=8):
if beta is None:
correction_per_col = 3 / (2 * log(2) * n)
desired_ic_for_beta = desired_ic + L * correction_per_col
beta = find_beta_for_mean_motif_ic(n, L, desired_ic_for_beta)
ps = count_ps_from_beta(n, beta)
count_sampler = inverse_cdf_sampler(enumerate_counts(n), ps)
def Q(motif):
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count) for count in counts]
motif_p = map(lambda site: "".join(site), transpose(cols))
return motif_p
def log_dQ(motif_p, motif):
return (beta * motif_ic(motif_p))
def log_f(motif):
in_range = abs(motif_ic(motif) - desired_ic) < epsilon
return 0 if in_range else -10.0**100
x0 = sample_until(lambda x: log_f(x) > -1, lambda: Q(None), 1)[0]
# first, determine probability of landing in range
ar = 0
iterations = 100
while ar == 0:
ar = mh(log_f,
proposal=Q,
dprop=log_dQ,
x0=x0,
iterations=iterations,
use_log=True,
verbose=False,
return_ar=True)
iterations *= 2
iterations = int(1.0 / ar * 10)
chain = mh(log_f,
proposal=Q,
dprop=log_dQ,
x0=x0,
iterations=iterations,
use_log=True,
verbose=False)
return chain
def uniform_motif_imh_tv(n, L, desired_ic, beta=None, epsilon=None, tv=0.01):
"""run uniform imh to within total variation bound tv"""
correction_per_col = 3 / (2 * log(2) * n)
desired_ic_for_beta = desired_ic + L * correction_per_col
if beta == None:
beta = find_beta_for_mean_motif_ic(n, L, desired_ic_for_beta)
if epsilon == None:
epsilon = 1.0 / (2 * beta)
print "maximally efficient epsilon:", epsilon
ps = count_ps_from_beta(n, beta)
count_sampler = inverse_cdf_sampler(enumerate_counts(n), ps)
def Qp(motif):
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count) for count in counts]
motif_p = map(lambda site: "".join(site), transpose(cols))
return motif_p
def Q(motif):
return sample_until(lambda m: abs(motif_ic(m) - desired_ic) < epsilon,
lambda: Qp(None), 1)[0]
def log_dQ(motif_p, motif):
return (beta * motif_ic(motif_p))
def log_f(motif):
in_range = abs(motif_ic(motif) - desired_ic) < epsilon
return 0 if in_range else -10.0**100
alpha = exp(-2 * beta * epsilon)
iterations = int(ceil(log(tv) / log(1 - alpha)))
print "iterations:", iterations
x0 = sample_until(lambda x: log_f(x) > -1, lambda: Q(None), 1)[0]
# first, determine probability of landing in range
chain = mh(log_f,
proposal=Q,
dprop=log_dQ,
x0=x0,
iterations=iterations,
use_log=True,
verbose=False)
return chain
def maxent_motif_with_ic(n,
L,
desired_ic,
tolerance=10**-10,
beta=None,
verbose=False):
"""sample motif from max ent distribution with mean desired_ic"""
# first we adjust the desired ic upwards so that when motif_ic is
# called with 1st order correction, we get the desired ic.
if beta is None:
if verbose:
print "finding beta"
correction_per_col = 3 / (2 * log(2) * n)
desired_ic += L * correction_per_col
beta = find_beta_for_mean_motif_ic(n,
L,
desired_ic,
tolerance=tolerance,
verbose=verbose)
ps = count_ps_from_beta(n, beta)
count_sampler = inverse_cdf_sampler(enumerate_counts(n), ps)
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count) for count in counts]
return map(lambda site: "".join(site), transpose(cols))