def avg_ic_from_theta(theta, N, L, trials=3):
sigma, mu, Ne = theta
matrices = [sample_matrix(L, sigma) for i in xrange(trials)]
motifs = [sample_motif_cftp(matrix, mu, Ne, N) for matrix in matrices]
ics = map(motif_ic,motifs)
mean_ic = mean(ics)
return mean_ic
def sample_motifs_evo_ic(motif, iterations=1000, verbose=False, theta=None):
N = len(motif)
L = len(motif[0])
des_ic = motif_ic(motif)
chain = evo_ic_sample_motif2(N, L, des_ic, iterations=iterations, verbose=False, theta=theta)
motifs = [sample_motif_cftp(sample_matrix(L, sigma), mu, Ne, N) for (sigma, mu, Ne) in tqdm(chain)]
return chain, motifs
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 avg_ic_from_theta(theta, N, L, trials=3):
sigma, mu, Ne = theta
matrices = [sample_matrix(L, sigma) for i in xrange(trials)]
motifs = [sample_motif_cftp(matrix, mu, Ne, N) for matrix in matrices]
ics = map(motif_ic, motifs)
mean_ic = mean(ics)
return mean_ic
def f(theta):
sigma, mu, Ne = theta
matrices = [sample_matrix(L, sigma) for i in xrange(trials)]
motifs = [sample_motif_cftp(matrix, mu, Ne, N) for matrix in matrices]
ics = map(motif_ic,motifs)
ic = mean(ics)
print "sigma, mu, Ne:", sigma, mu, Ne
print "mean IC:", ic
return exp(-beta*(ic - des_ic)**2)
def sample_mis(L, sigma, copy_factor, Ne, N, trials=100):
mis = []
for _ in trange(trials):
matrix = sample_matrix(L, sigma)
copies = copy_factor * N
mu = approx_mu(matrix, copies)
motif = sample_motif_cftp(matrix, mu, Ne, N)
mis.append(motif_mi(motif))
return mis
def f(theta):
sigma, mu, Ne = theta
matrices = [sample_matrix(L, sigma) for i in xrange(trials)]
motifs = [sample_motif_cftp(matrix, mu, Ne, N) for matrix in matrices]
ics = map(motif_ic, motifs)
ic = mean(ics)
print "sigma, mu, Ne:", sigma, mu, Ne
print "mean IC:", ic
return exp(-beta * (ic - des_ic)**2)
def resample_from_post_chain(chain, N):
"""given chain of the form [(mat, mu, Ne)], perform reduction:
mat -> sigma -> mat' -> motif'
Conclusion: heavily underestimates IC.
"""
L = len(chain[0][0])
sigmas = [sigma_from_matrix(mat) for (mat, mu, Ne) in chain]
matrices = [sample_matrix(L, sigma) for sigma in sigmas]
motifs = [sample_motif_cftp(matrix, mu, Ne, N) for matrix, (_, mu, Ne) in tqdm(zip(matrices, chain))]
return motifs
def resample_from_post_chain(chain, N):
"""given chain of the form [(mat, mu, Ne)], perform reduction:
mat -> sigma -> mat' -> motif'
Conclusion: heavily underestimates IC.
"""
L = len(chain[0][0])
sigmas = [sigma_from_matrix(mat) for (mat, mu, Ne) in chain]
matrices = [sample_matrix(L, sigma) for sigma in sigmas]
motifs = [
sample_motif_cftp(matrix, mu, Ne, N)
for matrix, (_, mu, Ne) in tqdm(zip(matrices, chain))
]
return motifs
def test_predict_ic(trials=100):
pred_ics = []
obs_ics = []
for trial in trange(trials):
sigma = random.random() * 5 + 0.1
L = random.randrange(5, 15)
matrix = sample_matrix(L, sigma)
mu = random.random() * (-20)
Ne = random.random() * 5 + 1
pred_ic = predict_ic(matrix, mu, Ne)
obs_ic = motif_ic(sample_motif_cftp(matrix, mu, Ne, n=100))
pred_ics.append(pred_ic)
obs_ics.append(obs_ic)
r, p = scatter(pred_ics, obs_ics)
print r, p
def sample_motifs_evo_ic(motif, iterations=1000, verbose=False, theta=None):
N = len(motif)
L = len(motif[0])
des_ic = motif_ic(motif)
chain = evo_ic_sample_motif2(N,
L,
des_ic,
iterations=iterations,
verbose=False,
theta=theta)
motifs = [
sample_motif_cftp(sample_matrix(L, sigma), mu, Ne, N)
for (sigma, mu, Ne) in tqdm(chain)
]
return chain, motifs
def test_predict_ic(trials=100):
pred_ics = []
obs_ics = []
for trial in trange(trials):
sigma = random.random() * 5 + 0.1
L = random.randrange(5, 15)
matrix = sample_matrix(L, sigma)
mu = random.random() * (-20)
Ne = random.random() * 5 + 1
pred_ic = predict_ic(matrix, mu, Ne)
obs_ic = motif_ic(sample_motif_cftp(matrix, mu, Ne, n=100))
pred_ics.append(pred_ic)
obs_ics.append(obs_ic)
r, p = scatter(pred_ics, obs_ics)
print r, p
def posterior_chain(motif,
iterations=50000,
theta0=None,
sigma=1,
num_spoof_sites='N',
verbose=False):
"""do MH with doubly intractable MCMC one-point estimator"""
L = len(motif[0])
N = len(motif)
if num_spoof_sites == 'N':
num_spoof_sites = N # should this be N or 1?
if theta0 is None:
matrix0 = [[0, 0, 0, 0] for i in range(L)]
mu0 = -10
Ne0 = 3
theta = (matrix0, mu0, Ne0)
else:
theta = theta0
log_f_theta = log_fhat(theta, motif)
chain = []
acceptances = 0
for it in trange(iterations):
theta_p = prop2(theta, sigma)
log_f_theta_p = log_fhat(theta_p, motif)
matrix_p, mu_p, Ne_p = theta_p
xp = sample_motif_cftp(matrix_p, mu_p, Ne_p, num_spoof_sites)
log_Z = log_fhat(theta, xp)
log_Z_p = log_fhat(theta_p, xp)
log_ar = log_f_theta_p - log_f_theta + N / num_spoof_sites * (log_Z -
log_Z_p)
if log(random.random()) < log_ar:
theta = theta_p
log_f_theta = log_f_theta_p
log_Z = log_Z_p
acceptances += 1
chain.append(theta)
if verbose:
print "log(f), log_Z:", log_f_theta, log_Z
print "mean_ep:", mean(score_seq(theta[0], site) for site in motif)
print "mean_occ:", mean(occs(theta, motif))
print "mu, Ne:", theta[1], theta[2]
print "acceptances:", acceptances / float(it + 1)
return chain
def sanity_check(trials = 1000):
L = 10
matrix = [[-2,0,0,0] for i in range(L)]
mu = -10
Ne = 2
nu = Ne - 1
log_match_phats = [-nu * log(1+exp(-2*k - mu)) + log_choose(L,k) + k * log(1/4.0) + (L-k) * log(3/4.0)
for k in range(L+1)]
match_ps = normalize(map(exp, log_match_phats))
mh_motif = sample_motif_mh(matrix, mu, Ne, trials)
mh_match_counts = Counter([site.count('A') for site in mh_motif])
mh_match_ps = [mh_match_counts[k]/float(trials) for k in range(L+1)]
cftp_motif = sample_motif_cftp(matrix, mu, Ne, trials)
cftp_match_counts = Counter([site.count('A') for site in cftp_motif])
cftp_match_ps = [cftp_match_counts[k]/float(trials) for k in range(L+1)]
plt.plot(match_ps, label="Analytic")
plt.plot(mh_match_ps, label="MH")
plt.plot(cftp_match_ps, label="CFTP")
plt.xlabel("Matches")
plt.ylabel("Frequency")
def posterior_chain(motif, iterations=50000, theta0=None, sigma=1, num_spoof_sites='N', verbose=False):
"""do MH with doubly intractable MCMC one-point estimator"""
L = len(motif[0])
N = len(motif)
if num_spoof_sites == 'N':
num_spoof_sites = N # should this be N or 1?
if theta0 is None:
matrix0 = [[0,0,0,0] for i in range(L)]
mu0 = -10
Ne0 = 3
theta = (matrix0, mu0, Ne0)
else:
theta = theta0
log_f_theta = log_fhat(theta, motif)
chain = []
acceptances = 0
for it in trange(iterations):
theta_p = prop2(theta, sigma)
log_f_theta_p = log_fhat(theta_p, motif)
matrix_p, mu_p, Ne_p = theta_p
xp = sample_motif_cftp(matrix_p, mu_p, Ne_p, num_spoof_sites)
log_Z = log_fhat(theta, xp)
log_Z_p = log_fhat(theta_p, xp)
log_ar = log_f_theta_p - log_f_theta + N/num_spoof_sites * (log_Z - log_Z_p)
if log(random.random()) < log_ar:
theta = theta_p
log_f_theta = log_f_theta_p
log_Z = log_Z_p
acceptances += 1
chain.append(theta)
if verbose:
print "log(f), log_Z:", log_f_theta, log_Z
print "mean_ep:", mean(score_seq(theta[0],site) for site in motif)
print "mean_occ:", mean(occs(theta, motif))
print "mu, Ne:", theta[1], theta[2]
print "acceptances:", acceptances/float(it+1)
return chain
def sanity_check(trials=1000):
L = 10
matrix = [[-2, 0, 0, 0] for i in range(L)]
mu = -10
Ne = 2
nu = Ne - 1
log_match_phats = [
-nu * log(1 + exp(-2 * k - mu)) + log_choose(L, k) + k * log(1 / 4.0) +
(L - k) * log(3 / 4.0) for k in range(L + 1)
]
match_ps = normalize(map(exp, log_match_phats))
mh_motif = sample_motif_mh(matrix, mu, Ne, trials)
mh_match_counts = Counter([site.count('A') for site in mh_motif])
mh_match_ps = [mh_match_counts[k] / float(trials) for k in range(L + 1)]
cftp_motif = sample_motif_cftp(matrix, mu, Ne, trials)
cftp_match_counts = Counter([site.count('A') for site in cftp_motif])
cftp_match_ps = [
cftp_match_counts[k] / float(trials) for k in range(L + 1)
]
plt.plot(match_ps, label="Analytic")
plt.plot(mh_match_ps, label="MH")
plt.plot(cftp_match_ps, label="CFTP")
plt.xlabel("Matches")
plt.ylabel("Frequency")
def sample_motif((sigma, cf, Ne)):
matrix = sample_matrix(L, sigma)
mu = approx_mu(matrix, cf * N)
return sample_motif_cftp(matrix, mu, Ne, N)
def f(theta):
matrix, mu, Ne = theta
motif = sample_motif_cftp(matrix, mu, Ne, N)
return exp(-beta * (motif_ic(motif) - des_ic)**2)
def eps_from_theta(theta, L, N=100):
matrix = sample_matrix(L, sigma)
motif = sample_motif_cftp(matrix, mu, Ne, N)
eps = [score_seq(matrix, site) for site in motif]
return eps
theta = theta_p
log_f_theta = log_f_theta_p
log_Z = log_Z_p
acceptances += 1
chain.append(theta)
if verbose:
print "log(f), log_Z:", log_f_theta, log_Z
print "mean_ep:", mean(score_seq(theta[0], site) for site in motif)
print "mean_occ:", mean(occs(theta, motif))
print "mu, Ne:", theta[1], theta[2]
print "acceptances:", acceptances / float(it + 1)
return chain
def motif_from_theta((matrix, mu, Ne), N):
return sample_motif_cftp(matrix, mu, Ne, N)
def logmod(x):
return sign(x) * log(abs(x) + 1)
def interpret_chain(chain, motif, filename=None):
N = len(motif)
log_fhats = [log_fhat(theta, motif) for theta in chain]
log_Zs = [log_ZM_hack(theta, N) for theta in chain]
log_ps = [lf - log_Z for (lf, log_Z) in zip(log_fhats, log_Zs)]
plt.plot(
map(logmod,
[mean(score_seq(x[0], site) for site in motif) for x in chain]),
label="Mean Site Energy (kBT)")
def eps_from_theta(theta, L, N=100):
matrix = sample_matrix(L, sigma)
motif = sample_motif_cftp(matrix, mu, Ne, N)
eps = [score_seq(matrix, site) for site in motif]
return eps
def observe_ic_from_theta(theta, L, num_matrices=3):
sigma, mu, Ne = theta
return mean((motif_ic(sample_motif_cftp(sample_matrix(L, sigma), mu, Ne, n=100))
for _ in range(num_matrices)))
def f(theta):
matrix, mu, Ne = theta
motif = sample_motif_cftp(matrix, mu, Ne, N)
return exp(-beta*(motif_ic(motif) - des_ic)**2)
def observe_ic_from_theta(theta, L, num_matrices=3):
sigma, mu, Ne = theta
return mean(
(motif_ic(sample_motif_cftp(sample_matrix(L, sigma), mu, Ne, n=100))
for _ in range(num_matrices)))
if log(random.random()) < log_ar:
theta = theta_p
log_f_theta = log_f_theta_p
log_Z = log_Z_p
acceptances += 1
chain.append(theta)
if verbose:
print "log(f), log_Z:", log_f_theta, log_Z
print "mean_ep:", mean(score_seq(theta[0],site) for site in motif)
print "mean_occ:", mean(occs(theta, motif))
print "mu, Ne:", theta[1], theta[2]
print "acceptances:", acceptances/float(it+1)
return chain
def motif_from_theta((matrix, mu, Ne), N):
return sample_motif_cftp(matrix, mu, Ne, N)
def logmod(x):
return sign(x)*log(abs(x) + 1)
def interpret_chain(chain, motif, filename=None):
N = len(motif)
log_fhats = [log_fhat(theta,motif) for theta in chain]
log_Zs = [log_ZM_hack(theta,N) for theta in chain]
log_ps = [lf - log_Z for (lf, log_Z) in zip(log_fhats, log_Zs)]
plt.plot(map(logmod, [mean(score_seq(x[0],site) for site in motif) for x in chain]),
label="Mean Site Energy (kBT)")
plt.plot(map(logmod, [x[1] for x in chain]),label="$\mu$ (kBT)")
plt.plot(map(logmod, [x[2] for x in chain]),label="$Ne$")
plt.plot(map(logmod, log_fhats),label="log fhat")
plt.plot(map(logmod, log_Zs),label="log_ZM")