def ci_cmle_is(X, v, theta_grid, alpha_level, T = 100, verbose = False):
cmle_is = np.empty_like(theta_grid)
r = X.sum(1)
c = X.sum(0)
for l, theta_l in enumerate(theta_grid):
logit_P_l = theta_l * v
w_l = np.exp(logit_P_l)
z = cond_a_sample(r, c, w_l, T)
logf = np.empty(T)
for t in range(T):
logQ, logP = z[t][1], z[t][2]
logf[t] = logP - logQ
logkappa = -np.log(T) + logsumexp(logf)
if verbose:
logcvsq = -np.log(T - 1) - 2 * logkappa + \
logsumexp(2 * logabsdiffexp(logf, logkappa))
print 'est. cv^2 = %.2f (T = %d)' % (np.exp(logcvsq), T)
cmle_is[l] = np.sum(np.log(w_l[X])) - logkappa
crit = -0.5 * chi2.ppf(1 - alpha_level, 1)
ci = invert_test(theta_grid, cmle_is - cmle_is.max(), crit)
if params['plot']:
plot_statistics(ax_cmle_is, theta_grid, cmle_is - cmle_is.max(), crit)
cmle_is_coverage_data['cis'].append(ci)
cmle_is_coverage_data['theta_grid'] = theta_grid
cmle_is_coverage_data['crit'] = crit
return ci
def log_partition_is(z, cvsq = False):
"""From importance-weighted sampled, estimate log-partition function."""
T = len(z)
logf = np.empty(T)
for t in range(T):
logf[t] = z[t][2] - z[t][1]
logkappa = -np.log(T) + logsumexp(logf)
if not cvsq:
return logkappa
else:
logcvsq = -np.log(T - 1) - 2 * logkappa + \
logsumexp(2 * logabsdiffexp(logf, logkappa))
return logkappa, logcvsq
def log_partition_is(z, cvsq=False):
"""From importance-weighted sampled, estimate log-partition function."""
T = len(z)
logf = np.empty(T)
for t in range(T):
logf[t] = z[t][2] - z[t][1]
logkappa = -np.log(T) + logsumexp(logf)
if not cvsq:
return logkappa
else:
logcvsq = -np.log(T - 1) - 2 * logkappa + \
logsumexp(2 * logabsdiffexp(logf, logkappa))
return logkappa, logcvsq
def ci_cmle_is(X, v, theta_grid, alpha_level, T = 100, verbose = False):
cmle_is = np.empty_like(theta_grid)
r = X.sum(1)
c = X.sum(0)
for l, theta_l in enumerate(theta_grid):
logit_P_l = theta_l * v
w_l = np.exp(logit_P_l)
z = cond_a_sample(r, c, w_l, T)
logf = np.empty(T)
for t in range(T):
logQ, logP = z[t][1], z[t][2]
logf[t] = logP - logQ
logkappa = -np.log(T) + logsumexp(logf)
if verbose:
logcvsq = -np.log(T - 1) - 2 * logkappa + \
logsumexp(2 * logabsdiffexp(logf, logkappa))
print 'est. cv^2 = %.2f (T = %d)' % (np.exp(logcvsq), T)
cmle_is[l] = np.sum(np.log(w_l[X])) - logkappa
return invert_test(theta_grid, cmle_is - cmle_is.max(),
-0.5 * chi2.ppf(1 - alpha_level, 1))
def ci_cmle_is(X, v, theta_grid, alpha_level, T=100, verbose=False):
cmle_is = np.empty_like(theta_grid)
r = X.sum(1)
c = X.sum(0)
for l, theta_l in enumerate(theta_grid):
logit_P_l = theta_l * v
w_l = np.exp(logit_P_l)
z = cond_a_sample(r, c, w_l, T)
logf = np.empty(T)
for t in range(T):
logQ, logP = z[t][1], z[t][2]
logf[t] = logP - logQ
logkappa = -np.log(T) + logsumexp(logf)
if verbose:
logcvsq = -np.log(T - 1) - 2 * logkappa + \
logsumexp(2 * logabsdiffexp(logf, logkappa))
print 'est. cv^2 = %.2f (T = %d)' % (np.exp(logcvsq), T)
cmle_is[l] = np.sum(np.log(w_l[X])) - logkappa
return invert_test(theta_grid, cmle_is - cmle_is.max(),
-0.5 * chi2.ppf(1 - alpha_level, 1))
