def test_data_carving_IC(n=100,
p=200,
s=7,
sigma=5,
rho=0.3,
snr=7.,
split_frac=0.9,
ndraw=5000,
burnin=1000,
df=np.inf,
coverage=0.90,
compute_intervals=False):
counter = 0
while True:
counter += 1
X, y, beta, active, sigma = instance(n=n,
p=p,
s=s,
sigma=sigma,
rho=rho,
snr=snr,
df=df)
mu = np.dot(X, beta)
splitn = int(n*split_frac)
indices = np.arange(n)
np.random.shuffle(indices)
stage_one = indices[:splitn]
FS = info_crit_stop(y, X, sigma, cost=np.log(n), subset=stage_one)
if set(range(s)).issubset(FS.active):
results, FS = data_carving_IC(y, X, sigma,
stage_one=stage_one,
splitting=True,
ndraw=ndraw,
burnin=burnin,
coverage=coverage,
compute_intervals=compute_intervals,
cost=np.log(n))
carve = [r[1] for r in results]
split = [r[3] for r in results]
Xa = X[:,FS.variables[:-1]]
truth = np.dot(np.linalg.pinv(Xa), mu)
split_coverage = []
carve_coverage = []
for result, t in zip(results, truth):
_, _, ci, _, si = result
carve_coverage.append((ci[0] < t) * (t < ci[1]))
split_coverage.append((si[0] < t) * (t < si[1]))
return ([carve[j] for j, i in enumerate(FS.active) if i >= s],
[split[j] for j, i in enumerate(FS.active) if i >= s],
[carve[j] for j, i in enumerate(FS.active) if i < s],
[split[j] for j, i in enumerate(FS.active) if i < s],
counter, carve_coverage, split_coverage)
def test_BIC(k=10, do_sample=True):
n, p = 100, 200
X = np.random.standard_normal((n,p)) + 0.4 * np.random.standard_normal(n)[:,None]
X /= (X.std(0)[None,:] * np.sqrt(n))
Y = np.random.standard_normal(100) * 0.5
FS = info_crit_stop(Y, X, 0.5, cost=np.log(n))
final_model = len(FS.variables) - 1
if do_sample:
return [p[-1] for p in FS.model_pivots(final_model, saturated=False, burnin=5000, ndraw=5000)]
else:
saturated_pivots = FS.model_pivots(final_model)
return [p[-1] for p in saturated_pivots]
def test_BIC(do_sample=True, ndraw=8000, burnin=2000,
force=False):
X, Y, beta, active, sigma, _ = gaussian_instance()
n, p = X.shape
FS = info_crit_stop(Y, X, sigma, cost=np.log(n))
final_model = len(FS.variables)
active = set(list(active))
if active.issubset(FS.variables) or force:
which_var = [v for v in FS.variables if v not in active]
if do_sample:
return [pval[-1] for pval in FS.model_pivots(final_model, saturated=False, burnin=burnin, ndraw=ndraw, which_var=which_var)]
else:
saturated_pivots = FS.model_pivots(final_model, which_var=which_var)
return [pval[-1] for pval in saturated_pivots]
return []
def test_BIC(do_sample=True, ndraw=8000, burnin=2000, nsim=None,
force=False):
X, Y, beta, active, sigma = instance()
n, p = X.shape
FS = info_crit_stop(Y, X, sigma, cost=np.log(n))
final_model = len(FS.variables)
active = set(list(active))
if active.issubset(FS.variables) or force:
which_var = [v for v in FS.variables if v not in active]
if do_sample:
return [pval[-1] for pval in FS.model_pivots(final_model, saturated=False, burnin=burnin, ndraw=ndraw, which_var=which_var)]
else:
saturated_pivots = FS.model_pivots(final_model, which_var=which_var)
return [pval[-1] for pval in saturated_pivots]
return []
def test_BIC(k=10, do_sample=True):
n, p = 100, 200
X = np.random.standard_normal(
(n, p)) + 0.4 * np.random.standard_normal(n)[:, None]
X /= (X.std(0)[None, :] * np.sqrt(n))
Y = np.random.standard_normal(100) * 0.5
FS = info_crit_stop(Y, X, 0.5, cost=np.log(n))
final_model = len(FS.variables) - 1
if do_sample:
return [
p[-1] for p in FS.model_pivots(
final_model, saturated=False, burnin=5000, ndraw=5000)
]
else:
saturated_pivots = FS.model_pivots(final_model)
return [p[-1] for p in saturated_pivots]
def test_data_carving_IC(nsim=500,
n=100,
p=200,
s=7,
sigma=5,
rho=0.3,
signal=7.,
split_frac=0.9,
ndraw=5000,
burnin=1000,
df=np.inf,
coverage=0.90,
compute_intervals=False):
counter = 0
while counter < nsim:
counter += 1
X, y, beta, active, sigma, _ = gaussian_instance(n=n,
p=p,
s=s,
sigma=sigma,
rho=rho,
signal=signal,
df=df)
mu = np.dot(X, beta)
splitn = int(n*split_frac)
indices = np.arange(n)
np.random.shuffle(indices)
stage_one = indices[:splitn]
FS = info_crit_stop(y, X, sigma, cost=np.log(n), subset=stage_one)
if set(active).issubset(FS.active):
results, FS = data_carving_IC(y, X, sigma,
stage_one=stage_one,
splitting=True,
ndraw=ndraw,
burnin=burnin,
coverage=coverage,
compute_intervals=compute_intervals,
cost=np.log(n))
carve_split = [(r[1], r[3]) for r in results]
carve = np.array(carve_split)[:,0]
split = np.array(carve_split)[:,1]
Xa = X[:,FS.variables[:-1]]
truth = np.dot(np.linalg.pinv(Xa), mu)
split_coverage = []
carve_coverage = []
for result, t in zip(results, truth):
_, _, ci, _, si = result
carve_coverage.append((ci[0] < t) * (t < ci[1]))
split_coverage.append((si[0] < t) * (t < si[1]))
print(carve, 'carve')
print(split, 'split')
print(results, 'results')
return ([carve[j] for j, i in enumerate(FS.active) if i >= s],
[split[j] for j, i in enumerate(FS.active) if i >= s],
[carve[j] for j, i in enumerate(FS.active) if i < s],
[split[j] for j, i in enumerate(FS.active) if i < s],
counter, carve_coverage, split_coverage)
def test_data_carving_IC(n=600,
p=100,
s=10,
sigma=5,
rho=0.25,
signal=(3.5,5.),
split_frac=0.9,
ndraw=25000,
burnin=5000,
df=np.inf,
coverage=0.90,
compute_intervals=False):
X, y, beta, active, sigma, _ = gaussian_instance(n=n,
p=p,
s=s,
sigma=sigma,
rho=rho,
signal=signal,
df=df,
equicorrelated=False)
mu = np.dot(X, beta)
splitn = int(n*split_frac)
indices = np.arange(n)
np.random.shuffle(indices)
stage_one = indices[:splitn]
FS = info_crit_stop(y, X, sigma, cost=np.log(n), subset=stage_one)
con = FS.constraints()
X_E = X[:,FS.active]
X_Ei = np.linalg.pinv(X_E)
beta_bar = X_Ei.dot(y)
mu_E = X_E.dot(beta_bar)
sigma_E = np.linalg.norm(y-mu_E) / np.sqrt(n - len(FS.active))
con.mean[:] = mu_E
con.covariance = sigma_E**2 * np.identity(n)
print(sigma_E, sigma)
Z = sample_from_constraints(con,
y,
ndraw=ndraw,
burnin=burnin)
pvalues = []
for idx, var in enumerate(FS.active):
active = copy(FS.active)
active.remove(var)
X_r = X[:,active] # restricted design
mu_r = X_r.dot(np.linalg.pinv(X_r).dot(y))
delta_mu = (mu_r - mu_E) / sigma_E**2
W = np.exp(Z.dot(delta_mu))
fam = discrete_family(Z.dot(X_Ei[idx].T), W)
pval = fam.cdf(0, x=beta_bar[idx])
pval = 2 * min(pval, 1 - pval)
pvalues.append((pval, beta[var]))
return pvalues
