def test_subset(k=10):
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
subset = np.ones(n, np.bool)
subset[-10:] = 0
FS = forward_stepwise(X, Y, subset=subset,
covariance=0.5**2 * np.identity(n))
for i in range(k):
FS.next()
print 'first %s variables selected' % k, FS.variables
print 'pivots for last variable of 3rd selected model knowing that we performed %d steps of forward stepwise' % k
print FS.model_pivots(3, saturated=True)
print FS.model_pivots(3, saturated=False, which_var=[FS.variables[2]], burnin=5000, ndraw=5000)
FS = forward_stepwise(X, Y, subset=subset)
for i in range(k):
FS.next()
print FS.model_pivots(3, saturated=False, which_var=[FS.variables[2]], burnin=5000, ndraw=5000)
def test_full_pvals(n=100, p=40, rho=0.3, snr=4):
X, y, beta, active, sigma = instance(n=n, p=p, snr=snr, rho=rho)
FS = forward_stepwise(X, y, covariance=sigma**2 * np.identity(n))
from scipy.stats import norm as ndist
pval = []
completed_yet = False
for i in range(min(n, p)):
FS.next()
var_select, pval_select = FS.model_pivots(i+1, alternative='twosided',
which_var=[FS.variables[-1]],
saturated=False,
burnin=2000,
ndraw=8000)[0]
pval_saturated = FS.model_pivots(i+1, alternative='twosided',
which_var=[FS.variables[-1]],
saturated=True)[0][1]
# now, nominal ones
LSfunc = np.linalg.pinv(FS.X[:,FS.variables])
Z = np.dot(LSfunc[-1], FS.Y) / (np.linalg.norm(LSfunc[-1]) * sigma)
pval_nominal = 2 * ndist.sf(np.fabs(Z))
pval.append((var_select, pval_select, pval_saturated, pval_nominal))
if set(active).issubset(np.array(pval)[:,0]) and not completed_yet:
completed_yet = True
completion_index = i + 1
return X, y, beta, active, sigma, np.array(pval), completion_index
def test_FS(k=10):
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 = forward_stepwise(X, Y, covariance=0.5**2 * np.identity(n))
for i in range(k):
FS.next()
print 'first %s variables selected' % k, FS.variables
print 'pivots for 3rd selected model knowing that we performed %d steps of forward stepwise' % k
print FS.model_pivots(3)
print FS.model_pivots(3,
saturated=False,
which_var=[FS.variables[2]],
burnin=5000,
ndraw=5000)
print FS.model_quadratic(3)
def test_full_pvals(n=100, p=40, rho=0.3, snr=4):
X, y, beta, active, sigma = instance(n=n, p=p, snr=snr, rho=rho)
FS = forward_stepwise(X, y, covariance=sigma**2 * np.identity(n))
from scipy.stats import norm as ndist
pval = []
completed_yet = False
for i in range(min(n, p)):
FS.next()
var_select, pval_select = FS.model_pivots(i + 1,
alternative='twosided',
which_var=[FS.variables[-1]],
saturated=False,
burnin=2000,
ndraw=8000)[0]
pval_saturated = FS.model_pivots(i + 1,
alternative='twosided',
which_var=[FS.variables[-1]],
saturated=True)[0][1]
# now, nominal ones
LSfunc = np.linalg.pinv(FS.X[:, FS.variables])
Z = np.dot(LSfunc[-1], FS.Y) / (np.linalg.norm(LSfunc[-1]) * sigma)
pval_nominal = 2 * ndist.sf(np.fabs(Z))
pval.append((var_select, pval_select, pval_saturated, pval_nominal))
if set(active).issubset(np.array(pval)[:, 0]) and not completed_yet:
completed_yet = True
completion_index = i + 1
return X, y, beta, active, sigma, np.array(pval), completion_index
def test_subset(k=10):
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
subset = np.ones(n, np.bool)
subset[-10:] = 0
FS = forward_stepwise(X,
Y,
subset=subset,
covariance=0.5**2 * np.identity(n))
for i in range(k):
FS.next()
print 'first %s variables selected' % k, FS.variables
print 'pivots for last variable of 3rd selected model knowing that we performed %d steps of forward stepwise' % k
print FS.model_pivots(3, saturated=True)
print FS.model_pivots(3,
saturated=False,
which_var=[FS.variables[2]],
burnin=5000,
ndraw=5000)
FS = forward_stepwise(X, Y, subset=subset)
for i in range(k):
FS.next()
print FS.model_pivots(3,
saturated=False,
which_var=[FS.variables[2]],
burnin=5000,
ndraw=5000)
def simulate_null(saturated=True):
n, p = 100, 40
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 = forward_stepwise(X, Y, covariance=0.5**2 * np.identity(n))
for i in range(5):
FS.next()
return [p[-1] for p in FS.model_pivots(3, saturated=saturated,
use_new=False)]
def simulate_null(saturated=True):
n, p = 100, 40
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 = forward_stepwise(X, Y, covariance=0.5**2 * np.identity(n))
for i in range(5):
FS.next()
return [
p[-1] for p in FS.model_pivots(3, saturated=saturated, use_new=False)
]
def test_FS_unknown(k=10):
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 = forward_stepwise(X, Y)
for i in range(k):
FS.next()
print 'first %s variables selected' % k, FS.variables
print 'pivots for last variable of 3rd selected model knowing that we performed %d steps of forward stepwise' % k
print FS.model_pivots(3, saturated=False, which_var=[FS.variables[2]], burnin=5000, ndraw=5000)
