def simulate(n=200, p=100, s=10, signal=(0.5, 1), sigma=2, alpha=0.1, B=3000):
# description of statistical problem
X, y, truth = gaussian_instance(n=n,
p=p,
s=s,
equicorrelated=False,
rho=0.5,
sigma=sigma,
signal=signal,
random_signs=True,
scale=False)[:3]
dispersion = sigma**2
S = X.T.dot(y)
covS = dispersion * X.T.dot(X)
splitting_sampler = split_sampler(X * y[:, None], covS)
def meta_algorithm(X, XTXi, resid, sampler):
S = sampler(scale=0.) # deterministic with scale=0
ynew = X.dot(XTXi).dot(S) + resid # will be ok for n>p and non-degen X
G = lasso_glmnet(X, ynew, *[None]*4)
select = G.select()
return set(list(select[0]))
XTX = X.T.dot(X)
XTXi = np.linalg.inv(XTX)
resid = y - X.dot(XTXi.dot(X.T.dot(y)))
dispersion = np.linalg.norm(resid)**2 / (n-p)
selection_algorithm = functools.partial(meta_algorithm, X, XTXi, resid)
# run selection algorithm
print('SNR', np.linalg.norm(X.dot(truth)) / np.linalg.norm(y-X.dot(truth)))
print('R2', 1 - np.linalg.norm(y-X.dot(truth))**2 / np.linalg.norm(y)**2)
return full_model_inference(X,
y,
truth,
selection_algorithm,
splitting_sampler,
success_params=(1, 1),
B=B,
fit_probability=keras_fit,
fit_args={'epochs':10, 'sizes':[100]*5, 'dropout':0., 'activation':'relu'})
def simulate(n=200, p=100, s=10, signal=(0.5, 1), sigma=2, alpha=0.1, B=2000):
# description of statistical problem
X, y, truth = gaussian_instance(n=n,
p=p,
s=s,
equicorrelated=False,
rho=0.1,
sigma=sigma,
signal=signal,
random_signs=True,
scale=True)[:3]
dispersion = sigma**2
S = X.T.dot(y)
covS = dispersion * X.T.dot(X)
splitting_sampler = split_sampler(X * y[:, None], covS)
def meta_algorithm(XTX, XTXi, sampler):
min_success = 6
ntries = 10
def _alpha_grid(X, y, center, XTX):
n, p = X.shape
alphas, coefs, _ = lasso_path(X, y, Xy=center, precompute=XTX)
nselected = np.count_nonzero(coefs, axis=0)
return alphas[nselected < np.sqrt(0.8 * p)]
alpha_grid = _alpha_grid(X, y, sampler(scale=0.), XTX)
success = np.zeros((p, alpha_grid.shape[0]))
for _ in range(ntries):
scale = 1. # corresponds to sub-samples of 50%
noisy_S = sampler(scale=scale)
_, coefs, _ = lasso_path(X, y, Xy = noisy_S, precompute=XTX, alphas=alpha_grid)
success += np.abs(np.sign(coefs))
selected = np.apply_along_axis(lambda row: any(x>min_success for x in row), 1, success)
vars = set(np.nonzero(selected)[0])
return vars
XTX = X.T.dot(X)
XTXi = np.linalg.inv(XTX)
resid = y - X.dot(XTXi.dot(X.T.dot(y)))
dispersion = np.linalg.norm(resid)**2 / (n-p)
selection_algorithm = functools.partial(meta_algorithm, XTX, XTXi)
# run selection algorithm
return full_model_inference(X,
y,
truth,
selection_algorithm,
splitting_sampler,
success_params=(1, 1),
B=B,
fit_probability=keras_fit,
fit_args={'epochs':10, 'sizes':[100]*5, 'dropout':0., 'activation':'relu'})