def get_abc_data(banded=True, p=50, n=100):
from scipy.stats import zscore
if banded:
weights = np.asarray([1.0, 100.0, 10000.])
else:
weights = np.ones(3)
weights /= np.linalg.norm(weights)
Aw, (A, Atest), (Yat, Yav) = tikutils.generate_data(n=n,
p=p,
v=20,
testsize=50,
feature_sparsity=0.5,
noise=0.)
Bw, (B, Btest), (Ybt, Ybv) = tikutils.generate_data(n=n,
p=p,
v=20,
testsize=50,
feature_sparsity=0.5,
noise=0.)
Cw, (C, Ctest), (Yct, Ycv) = tikutils.generate_data(n=n,
p=p,
v=20,
testsize=50,
feature_sparsity=0.5,
noise=0.)
responses_train = zscore(Yat * weights[0] + Ybt * weights[1] +
Yct * weights[2])
responses_test = zscore(Yav * weights[0] + Ybv * weights[1] +
Ycv * weights[2])
for rdx in range(responses_train.shape[-1]):
# different noise levels
noise = np.log(rdx + 1)
responses_train[:, rdx] += np.random.randn(
responses_train.shape[0]) * noise
responses_test[:,
rdx] += np.random.randn(responses_test.shape[0]) * noise
responses_train = tikutils.hrf_convolution(responses_train)
responses_test = tikutils.hrf_convolution(responses_test)
features_train = [
A.astype(np.float64),
B.astype(np.float64),
C.astype(np.float64)
]
features_test = [
Atest.astype(np.float64),
Btest.astype(np.float64),
Ctest.astype(np.float64)
]
return (features_train, features_test, responses_train, responses_test)
def test_solve_l2_primal():
ridges = [0.0, 10.0, 100.0, 1000.0]
ridge_test = 1
# get some data
B, (Xtrn, Xtest), (Ytrn, Ytest) = tikutils.generate_data(n=100, p=20,
noise=0, testsize=20, dozscore=False)
# get direct solution
Bhat_direct = simple_ridge_primal(Xtrn, Ytrn, ridge=ridges[ridge_test]**2)
fit = solve_l2_primal(Xtrn, Ytrn, Xtest=Xtest, Ytest=zscore(Ytest),
ridges=ridges, verbose=False, EPS=0, # NO EPS threshold
weights=True, predictions=False, performance=False)
Bhat_indirect = fit['weights']
assert np.allclose(Bhat_indirect[ridge_test], Bhat_direct)
# check we can get OLS
Bols = ols(Xtrn, Ytrn)
Bhat_indirect_ols = fit['weights'][0]
assert np.allclose(Bols, Bhat_indirect_ols)
# test keyword arguments work as expected
fit = solve_l2_primal(Xtrn, Ytrn, Xtest=Xtest, Ytest=zscore(Ytest),
ridges=ridges, verbose=False, EPS=0, # NO EPS threshold
weights=False, predictions=True, performance=True)
assert ('predictions' in fit) and ('performance' in fit) and ('weights' not in fit)
# check predictions
Yhat_direct = np.dot(Xtest, Bhat_direct)
Yhat_indirect = fit['predictions']
assert np.allclose(Yhat_indirect[ridge_test], Yhat_direct)
# check performance
cc_direct = tikutils.columnwise_correlation(Yhat_direct, Ytest)
cc_indirect = fit['performance']
assert np.allclose(cc_direct, cc_indirect[ridge_test])
def test_solve_l2_dual():
ridges = [0.0, 10.0, 100.0, 1000.0]
ridge_test = 2
# get some data
B, (Xtrn, Xtest), (Ytrn, Ytest) = tikutils.generate_data(n=100, p=20,
noise=0, testsize=20, dozscore=False)
# get direct solution
Bhat_direct = simple_ridge_dual(Xtrn, Ytrn, ridge=ridges[ridge_test]**2)
Ktrn = np.dot(Xtrn, Xtrn.T)
Ktest = np.dot(Xtest, Xtrn.T)
fit = solve_l2_dual(Ktrn, Ytrn, Ktest=Ktest, Ytest=zscore(Ytest),
ridges=ridges, verbose=False, EPS=0, # NO EPS threshold
weights=True, predictions=False, performance=False)
# project to linear space
Bhat_indirect = np.tensordot(Xtrn.T, fit['weights'], (1,1)).swapaxes(0,1)
assert np.allclose(Bhat_indirect[ridge_test], Bhat_direct)
# check we can get OLS
Bols = ols(Xtrn, Ytrn)
# project to linear space
Bhat_indirect_ols = np.dot(Xtrn.T, fit['weights'][0])
assert np.allclose(Bols, Bhat_indirect_ols)
# test keyword arguments work as expected
fit = solve_l2_dual(Ktrn, Ytrn, Ktest=Ktest, Ytest=zscore(Ytest),
ridges=ridges, verbose=False, EPS=0, # NO EPS threshold
weights=False, predictions=True, performance=True)
assert ('predictions' in fit) and ('performance' in fit) and ('weights' not in fit)
# check predictions
Yhat_direct = np.dot(Xtest, Bhat_direct)
Yhat_indirect = fit['predictions']
assert np.allclose(Yhat_indirect[ridge_test], Yhat_direct)
# check performance
cc_direct = tikutils.columnwise_correlation(Yhat_direct, Ytest)
cc_indirect = fit['performance']
assert np.allclose(cc_direct, cc_indirect[ridge_test])
# compare against primal representation
fit_primal = solve_l2_primal(Xtrn, Ytrn, Xtest=Xtest, Ytest=zscore(Ytest),
ridges=ridges, verbose=False, EPS=0, # NO EPS threshold
weights=True, predictions=False, performance=False)
Bhat_primal = fit_primal['weights']
assert np.allclose(Bhat_primal, Bhat_indirect)
# test non-linear kernel
kernels_to_test = ['gaussian', 'ihpolykern', 'hpolykern', 'multiquad']
kernel_params_to_test = [10., 3., 2., 20.]
ridges = [0] # No regularization
for kernel_name, kernel_param in zip(kernels_to_test, kernel_params_to_test):
lzk = lazy_kernel(Xtrn, kernel_type=kernel_name)
lzk.update(kernel_param)
rlambdas = zscore(np.random.randn(Xtrn.shape[0], 20))
Y = np.dot(lzk.kernel, rlambdas)
# NB: multiquad kernel produces negative eigen-values! This means that
# thresholding the eigen-values to be positive (EPS > 0) will lead to
# inperfect weight recovery. For this reason, the test uses EPS=None.
EPS = None if kernel_name == 'multiquad' else 0
fit = solve_l2_dual(lzk.kernel, Y,
ridges=ridges, verbose=False, EPS=EPS,
weights=True, predictions=False, performance=False)
assert np.allclose(rlambdas, fit['weights'].squeeze())
def test_olspred():
B, (Xtrn, Xtest), (Ytrn, Ytest) = tikutils.generate_data(noise=0, testsize=20, dozscore=False)
Bh = ols(Xtrn, Ytrn)
Ytest_direct = np.dot(Xtest, Bh) # Explicit predictions
Ytest_tricks = olspred(Xtrn, Ytrn, Xtest=Xtest) # implicit predictions
assert np.allclose(Ytest_tricks, Ytest_direct)
# implicit within-set predictions
Ytrn_hat = olspred(Xtrn, Ytrn)
assert np.allclose(Ytrn_hat, Ytrn)
def test_generalized_tikhonov():
Ns = [100, 50]
Ps = [50, 100]
for N, p in zip(Ns, Ps):
B, (X, Xtest), (Y, Ytest) = tikutils.generate_data(n=N, p=p, testsize=30)
Ytest = zscore(Ytest)
L = np.random.randint(0, 100, (p,p))
Li = LA.inv(L)
ridge = 10.0
direct = simple_generalized_tikhonov(X, Y, L, ridge=ridge**2)
stdform = generalized_tikhonov(X, Y, Li, ridge=ridge**2)
stdform_dual = _generalized_tikhonov_dual(X, Y, Li, ridge=ridge**2)
assert np.allclose(direct, stdform)
assert np.allclose(direct, stdform_dual)
# compute predictions and performance
Yhat = np.dot(Xtest, direct)
cc = tikutils.columnwise_correlation(Yhat, Ytest)
# use standard machinery
Atrn = np.dot(X, Li)
Atest = np.dot(Xtest, Li)
fit = solve_l2_primal(Atrn, Y, Atest, Ytest=Ytest,
ridges=[ridge], performance=True,
weights=True, predictions=True)
W = np.dot(Li, fit['weights'].squeeze())
assert np.allclose(W, direct)
assert np.allclose(fit['predictions'], Yhat)
assert np.allclose(fit['performance'], cc)
# use standard machiner dual
Atrn = np.dot(X, Li)
Atest = np.dot(Xtest, Li)
Ktrn = np.dot(Atrn, Atrn.T)
Ktest = np.dot(Atest, Atrn.T)
fit = solve_l2_dual(Ktrn, Y, Ktest, Ytest=Ytest,
ridges=[ridge], performance=True,
weights=True, predictions=True)
W = np.dot(Li, np.dot(Atrn.T, fit['weights'].squeeze()))
assert np.allclose(W, direct)
assert np.allclose(fit['predictions'], Yhat)
assert np.allclose(fit['performance'], cc)
# Check that it works
fit = cvridge(X, Y, Xtest=Xtest, Ytest=Ytest,
ridges=[ridge], Li=Li,
verbose=False,
weights=True,
performance=True,
predictions=True)
cvresults = fit['cvresults']
assert np.allclose(fit['weights'], direct)
assert np.allclose(fit['performance'], cc)
assert np.allclose(fit['predictions'], Yhat)
def test_ols():
B, X, Y = tikutils.generate_data(noise=0, dozscore=False)
Bh = ols(X, Y)
assert np.allclose(Bh, B)
Bh = _ols(X, Y)
assert np.allclose(Bh, B)
def test_cvridge():
ridges = np.logspace(1, 3, 10)
voxel = 20
ridge = 5
ps = [50, 100]
ns = [100, 50]
# test primal and dual
for N, P in zip(ns, ps):
# get fake data
B, (Xt, Xv), (Yt, Yv) = tikutils.generate_data(n=N,
p=P,
testsize=30,
v=100,
noise=2.0)
# Check all works for 1 voxel case
fit = cvridge(Xt,
Yt[:, voxel].squeeze(),
Xtest=Xv,
Ytest=Yv[:, voxel].squeeze(),
ridges=ridges,
kernel_name='linear',
kernel_params=None,
folds='cv',
nfolds=5,
blocklen=5,
verbose=False,
EPS=0,
withinset_test=False,
performance=True,
predictions=True,
weights=True)
cvres = fit['cvresults']
optidx = np.argmax(cvres.squeeze().mean(0))
optridge = ridges[optidx]
B = simple_ridge_primal(Xt, Yt, ridge=optridge**2)
assert np.allclose(fit['weights'].squeeze(), B[:, voxel])
# check all works for 1 ridge case
fit = cvridge(Xt,
Yt,
Xtest=Xv,
Ytest=Yv,
ridges=[ridges[ridge]],
kernel_name='linear',
kernel_params=None,
folds='cv',
nfolds=5,
blocklen=5,
verbose=False,
EPS=0,
withinset_test=False,
performance=True,
predictions=True,
weights=True)
cvres = fit['cvresults']
B = simple_ridge_primal(Xt, Yt, ridge=ridges[ridge]**2)
assert np.allclose(fit['weights'].squeeze(), B)
# one ridge, one voxel
fit = cvridge(Xt,
Yt[:, voxel].squeeze(),
Xtest=Xv,
Ytest=Yv[:, voxel].squeeze(),
ridges=[ridges[ridge]],
kernel_name='linear',
kernel_params=None,
folds='cv',
nfolds=5,
blocklen=5,
verbose=False,
EPS=0,
withinset_test=False,
performance=True,
predictions=True,
weights=True)
cvres = fit['cvresults']
B = simple_ridge_primal(Xt, Yt, ridge=ridges[ridge]**2)
assert np.allclose(fit['weights'].squeeze(), B[:, voxel])
# check predictions work
fit = cvridge(Xt,
Yt,
Xtest=Xv,
Ytest=Yv,
ridges=ridges,
kernel_name='linear',
kernel_params=None,
folds='cv',
nfolds=5,
blocklen=5,
verbose=False,
EPS=0,
withinset_test=False,
performance=True,
predictions=True,
weights=True)
cvres = fit['cvresults']
optidx = np.argmax(cvres.squeeze().mean(0).mean(-1))
optridge = ridges[optidx]
B = simple_ridge_primal(Xt, Yt, ridge=optridge**2)
assert np.allclose(fit['weights'], B)
# test cv results
folds = [
(np.arange(10, N), np.arange(10)),
(np.arange(20, N), np.arange(20)),
(np.arange(30, N), np.arange(30)),
]
fit = cvridge(Xt,
Yt,
Xtest=Xv,
Ytest=Yv,
ridges=ridges,
kernel_name='linear',
kernel_params=None,
folds=folds,
nfolds=5,
blocklen=5,
verbose=False,
EPS=0,
withinset_test=False,
performance=True,
predictions=True,
weights=True)
cvres = fit['cvresults']
for fdx in range(len(folds)):
# compute the fold prediction performance
B = simple_ridge_primal(Xt[folds[fdx][0]],
Yt[folds[fdx][0]],
ridge=ridges[ridge]**2)
Yhat = np.dot(Xt[folds[fdx][1]], B)
cc = tikutils.columnwise_correlation(Yhat, Yt[folds[fdx][1]])
assert np.allclose(cc, cvres[fdx, 0, ridge])
# test non-linear kernel CV
Ns = [100, 50]
Ps = [50, 100]
from scipy import linalg as LA
np.random.seed(8)
for N, P in zip(Ns, Ps):
B, (Xtrn, Xtest), (Ytrn,
Ytest) = tikutils.generate_data(n=N,
p=P,
noise=0,
testsize=20,
dozscore=False)
# test non-linear kernel
kernels_to_test = ['gaussian', 'ihpolykern', 'hpolykern', 'multiquad']
kernel_params = [10., 3., 2., 100.]
ridges = [0.0]
for kernel_name, kernel_param in zip(kernels_to_test, kernel_params):
lzk = lazy_kernel(Xtrn, kernel_type=kernel_name)
lzk.update(kernel_param)
rlambdas = zscore(np.random.randn(Xtrn.shape[0], 20))
Y = np.dot(lzk.kernel, rlambdas)
# NB: multiquad kernel produces negative eigen-testues! This means that
# thresholding the eigen-testues to be positive (EPS > 0) will lead to
# inperfect weight recovery. For this reason, the test uses EPS=None.
EPS = None if kernel_name == 'multiquad' else 0
fit = cvridge(Xtrn,
Y,
ridges=ridges,
kernel_name=kernel_name,
kernel_params=kernel_params,
folds='cv',
nfolds=5,
blocklen=5,
trainpct=0.8,
verbose=True,
EPS=EPS,
weights=True,
predictions=False,
performance=False)
cvres = fit['cvresults']
surface = np.nan_to_num(cvres.mean(0)).mean(-1)
# find the best point in the 2D space
max_point = np.where(surface.max() == surface)
# make sure it's unique (conservative-ish biggest ridge/parameter)
max_point = map(max, max_point)
# The maximum point
kernmax, ridgemax = max_point
kernopt, ridgeopt = kernel_params[kernmax], ridges[ridgemax]
# Solve explicitly
lzk.update(kernopt)
L, Q = LA.eigh(lzk.kernel)
rlambda_hat = np.dot(np.dot(Q, np.diag(1.0 / L)), np.dot(Q.T, Y))
assert np.allclose(rlambda_hat, fit['weights'].squeeze())
if N > P:
# N < P cross-testidation will not always work in recovering the true
# kernel parameter because similar kernel parameters yield close to
# optimal answers in the folds
# NB: gaussian kernel doesn't always pass this test because
# the optimal kernel parameter is not always found.
# the np.seed fixes this.
assert np.allclose(rlambdas, fit['weights'].squeeze())