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UBIC.py
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UBIC.py
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import numpy as np
import statsmodels.api as sm
def find_modes(arr):
assert len(arr) > 0
uniques, counts = np.unique(arr, return_counts=True)
max_count = np.max(counts)
return uniques[counts == max_count], list(counts).index(max_count)
def decreasing_values_indices(arr):
mini = max(arr)+1; out = []
for i, e in enumerate(arr):
if e < mini:
mini = e
out.append(i)
return np.array(out)
def log_like_value(prediction, ground):
nobs = float(ground.shape[0])
ssr = np.sum(np.abs(ground - prediction)**2)
def ssr2llf(ssr, nobs):
# keep the constant term nobs2
nobs2 = nobs / 2.0
llf = -nobs2 * np.log(2 * np.pi) - nobs2 * np.log(ssr / nobs) - nobs2
# llf2 = -nobs2 * np.log(np.pi) - nobs2 * np.log(ssr / nobs2) - nobs2 # should be faster
# assert np.allclose(llf, llf2)
return llf
return ssr2llf(ssr, nobs)
def BIC_AIC(prediction, ground, nparams, reg_func=lambda x:x):
nparams = reg_func(nparams)
llf = log_like_value(prediction, ground)
return -2*llf + np.log(ground.shape[0])*nparams, -2*llf + 2*nparams
def baye_uncertainties(best_subsets, dataset, u_type='var', take_sqrt=True, ridge_lambda=0, unbiased=False):
# if you want u_type='std', then call u_type='var' and take_sqrt=True
XX, yy = dataset
assert u_type == 'var' or 'cv' in u_type
assert len(XX) == len(yy)
yy = yy.reshape(-1, 1)
post_means = np.zeros((XX.shape[-1], len(best_subsets)))
bics = []
uns = []
for k, efi in enumerate(best_subsets):
com = len(efi)
Phi = XX[:, list(efi)]
w = np.linalg.lstsq(Phi, yy, rcond=None)[0]
err = yy-Phi@w
# By MLE, we have variance_y written as follows:
variance_y = np.mean(err**2)
if unbiased: variance_y = variance_y*len(err)/(len(err)-com)
w = w[np.abs(w)>0].reshape((com, 1))
# prior_mean = np.zeros((com, 1))
prior_mean = w
prior_cov = np.identity(com)
if ridge_lambda > 0: prior_cov = (variance_y/ridge_lambda)*prior_cov
prior_cov_inv = np.linalg.pinv(prior_cov)
posterior_cov = variance_y*np.linalg.pinv(variance_y * prior_cov_inv + Phi.T@Phi)
posterior_mean = posterior_cov@(prior_cov_inv@prior_mean + (Phi.T@yy)/variance_y)
post_means[:, k:k+1][list(efi)] = posterior_mean
# collecting bics
bics.append(BIC_AIC(Phi@posterior_mean, yy, com)[0])
# collecting uns
posterior_variance = np.diag(posterior_cov)
if take_sqrt:
posterior_variance = np.sqrt(posterior_variance)
mm = posterior_mean
ss = posterior_variance
if u_type == 'var':
uns.append(ss.sum())
elif 'cv' in u_type:
code = u_type.replace('cv', '')
if len(code) == 0: order = 1
else: order = int(u_type.replace('cv', ''))
mm = np.linalg.norm(mm[:, 0], ord=order)
ss = np.linalg.norm(ss, ord=order)
uns.append(ss/mm)
uns = np.array(uns)
uns = uns/min(uns)
return post_means, bics, uns
def BICs(best_subsets, dataset, u_type='var', take_sqrt=True):
assert u_type == 'var' or 'cv' in u_type
XX, yy = dataset
bics = []
uncertainties = []
for efi in best_subsets:
fit_res = sm.OLS(yy, XX[:, efi]).fit()
bics.append(fit_res.bic)
mm = fit_res.params
ss = fit_res.bse
if not take_sqrt:
ss = ss**2
if u_type == 'var':
uncertainties.append(ss.sum())
elif 'cv' in u_type:
code = u_type.replace('cv', '')
if len(code) == 0: order = 1
else: order = int(u_type.replace('cv', ''))
mm = np.linalg.norm(mm, ord=order)
ss = np.linalg.norm(ss, ord=order)
uncertainties.append(ss/mm)
bics = np.array(bics)
uncertainties = np.array(uncertainties)
uncertainties = uncertainties/min(uncertainties)
return bics, uncertainties
def UBIC(BICs, uncertainties, n_samples, hyp=1, scale=None):
assert len(BICs) == len(uncertainties)
if scale is None:
scale = np.log(n_samples)
return BICs + hyp*scale*uncertainties
def UBICs(best_subsets, dataset, u_type='var', take_sqrt=True, use_baye=False, ridge_lambda=0, delta=1, n_lams=3, max_lam=11):
assert u_type == 'var' or 'cv' in u_type
assert n_lams > 1 and len(dataset) == 2
print(f"n_lams = {n_lams}") # Use ics[-n_lams]
delta = float(delta)
n_samples = dataset[0].shape[0]
if use_baye:
print("Using baye_uncertainties")
_, bics, uncertainties = baye_uncertainties(best_subsets, dataset, u_type, take_sqrt, ridge_lambda)
else:
print("Using OLS's uncertainties")
bics, uncertainties = BICs(best_subsets, dataset, u_type, take_sqrt)
print(uncertainties)
lam = 0
ics = []
bcs = []
bc2lam = {}
uniq = []
while lam <= max_lam:
hyp = 10**lam
ic = UBIC(bics, uncertainties, n_samples, hyp)
bc = np.argmin(ic)
if bc > 0:
ics.append(ic)
bcs.append(bc)
if bc not in bc2lam:
bc2lam[bc] = lam
print(lam, '--->', bc+1)
else:
lam -= delta
break
bcl = bcs[-n_lams:]
if len(bcl) == n_lams:
uniq = np.unique(bcl)
if len(uniq) == 1:
break
lam += delta
if len(uniq) == 0:
uniq, idx = find_modes(bcs)
uniq = sorted(uniq)
uniq = min(uniq)
lam = bc2lam[uniq]
print(UBIC(bics, uncertainties, n_samples, 10**lam))
# Checking improvement
bad_condition = True
if bics[uniq] < bics[uniq-1]:
percent_improve = abs((bics[uniq]-bics[uniq-1])/bics[uniq-1])
# print(percent_improve)
if percent_improve > 0.08:
bad_condition = False
if bad_condition:
print(f"{uniq} to {uniq+1} complexity may not be worthy with percent_improve = {percent_improve}.")
print(f"Staying at {uniq} complexity...")
uniq = uniq-1
if uniq < 0:
print("Warning: consider decreasing delta to get more sensible results!")
print(f"The optimal complexity is currently at the support sizes of {uniq+1}.")
return ics, uniq, lam