def select_predictive_length(
X: np.ndarray,
A: np.ndarray,
k: int,
optimality: str = 'A') -> Tuple[np.ndarray, float]:
"""
:param X: np.ndarray, matrix of features
:param A: np.ndarray, prior precision matrix
:param k: int, number of samples to select
:param optimality: str, optimality type, one of ["A", "C", "D", "V"]
:return: indexes of samples subset
"""
optimalty_func = _get_optimalty(optimality)
num_samples = X.shape[0]
assert num_samples >= k, f'number of samples should be greater than k'
probs = np.linalg.norm(X, axis=1)
probs = probs / np.sum(probs)
selected_ixs = np.random.choice(num_samples,
size=k,
replace=False,
p=probs)
optimality_value = optimalty_func(Sigma=subset_covariance(X[selected_ixs]),
A=A,
X=X)
return selected_ixs, optimality_value
def select_bayesian_dpp(X: np.ndarray,
A: np.ndarray,
k: int,
optimality: str = 'A',
with_sdp: bool = False) -> \
Tuple[np.ndarray, float]:
"""
:param sigma: float, variance
:param X: np.ndarray, matrix of features
:param A: np.ndarray, prior precision matrix
:param k: int, number of samples to select
:param optimality: str, optimality type, one of ["A", "C", "D", "V"]
:return: indexes of samples subset
"""
optimalty_func = _get_optimalty(optimality)
num_samples = X.shape[0]
assert num_samples >= k, f'number of samples should be greater than k'
if with_sdp:
p = sdp(X, A, k, optimalty_func)
else:
p = k/num_samples * np.ones(num_samples)
Z = A + (X.T * p) @ X
B = (np.sqrt(p[:,None]) * X) @ frac_power(Z,-0.5)
DPP = dpp(B)
DPP.sample_exact()
all_n = np.arange(num_samples)
b = set(all_n[np.random.uniform(size = num_samples) < p])
selected_ixs = set(DPP.list_of_samples[0]) | b
selected_ixs = np.array(list(selected_ixs))
optimality_value = optimalty_func(Sigma=subset_covariance(X[selected_ixs]), A=A, X=X)
return selected_ixs, optimality_value
def select_bottom_up(X: np.ndarray,
A: np.ndarray,
k: int,
optimality: str = 'A') -> Tuple[np.ndarray, float]:
"""
:param X: np.ndarray, matrix of features
:param A: np.ndarray, prior precision matrix
:param k: int, number of samples to select
:param optimality: str, optimality type, one of ["A", "C", "D", "V"]
:return: indexes of samples subset, optimality for them
"""
num_samples = X.shape[0]
assert num_samples >= k, f'number of samples should be greater than k'
selected_ixs = []
full_samples_set = set(list(range(num_samples)))
optimalty_func = _get_optimalty(optimality)
global_score = None
for i in range(k):
candidate_samples = list(full_samples_set - set(selected_ixs))
current_optimalty = np.Inf
optimal_sample = None
for candidate_sample in candidate_samples:
candidate_ixs = np.append(selected_ixs,
[candidate_sample]).astype(int)
candidate_optimality = optimalty_func(Sigma=subset_covariance(
X[candidate_ixs]),
A=A,
X=X)
if candidate_optimality < current_optimalty:
current_optimalty = candidate_optimality
optimal_sample = candidate_sample
if optimal_sample is not None:
selected_ixs.append(optimal_sample)
if i == k - 1:
global_score = current_optimalty
return np.array(selected_ixs), global_score
to_plot = []
for optimality in opt_types:
upper_estimation_bottom_up = []
for ix in tqdm(range(len(k_linspace))):
k = k_linspace[ix]
# Sigma
assert num_samples >= k, f'number of samples should be greater than k'
selected_ixs = []
full_samples_set = set(list(range(num_samples)))
candidate_samples = list(full_samples_set -
set(selected_ixs))
for candidate_sample in candidate_samples:
candidate_ixs = np.append(
selected_ixs, [candidate_sample]).astype(int)
Sigma = subset_covariance(X[candidate_ixs])
upper_estimation_bottom_up.append(
upper_estimation(X=X,
A=A,
k=k,
Sigma=Sigma,
opt_type=optimality))
plot_prop = {'label': optimality}
object_to_plot = get_object_to_plot(
X=k_linspace,
Y=upper_estimation_bottom_up,
plot_prop=plot_prop)
to_plot.append(object_to_plot)