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mcmc_svm.py
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mcmc_svm.py
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import numpy as np
from utils import compute_target, compute_std_and_var
def compute_mcmc_svm(X, y, nu, abs_eps, max_iterations, noisy=False, noise_period=20, seed=None):
"""
Implementation of algorithm MCMC-SVM for a value alpha of 1.
Parameters
----------
X : ndarary
An n by d array of n observation in an d-dimensional space.
y : ndarray
An n by 1 array of n responses.
alpha : float
Parameter used for L-regularization.
nu : float
Constant used for L-regularization.
abs_eps : float
Absolute tolerance used to confirm convergence.
max_iterations : int
Maximum number of iterations to run.
noisy : bool
Flag indicating whether or not to produce logs.
noise_period : in
Wait noise_period iterations before logging.
seed : int or None
Random seed used to seed numpy.random. No seeding is performed if None is passed.
Returns
-------
betas : ndarray
An N x d x 1 array of the N successive beta values. N is the number of iterations
b_values : ndarray
An N x d x 1 array of the N successive prior mean values of beta. N is the number of iterations
"""
if seed is not None:
np.random.seed(seed)
if noisy:
n_fill = int(np.log10(max_iterations)) + 1
_, d = X.shape
yX = y * X
std, var = compute_std_and_var(X)
inv_var_matrix = np.diagflat(1 / var)
beta = np.random.randn(d, 1)
betas = [beta]
omega_inv = (nu * std) / np.abs(beta)
lam_inv = np.abs(1 - yX @ beta)
b_values = []
iteration = 1
while True:
if noisy and iteration % noise_period == 0:
loss = compute_target(X, y, 1, nu, beta)
print(f'At iteration ({str(iteration).zfill(n_fill)}/{str(max_iterations).zfill(n_fill)}), loss = {loss:.3f}')
# prepping step 1
B = np.linalg.inv(inv_var_matrix @ np.diagflat(omega_inv) / (nu ** 2) + yX.T @ np.diagflat(lam_inv) @ yX)
b = B @ yX.T @ (1 + lam_inv)
b_values.append(b)
# step 1
new_beta = np.random.multivariate_normal(b.squeeze(), B).reshape(-1, 1)
if np.abs(beta - new_beta).max() <= abs_eps or iteration == max_iterations:
if noisy:
loss = compute_target(X, y, 1, nu, beta)
print(f'Finished run ({str(iteration).zfill(n_fill)}/{str(max_iterations).zfill(n_fill)}), loss = {loss:.3f}')
return np.array(betas), np.array(b_values)
beta = new_beta
betas.append(beta)
# step 2
gap = np.abs(1 - yX @ beta)
is_zero = np.isclose(gap, 0)
lam_inv = np.zeros_like(gap)
lam_inv[is_zero] = 1 / (np.random.normal(size=is_zero.sum()) ** 2)
lam_inv[~is_zero] = np.random.wald(1 / gap[~is_zero], 1)
# step 3
gap = np.abs(beta) / (nu * std)
is_zero = np.isclose(gap, 0)
omega_inv = np.zeros_like(gap)
omega_inv[is_zero] = 1 / (np.random.normal(size=is_zero.sum()) ** 2)
omega_inv[~is_zero] = np.random.wald(1 / gap[~is_zero], 1)
iteration += 1
def compute_mcmc_svm_with_nu(X, y, anu, bnu, abs_eps, max_iterations, noisy=False, noise_period=20, seed=None):
"""
Implementation of algorithm MCMC-SVM for a value alpha of 1.
Parameters
----------
X : ndarary
An n by d array of n observation in an d-dimensional space.
y : ndarray
An n by 1 array of n responses.
alpha : float
Parameter used for L-regularization.
anu : float
Constant used for the prior of nu.
bnu : float
Constant used for the prior of nu.
abs_eps : float
Absolute tolerance used to confirm convergence.
max_iterations : int
Maximum number of iterations to run.
noisy : bool
Flag indicating whether or not to produce logs.
noise_period : in
Wait noise_period iterations before logging.
seed : int or None
Random seed used to seed numpy.random. No seeding is performed if None is passed.
Returns
-------
betas : ndarray
An N x d x 1 array of the N successive beta values. N is the number of iterations
b_values : ndarray
An N x d x 1 array of the N successive prior mean values of beta. N is the number of iterations
"""
if seed is not None:
np.random.seed(seed)
if noisy:
n_fill = int(np.log10(max_iterations)) + 1
_, d = X.shape
yX = y * X
std, var = compute_std_and_var(X)
inv_var_matrix = np.diagflat(1 / var)
beta = np.random.randn(d, 1)
betas = [beta]
nu = 1
nu_values = [nu]
omega_inv = (nu * std) / np.abs(beta)
lam_inv = np.abs(1 - yX @ beta)
b_values = []
iteration = 1
while True:
if noisy and iteration % noise_period == 0:
loss = compute_target(X, y, 1, nu, beta)
print(f'At iteration ({str(iteration).zfill(n_fill)}/{str(max_iterations).zfill(n_fill)}), loss = {loss:.3f}')
# prepping step 1
B = np.linalg.inv(inv_var_matrix @ np.diagflat(omega_inv) / (nu ** 2) + yX.T @ np.diagflat(lam_inv) @ yX)
b = B @ yX.T @ (1 + lam_inv)
b_values.append(b)
# step 1
new_beta = np.random.multivariate_normal(b.squeeze(), B).reshape(-1, 1)
if np.abs(beta - new_beta).max() <= abs_eps or iteration == max_iterations:
if noisy:
loss = compute_target(X, y, 1, nu, beta)
print(f'Finished run ({str(iteration).zfill(n_fill)}/{str(max_iterations).zfill(n_fill)}), loss = {loss:.3f}')
return np.array(betas), np.array(b_values), np.array(nu_values).reshape(-1, 1)
beta = new_beta
betas.append(beta)
# step 2
gap = np.abs(1 - yX @ beta)
is_zero = np.isclose(gap, 0)
lam_inv = np.zeros_like(gap)
lam_inv[is_zero] = 1 / (np.random.normal(size=is_zero.sum()) ** 2)
lam_inv[~is_zero] = np.random.wald(1 / gap[~is_zero], 1)
# step 3
gap = np.abs(beta) / (nu * std)
is_zero = np.isclose(gap, 0)
omega_inv = np.zeros_like(gap)
omega_inv[is_zero] = 1 / (np.random.normal(size=is_zero.sum()) ** 2)
omega_inv[~is_zero] = np.random.wald(1 / gap[~is_zero], 1)
# step 4
nu = 1 / np.random.gamma(shape=anu + d, scale=1 / (bnu + np.abs(beta).sum()))
nu_values.append(nu)
iteration += 1