def main():
Log.set_loglevel(logging.DEBUG)
prior = Gaussian(Sigma=eye(2) * 100)
posterior = OzonePosterior(prior, logdet_alg="scikits",
solve_method="scikits")
proposal_cov = diag([ 4.000000000000000e-05, 1.072091680000000e+02])
mcmc_sampler = StandardMetropolis(posterior, scale=1.0, cov=proposal_cov)
start = asarray([-11.35, -13.1])
mcmc_params = MCMCParams(start=start, num_iterations=5000)
chain = MCMCChain(mcmc_sampler, mcmc_params)
chain.append_mcmc_output(StatisticsOutput(print_from=1, lag=1))
home = expanduser("~")
folder = os.sep.join([home, "sample_ozone_posterior_average_serial"])
store_chain_output = StoreChainOutput(folder)
chain.append_mcmc_output(store_chain_output)
loaded = store_chain_output.load_last_stored_chain()
if loaded is None:
logging.info("Running chain from scratch")
else:
logging.info("Running chain from iteration %d" % loaded.iteration)
chain = loaded
chain.run()
f = open(folder + os.sep + "final_chain", "w")
dump(chain, f)
f.close()
def low_rank_approx(K, d):
"""
Returns a low rank approximation factor L of the given psd matrix such that
LL^T \approx K with a given number of principal components to use
K - psd matrix to compute low-rank approximation of
d - number of principal components to use
returns (L, s, V) where
L - LL^T \approx K
s - 1D vector of Eigenvalues
V - matrix containing Eigen-row-vectors
"""
# perform SVD and only use first d components. Note that U^T=V if K psd and
# rows of V are Eigenvectors of K
U, s, V = svd(K)
U = U[:, 0:d]
V = V[0:d, :]
s = s[0:d]
S = diag(s)
# K \approx=U.dot(S.dot(V))
L = sqrt(S).dot(V)
# LL^T \approx K
return (L, s, V)
def fit(self, func, params_dist, pre_X = None, pre_y = None):
time_start = time.time()
if self.random_state is not None: np.random.seed(self.random_state)
grid, grid_scaled = self.get_grid(params_dist)
mu = np.zeros(self.n_grid) + self.mu_prior
sigma = np.ones(self.n_grid)*self.sigma_prior
X = np.zeros((self.max_iter, self.n_params))
X_scaled = np.matrix(np.zeros((self.max_iter, self.n_params)))
y = np.zeros(self.max_iter)
if (pre_X is not None) and (pre_y is not None):
pre_X_mat, pre_X_scaled = self.scale(pre_X, pre_y, params_dist)
X = np.vstack([pre_X_mat, X])
X_scaled = np.vstack([pre_X_scaled, X_scaled])
y = np.concatenate([pre_y, y])
pre_len = len(pre_y)
else: pre_len = 0
if self.verbose:
params_name = [i[:9] for i in self.params_name]
logger.info('%4s|%9s|%9s|%9s', 'Iter','Func','Max',
'|'.join(['{:9s}'.format(i) for i in params_name]))
for i in xrange(pre_len, pre_len + self.max_iter):
#beta = (i + 1)**2
if self.beta_mode == 'log':
d = len(self.params_name)
beta = 2*np.log(2 *(i + 1)**2 * np.pi**2 /.3) + \
2*d*np.log( (i+1)**2 * d * 2)
elif self.beta_mode == 'linear':
beta = i + 1
elif self.beta_mode == 'square':
beta = (i + 1)**2
else:
logger.error("What The Hell. Change Beta Parameter")
idx = np.argmax(mu + np.sqrt(beta)*sigma)
X[i,:] = grid[idx]
X_scaled[i] = grid_scaled[idx]
y[i] = func(**dict(zip(self.params_name, X[i])))
KT = self.kernel(X_scaled[:(i + 1)], X_scaled[:(i + 1)])*\
self.sigma_prior
invKT = inv(KT + self.sig**2*identity(i + 1))
grid, grid_scaled = self.get_grid(params_dist)
kT = self.kernel(X_scaled[:(i + 1)], grid_scaled)*\
self.sigma_prior**2
mu = self.mu_prior + \
kT.T.dot(invKT).dot(y[:(i + 1)] - self.mu_prior)
sigma2 = np.ones(self.n_grid)*self.sigma_prior**2 - \
diag(kT.T.dot(invKT).dot(kT))
sigma = np.sqrt(sigma2)
### Save Data
if self.verbose:
logger.info('%4d|%9.4g|%9.4g|%s', i, y[i], np.max(y[:(i + 1)]),
'|'.join(['{:9.4g}'.format(ii) for ii in X[i]]))
if time.time() - time_start > self.time_budget:
break
self.X = X[:(i + 1)]
self.y = y[:(i + 1)]
self.mu = mu
self.beta = beta
self.sigma = sigma
self.grid = grid
def corrcoef(x, y=None, rowvar=1, bias=0):
"""The correlation coefficients
"""
c = cov(x, y, rowvar, bias)
try:
d = diag(c)
except ValueError: # scalar covariance
return 1
return c/sqrt(multiply.outer(d,d))
def main():
Log.set_loglevel(logging.DEBUG)
prior = Gaussian(Sigma=eye(2) * 100)
num_estimates = 1000
home = expanduser("~")
folder = os.sep.join([home, "sample_ozone_posterior_rr_sge"])
# cluster admin set project jump for me to exclusively allocate nodes
parameter_prefix = "" # #$ -P jump"
cluster_parameters = BatchClusterParameters(foldername=folder,
memory=7.8,
loglevel=logging.DEBUG,
parameter_prefix=parameter_prefix,
max_walltime=60 * 60 * 24 - 1)
computation_engine = SGEComputationEngine(cluster_parameters, check_interval=10)
rr_instance = RussianRoulette(1e-3, block_size=400)
posterior = OzonePosteriorRREngine(rr_instance=rr_instance,
computation_engine=computation_engine,
num_estimates=num_estimates,
prior=prior)
posterior.logdet_method = "shogun_estimate"
proposal_cov = diag([ 4.000000000000000e-05, 1.072091680000000e+02])
mcmc_sampler = StandardMetropolis(posterior, scale=1.0, cov=proposal_cov)
start = asarray([-11.55, -10.1])
mcmc_params = MCMCParams(start=start, num_iterations=5000)
chain = MCMCChain(mcmc_sampler, mcmc_params)
# chain.append_mcmc_output(PlottingOutput(None, plot_from=1, lag=1))
chain.append_mcmc_output(StatisticsOutput(print_from=1, lag=1))
store_chain_output = StoreChainOutput(folder, lag=1)
chain.append_mcmc_output(store_chain_output)
loaded = store_chain_output.load_last_stored_chain()
if loaded is None:
logging.info("Running chain from scratch")
else:
logging.info("Running chain from iteration %d" % loaded.iteration)
chain = loaded
chain.run()
f = open(folder + os.sep + "final_chain", "w")
dump(chain, f)
f.close()
def log_pdf_at_quantile(self, alphas):
"""
Computes the log-pdf at a given 1d-vector of quantiles
"""
chi2_instance = chi2(self.dimension)
cuttoffs = chi2_instance.isf(1 - alphas)
log_determinant_part = -sum(log(diag(self.L)))
quadratic_part = -0.5 * cuttoffs
const_part = -0.5 * len(self.L) * log(2 * pi)
return const_part + log_determinant_part + quadratic_part
def calc_error(xi, sef):
Xk = self._get_X(xi).T
covarM = matrix(self.var_covar)
varY_hat = (Xk.T * covarM * Xk)
varY_hat = sum(diag(varY_hat))
if error_calc == 'sem':
se = sef * sqrt(varY_hat)
else:
se = sqrt(sef ** 2 + sef ** 2 * varY_hat)
return se
def main():
Log.set_loglevel(logging.DEBUG)
modulename = "sample_ozone_posterior_average_slurm"
if not FileSystem.cmd_exists("sbatch"):
engine = SerialComputationEngine()
else:
johns_slurm_hack = "#SBATCH --partition=intel-ivy,wrkstn,compute"
johns_slurm_hack = "#SBATCH --partition=intel-ivy,compute"
folder = os.sep + os.sep.join(["nfs", "data3", "ucabhst", modulename])
batch_parameters = BatchClusterParameters(foldername=folder, max_walltime=24 * 60 * 60,
resubmit_on_timeout=False, memory=3,
parameter_prefix=johns_slurm_hack)
engine = SlurmComputationEngine(batch_parameters, check_interval=1,
do_clean_up=True)
prior = Gaussian(Sigma=eye(2) * 100)
num_estimates = 100
posterior = OzonePosteriorAverageEngine(computation_engine=engine,
num_estimates=num_estimates,
prior=prior)
posterior.logdet_method = "shogun_estimate"
proposal_cov = diag([ 4.000000000000000e-05, 1.072091680000000e+02])
mcmc_sampler = StandardMetropolis(posterior, scale=1.0, cov=proposal_cov)
start = asarray([-11.35, -13.1])
mcmc_params = MCMCParams(start=start, num_iterations=2000)
chain = MCMCChain(mcmc_sampler, mcmc_params)
chain.append_mcmc_output(StatisticsOutput(print_from=1, lag=1))
home = expanduser("~")
folder = os.sep.join([home, modulename])
store_chain_output = StoreChainOutput(folder)
chain.append_mcmc_output(store_chain_output)
loaded = store_chain_output.load_last_stored_chain()
if loaded is None:
logging.info("Running chain from scratch")
else:
logging.info("Running chain from iteration %d" % loaded.iteration)
chain = loaded
chain.run()
f = open(folder + os.sep + "final_chain", "w")
dump(chain, f)
f.close()
def emp_quantiles(self, X, quantiles=arange(0.1, 1, 0.1)):
# need inverse chi2 cdf with self.dimension degrees of freedom
chi2_instance = chi2(self.dimension)
cutoffs = chi2_instance.isf(1 - quantiles)
# whitening
D, U = eig(self.L.dot(self.L.T))
D = D ** (-0.5)
W = (diag(D).dot(U.T).dot((X - self.mu).T)).T
norms_squared = array([norm(w) ** 2 for w in W])
results = zeros([len(quantiles)])
for jj in range(0, len(quantiles)):
results[jj] = mean(norms_squared < cutoffs[jj])
return results
def log_pdf(self, X):
assert(len(shape(X)) == 2)
assert(shape(X)[1] == self.dimension)
log_determinant_part = -sum(log(diag(self.L)))
quadratic_parts = zeros(len(X))
for i in range(len(X)):
x = X[i] - self.mu
# solve y=K^(-1)x = L^(-T)L^(-1)x
y = solve_triangular(self.L, x.T, lower=True)
y = solve_triangular(self.L.T, y, lower=False)
quadratic_parts[i] = -0.5 * x.dot(y)
const_part = -0.5 * len(self.L) * log(2 * pi)
return const_part + log_determinant_part + quadratic_parts
def main():
Log.set_loglevel(logging.DEBUG)
prior = Gaussian(Sigma=eye(2) * 100)
num_estimates = 2
home = expanduser("~")
folder = os.sep.join([home, "sample_ozone_posterior_rr_sge"])
computation_engine = SerialComputationEngine()
rr_instance = RussianRoulette(1e-3, block_size=10)
posterior = OzonePosteriorRREngine(
rr_instance=rr_instance, computation_engine=computation_engine, num_estimates=num_estimates, prior=prior
)
posterior.logdet_method = "shogun_estimate"
proposal_cov = diag([4.000000000000000e-05, 1.072091680000000e02])
mcmc_sampler = StandardMetropolis(posterior, scale=1.0, cov=proposal_cov)
start = asarray([-11.35, -13.1])
mcmc_params = MCMCParams(start=start, num_iterations=200)
chain = MCMCChain(mcmc_sampler, mcmc_params)
# chain.append_mcmc_output(PlottingOutput(None, plot_from=1, lag=1))
chain.append_mcmc_output(StatisticsOutput(print_from=1, lag=1))
store_chain_output = StoreChainOutput(folder, lag=50)
chain.append_mcmc_output(store_chain_output)
loaded = store_chain_output.load_last_stored_chain()
if loaded is None:
logging.info("Running chain from scratch")
else:
logging.info("Running chain from iteration %d" % loaded.iteration)
chain = loaded
chain.run()
f = open(folder + os.sep + "final_chain", "w")
dump(chain, f)
f.close()
def roots(p):
""" Return the roots of the polynomial coefficients in p.
The values in the rank-1 array p are coefficients of a polynomial.
If the length of p is n+1 then the polynomial is
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
"""
# If input is scalar, this makes it an array
p = atleast_1d(p)
if len(p.shape) != 1:
raise ValueError,"Input must be a rank-1 array."
# find non-zero array entries
non_zero = NX.nonzero(NX.ravel(p))[0]
# Return an empty array if polynomial is all zeros
if len(non_zero) == 0:
return NX.array([])
# find the number of trailing zeros -- this is the number of roots at 0.
trailing_zeros = len(p) - non_zero[-1] - 1
# strip leading and trailing zeros
p = p[int(non_zero[0]):int(non_zero[-1])+1]
# casting: if incoming array isn't floating point, make it floating point.
if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
p = p.astype(float)
N = len(p)
if N > 1:
# build companion matrix and find its eigenvalues (the roots)
A = diag(NX.ones((N-2,), p.dtype), -1)
A[0, :] = -p[1:] / p[0]
roots = _eigvals(A)
else:
roots = NX.array([])
# tack any zeros onto the back of the array
roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
return roots
def roots(p):
"""
Return the roots of a polynomial with coefficients given in p.
The values in the rank-1 array `p` are coefficients of a polynomial.
If the length of `p` is n+1 then the polynomial is described by::
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
Parameters
----------
p : array_like
Rank-1 array of polynomial coefficients.
Returns
-------
out : ndarray
An array containing the complex roots of the polynomial.
Raises
------
ValueError :
When `p` cannot be converted to a rank-1 array.
See also
--------
poly : Find the coefficients of a polynomial with a given sequence
of roots.
polyval : Evaluate a polynomial at a point.
polyfit : Least squares polynomial fit.
poly1d : A one-dimensional polynomial class.
Notes
-----
The algorithm relies on computing the eigenvalues of the
companion matrix [1]_.
References
----------
.. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*. Cambridge, UK:
Cambridge University Press, 1999, pp. 146-7.
Examples
--------
>>> coeff = [3.2, 2, 1]
>>> np.roots(coeff)
array([-0.3125+0.46351241j, -0.3125-0.46351241j])
"""
# If input is scalar, this makes it an array
p = atleast_1d(p)
if len(p.shape) != 1:
raise ValueError("Input must be a rank-1 array.")
# find non-zero array entries
non_zero = NX.nonzero(NX.ravel(p))[0]
# Return an empty array if polynomial is all zeros
if len(non_zero) == 0:
return NX.array([])
# find the number of trailing zeros -- this is the number of roots at 0.
trailing_zeros = len(p) - non_zero[-1] - 1
# strip leading and trailing zeros
p = p[int(non_zero[0]):int(non_zero[-1])+1]
# casting: if incoming array isn't floating point, make it floating point.
if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
p = p.astype(float)
N = len(p)
if N > 1:
# build companion matrix and find its eigenvalues (the roots)
A = diag(NX.ones((N-2,), p.dtype), -1)
A[0, :] = -p[1:] / p[0]
roots = eigvals(A)
else:
roots = NX.array([])
# tack any zeros onto the back of the array
roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
return roots
def roots(p):
"""
Return the roots of a polynomial with coefficients given in p.
The values in the rank-1 array `p` are coefficients of a polynomial.
If the length of `p` is n+1 then the polynomial is described by
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
Parameters
----------
p : array_like of shape(M,)
Rank-1 array of polynomial co-efficients.
Returns
-------
out : ndarray
An array containing the complex roots of the polynomial.
Raises
------
ValueError:
When `p` cannot be converted to a rank-1 array.
Examples
--------
>>> coeff = [3.2, 2, 1]
>>> print np.roots(coeff)
[-0.3125+0.46351241j -0.3125-0.46351241j]
"""
# If input is scalar, this makes it an array
p = atleast_1d(p)
if len(p.shape) != 1:
raise ValueError, "Input must be a rank-1 array."
# find non-zero array entries
non_zero = NX.nonzero(NX.ravel(p))[0]
# Return an empty array if polynomial is all zeros
if len(non_zero) == 0:
return NX.array([])
# find the number of trailing zeros -- this is the number of roots at 0.
trailing_zeros = len(p) - non_zero[-1] - 1
# strip leading and trailing zeros
p = p[int(non_zero[0]):int(non_zero[-1]) + 1]
# casting: if incoming array isn't floating point, make it floating point.
if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
p = p.astype(float)
N = len(p)
if N > 1:
# build companion matrix and find its eigenvalues (the roots)
A = diag(NX.ones((N - 2, ), p.dtype), -1)
A[0, :] = -p[1:] / p[0]
roots = eigvals(A)
else:
roots = NX.array([])
# tack any zeros onto the back of the array
roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
return roots
def GPUCB(func = f, kernel = DoubleExponential,
params_dist = {'x': Uniform(start = 0, end = 5)},
prev_X = None, prev_y = None,
sig = .1, mu_prior = 0, sigma_prior = 1, n_grid = 100, n_iter = 10,
seed = 2, time_budget = 36000):
time_start = time.time()
np.random.seed(seed)
n_params = len(params_dist)
params_name = params_dist.keys()
grid, grid_scaled = GetRandGrid(n_grid, params_dist)
mu = np.zeros(n_grid) + mu_prior
sigma = np.ones(n_grid)*sigma_prior
X = np.empty((n_iter, n_params))
X_scaled = np.matrix(np.empty((n_iter, n_params)))
y = np.empty(n_iter)
logger.info("%4s |%9s |%9s |%s", "Iter", "Func", "Max",
'|'.join(['{:6s}'.format(i) for i in params_name]))
for i in xrange(n_iter):
#beta = 2*np.log((i+1)**2*2*np.pi**2/3/.1) + \
# 2*n_params*np.log((i+1)**2*n_params)
beta = (i+1)**2
#ipdb.set_trace()
idx = np.argmax(mu + np.sqrt(beta)*sigma)
X[i,:] = grid[idx]
X_scaled[i] = grid_scaled[idx]
y[i] = func(**dict(zip(params_name, X[i])))
invKT = inv(kernel(X_scaled[:i+1], X_scaled[:i+1])*sigma_prior**2 +
sig**2*identity(i + 1))
grid, grid_scaled = GetRandGrid(n_grid, params_dist)
kT = kernel(X_scaled[:i+1], grid_scaled)*sigma_prior**2
mu = mu_prior + kT.T.dot(invKT).dot(y[:i+1] - mu_prior)
sigma2 = np.ones(n_grid)*sigma_prior**2 - diag(kT.T.dot(invKT).dot(kT))
sigma = np.sqrt(sigma2)
logger.info("%4d |%9.4g |%9.4g |%s" , i, y[i], np.max(y[:i+1]),
'|'.join(['{:6.2g}'.format(i) for i in X[i]]))
if time.time() - time_start > time_budget:
break
ipdb.set_trace()
if True:
figure(1); plt.clf(); xlim((0,5)); ylim(-4,10);
index = np.argsort(grid[:,0])
gr = grid[:,0]
plot(gr[index], mu[index], color = 'red', label = "Mean")
plot(gr[index], mu[index] + sigma[index], color = 'blue',
label = "Mean + Sigma")
plot(gr[index], mu[index] - sigma[index], color = 'blue',
label = "Mean - Sigma")
plot(X[:i+1,0], y[:i+1], 'o', color = 'green', label = "Eval Points")
plot(np.linspace(0,5, num = 500),func(np.linspace(0,5, num = 500)),
color = 'green', label = "True Func")
plot(gr[index], mu[index] + sqrt(beta)*sigma[index],
color = 'yellow', label = "Mean + sqrt(B)*Sigma")
plt.grid()
legend(loc = 2)
show()
return {'X': X,
'y': y,
'mu': mu,
'beta': beta,
'sigma': sigma,
'grid': grid}
def roots(p):
"""
Return the roots of a polynomial with coefficients given in p.
The values in the rank-1 array `p` are coefficients of a polynomial.
If the length of `p` is n+1 then the polynomial is described by
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
Parameters
----------
p : array_like of shape(M,)
Rank-1 array of polynomial co-efficients.
Returns
-------
out : ndarray
An array containing the complex roots of the polynomial.
Raises
------
ValueError:
When `p` cannot be converted to a rank-1 array.
Examples
--------
>>> coeff = [3.2, 2, 1]
>>> print np.roots(coeff)
[-0.3125+0.46351241j -0.3125-0.46351241j]
"""
# If input is scalar, this makes it an array
p = atleast_1d(p)
if len(p.shape) != 1:
raise ValueError,"Input must be a rank-1 array."
# find non-zero array entries
non_zero = NX.nonzero(NX.ravel(p))[0]
# Return an empty array if polynomial is all zeros
if len(non_zero) == 0:
return NX.array([])
# find the number of trailing zeros -- this is the number of roots at 0.
trailing_zeros = len(p) - non_zero[-1] - 1
# strip leading and trailing zeros
p = p[int(non_zero[0]):int(non_zero[-1])+1]
# casting: if incoming array isn't floating point, make it floating point.
if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
p = p.astype(float)
N = len(p)
if N > 1:
# build companion matrix and find its eigenvalues (the roots)
A = diag(NX.ones((N-2,), p.dtype), -1)
A[0, :] = -p[1:] / p[0]
roots = eigvals(A)
else:
roots = NX.array([])
# tack any zeros onto the back of the array
roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
return roots
def roots(p):
"""
Return the roots of a polynomial with coefficients given in p.
The values in the rank-1 array `p` are coefficients of a polynomial.
If the length of `p` is n+1 then the polynomial is described by::
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
Parameters
----------
p : array_like
Rank-1 array of polynomial coefficients.
Returns
-------
out : ndarray
An array containing the complex roots of the polynomial.
Raises
------
ValueError :
When `p` cannot be converted to a rank-1 array.
See also
--------
poly : Find the coefficients of a polynomial with a given sequence
of roots.
polyval : Evaluate a polynomial at a point.
polyfit : Least squares polynomial fit.
poly1d : A one-dimensional polynomial class.
Notes
-----
The algorithm relies on computing the eigenvalues of the
companion matrix [1]_.
References
----------
.. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*. Cambridge, UK:
Cambridge University Press, 1999, pp. 146-7.
Examples
--------
>>> coeff = [3.2, 2, 1]
>>> np.roots(coeff)
array([-0.3125+0.46351241j, -0.3125-0.46351241j])
"""
# If input is scalar, this makes it an array
p = atleast_1d(p)
if len(p.shape) != 1:
raise ValueError, "Input must be a rank-1 array."
# find non-zero array entries
non_zero = NX.nonzero(NX.ravel(p))[0]
# Return an empty array if polynomial is all zeros
if len(non_zero) == 0:
return NX.array([])
# find the number of trailing zeros -- this is the number of roots at 0.
trailing_zeros = len(p) - non_zero[-1] - 1
# strip leading and trailing zeros
p = p[int(non_zero[0]):int(non_zero[-1]) + 1]
# casting: if incoming array isn't floating point, make it floating point.
if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
p = p.astype(float)
N = len(p)
if N > 1:
# build companion matrix and find its eigenvalues (the roots)
A = diag(NX.ones((N - 2, ), p.dtype), -1)
A[0, :] = -p[1:] / p[0]
roots = eigvals(A)
else:
roots = NX.array([])
# tack any zeros onto the back of the array
roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
return roots
