##
# Copyright (C) 2012 Jasper Snoek, Hugo Larochelle and Ryan P. Adams
#
# This code is written for research and educational purposes only to
# supplement the paper entitled
# "Practical Bayesian Optimization of Machine Learning Algorithms"
# by Snoek, Larochelle and Adams
# Advances in Neural Information Processing Systems, 2012
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
# This code was modified to be compatible with NVAML project
"""
Chooser module for the Gaussian process expected improvement
acquisition function. Candidates are sampled densely in the unit
hypercube and then the highest EI point is selected. Slice sampling
is used to sample Gaussian process hyperparameters for the GP.
"""
import numpy as np
import numpy.random as npr
import scipy.linalg as spla
import scipy.stats as sps
from . import gp
from .utils import slice_sample
class GPEIChooser:
def __init__(self, covar="Matern52", mcmc_iters=10,
pending_samples=100, noiseless=False):
self.cov_func = getattr(gp, covar)
self.mcmc_iters = int(mcmc_iters)
self.pending_samples = pending_samples
self.D = -1
self.hyper_iters = 1
self.noiseless = bool(int(noiseless))
self.noise_scale = 0.1 # horseshoe prior
self.amp2_scale = 1 # zero-mean log normal prior
self.max_ls = 2 # top-hat prior on length scales
def _real_init(self, dims, values):
# Input dimensionality.
self.D = dims
# Initial length scales.
self.ls = np.ones(self.D)
# Initial amplitude.
self.amp2 = np.std(values) + 1e-4
# Initial observation noise.
self.noise = 1e-3
# Initial mean.
self.mean = np.mean(values)
def cov(self, x1, x2=None):
if x2 is None:
return self.amp2 * (self.cov_func(self.ls, x1, None)
+ 1e-6 * np.eye(x1.shape[0]))
else:
return self.amp2 * self.cov_func(self.ls, x1, x2)
def next(self, grid, values, durations, candidates, pending, complete):
# Don't bother using fancy GP stuff at first.
if complete.shape[0] < 2:
return int(candidates[0])
# Perform the real initialization.
if self.D == -1:
self._real_init(grid.shape[1], values[complete])
# Grab out the relevant sets.
comp = grid[complete, :]
cand = grid[candidates, :]
pend = grid[pending, :]
vals = values[complete]
if self.mcmc_iters > 0:
# Sample from hyperparameters.
overall_ei = np.zeros((cand.shape[0], self.mcmc_iters))
for mcmc_iter in range(self.mcmc_iters):
self.sample_hypers(comp, vals)
overall_ei[:, mcmc_iter] = self.compute_ei(comp, pend, cand, vals)
best_cand = np.argmax(np.mean(overall_ei, axis=1))
return int(candidates[best_cand])
else:
# Optimize hyperparameters
try:
self.optimize_hypers(comp, vals)
except:
# Initial length scales.
self.ls = np.ones(self.D)
# Initial amplitude.
self.amp2 = np.std(vals)
# Initial observation noise.
self.noise = 1e-3
ei = self.compute_ei(comp, pend, cand, vals)
best_cand = np.argmax(ei)
return int(candidates[best_cand])
def compute_ei(self, comp, pend, cand, vals):
if pend.shape[0] == 0:
# If there are no pending, don't do anything fancy.
# Current best.
best = np.min(vals)
# The primary covariances for prediction.
comp_cov = self.cov(comp)
cand_cross = self.cov(comp, cand)
# Compute the required Cholesky.
obsv_cov = comp_cov + self.noise * np.eye(comp.shape[0])
obsv_chol = spla.cholesky(obsv_cov, lower=True)
# Solve the linear systems.
alpha = spla.cho_solve((obsv_chol, True), vals - self.mean)
beta = spla.solve_triangular(obsv_chol, cand_cross, lower=True)
# Predict the marginal means and variances at candidates.
func_m = np.dot(cand_cross.T, alpha) + self.mean
func_v = self.amp2 * (1 + 1e-6) - np.sum(beta ** 2, axis=0)
# Expected improvement
func_s = np.sqrt(func_v)
u = (best - func_m) / func_s
ncdf = sps.norm.cdf(u)
npdf = sps.norm.pdf(u)
ei = func_s * (u * ncdf + npdf)
return ei
else:
# If there are pending experiments, fantasize their outcomes.
# Create a composite vector of complete and pending.
comp_pend = np.concatenate((comp, pend))
# Compute the covariance and Cholesky decomposition.
comp_pend_cov = self.cov(comp_pend) + self.noise * np.eye(
comp_pend.shape[0])
comp_pend_chol = spla.cholesky(comp_pend_cov, lower=True)
# Compute submatrices.
pend_cross = self.cov(comp, pend)
pend_kappa = self.cov(pend)
# Use the sub-Cholesky.
obsv_chol = comp_pend_chol[:comp.shape[0], :comp.shape[0]]
# Solve the linear systems.
alpha = spla.cho_solve((obsv_chol, True), vals - self.mean)
beta = spla.cho_solve((obsv_chol, True), pend_cross)
# Finding predictive means and variances.
pend_m = np.dot(pend_cross.T, alpha) + self.mean
pend_K = pend_kappa - np.dot(pend_cross.T, beta)
# Take the Cholesky of the predictive covariance.
pend_chol = spla.cholesky(pend_K, lower=True)
# Make predictions.
pend_fant = (
np.dot(pend_chol, npr.randn(pend.shape[0], self.pending_samples))
+ pend_m[:, None])
# Include the fantasies.
fant_vals = np.concatenate((np.tile(vals[:, np.newaxis],
(1, self.pending_samples)),
pend_fant))
# Compute bests over the fantasies.
bests = np.min(fant_vals, axis=0)
# Now generalize from these fantasies.
cand_cross = self.cov(comp_pend, cand)
# Solve the linear systems.
alpha = spla.cho_solve((comp_pend_chol, True), fant_vals - self.mean)
beta = spla.solve_triangular(comp_pend_chol, cand_cross, lower=True)
# Predict the marginal means and variances at candidates.
func_m = np.dot(cand_cross.T, alpha) + self.mean
func_v = self.amp2 * (1 + 1e-6) - np.sum(beta ** 2, axis=0)
# Expected improvement
func_s = np.sqrt(func_v[:, np.newaxis])
u = (bests[np.newaxis, :] - func_m) / func_s
ncdf = sps.norm.cdf(u)
npdf = sps.norm.pdf(u)
ei = func_s * (u * ncdf + npdf)
return np.mean(ei, axis=1)
def sample_hypers(self, comp, vals):
if self.noiseless:
self.noise = 1e-3
self._sample_noiseless(comp, vals)
else:
self._sample_noisy(comp, vals)
self._sample_ls(comp, vals)
def _sample_ls(self, comp, vals):
def logprob(ls):
if np.any(ls < 0) or np.any(ls > self.max_ls):
return -np.inf
cov = self.amp2 * (self.cov_func(ls, comp, None) + 1e-6 * np.eye(
comp.shape[0])) + self.noise * np.eye(comp.shape[0])
chol = spla.cholesky(cov, lower=True)
solve = spla.cho_solve((chol, True), vals - self.mean)
lp = -np.sum(np.log(np.diag(chol))) - 0.5 * np.dot(vals - self.mean,
solve)
return lp
self.ls = slice_sample(self.ls, logprob, compwise=True)
def _sample_noisy(self, comp, vals):
def logprob(hypers):
mean = hypers[0]
amp2 = hypers[1]
noise = hypers[2]
# This is pretty hacky, but keeps things sane.
if mean > np.max(vals) or mean < np.min(vals):
return -np.inf
if amp2 < 0 or noise < 0:
return -np.inf
cov = amp2 * (self.cov_func(self.ls, comp, None) +
1e-6 * np.eye(comp.shape[0])) + noise * np.eye(
comp.shape[0])
chol = spla.cholesky(cov, lower=True)
solve = spla.cho_solve((chol, True), vals - mean)
lp = -np.sum(np.log(np.diag(chol))) - 0.5 * np.dot(vals - mean, solve)
# Roll in noise horseshoe prior.
lp += np.log(np.log(1 + (self.noise_scale / noise) ** 2))
# Roll in amplitude lognormal prior
lp -= 0.5 * (np.log(amp2) / self.amp2_scale) ** 2
return lp
hypers = slice_sample(np.array([self.mean, self.amp2, self.noise]),
logprob, compwise=False)
self.mean = hypers[0]
self.amp2 = hypers[1]
self.noise = hypers[2]
def _sample_noiseless(self, comp, vals):
def logprob(hypers):
mean = hypers[0]
amp2 = hypers[1]
noise = 1e-3
if amp2 < 0:
return -np.inf
cov = amp2 * (self.cov_func(self.ls, comp, None) +
1e-6 * np.eye(comp.shape[0])) + noise * np.eye(
comp.shape[0])
chol = spla.cholesky(cov, lower=True)
solve = spla.cho_solve((chol, True), vals - mean)
lp = -np.sum(np.log(np.diag(chol))) - 0.5 * np.dot(vals - mean, solve)
# Roll in amplitude lognormal prior
lp -= 0.5 * (np.log(amp2) / self.amp2_scale) ** 2
return lp
hypers = slice_sample(np.array([self.mean, self.amp2, self.noise]), logprob,
compwise=False)
self.mean = hypers[0]
self.amp2 = hypers[1]
self.noise = 1e-3
def optimize_hypers(self, comp, vals):
mygp = gp.GP(self.cov_func.__name__)
mygp.real_init(comp.shape[1], vals)
mygp.optimize_hypers(comp, vals)
self.mean = mygp.mean
self.ls = mygp.ls
self.amp2 = mygp.amp2
self.noise = mygp.noise
