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step_without_prior.py
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step_without_prior.py
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from __future__ import absolute_import
from __future__ import print_function
import matplotlib.pyplot as plt
import autograd.numpy as np
import autograd.numpy.random as npr
from autograd import value_and_grad,grad
from scipy.optimize import minimize
from autograd.numpy.linalg import solve
import autograd.scipy.stats.multivariate_normal as mvn
from builtins import range
from autograd.scipy.misc import logsumexp
import itertools
import sys
from optparse import OptionParser
from autograd.util import quick_grad_check
from sklearn.cluster import KMeans
from scipy.stats import norm
import cProfile
import re
import pstats
def build_checker_dataset(n_data = 6, noise_std =0.1):
rs = npr.RandomState(0)
inputs = np.array([np.array([x,y]) for x in np.linspace(-1,1,n_data) for y in np.linspace(-1,1,n_data)])
targets = np.sign([np.prod(input) for input in inputs]) + rs.randn(n_data**2)*noise_std
return inputs, targets
def build_step_function_dataset(D=1, n_data=40, noise_std=0.1):
rs = npr.RandomState(0)
inputs = np.linspace(-2, 2, num=n_data)
targets = np.sign(inputs) + rs.randn(n_data) * noise_std
inputs = inputs.reshape((len(inputs), D))
return inputs, targets
def initialize(deep_map, X,num_pseudo_params):
smart_map = {}
for layer,layer_map in deep_map.iteritems():
smart_map[layer] = {}
for unit,gp_map in layer_map.iteritems():
smart_map[layer][unit] = {}
cov_params = gp_map['cov_params']
lengthscales = cov_params[1:]
if layer == 0:
pairs = itertools.combinations(X, 2)
dists = np.array([np.abs(p1-p2) for p1,p2 in pairs])
smart_lengthscales = np.array([np.log(np.median(dists[:,i])) for i in xrange(len(lengthscales))])
kmeans = KMeans(n_clusters = num_pseudo_params, init = 'k-means++')
fit = kmeans.fit(X)
smart_x0 = fit.cluster_centers_
#inds = npr.choice(len(X), num_pseudo_params, replace = False)
#smart_x0 = np.array(X)[inds,:]
smart_y0 = np.ndarray.flatten(smart_x0)
#smart_y0 = np.array(y)[inds]
smart_noise_scale = np.log(np.var(smart_y0))
else:
smart_x0 = gp_map['x0']
smart_y0 = np.ndarray.flatten(smart_x0[:,0])
smart_lengthscales = np.array([np.log(1) for i in xrange(len(lengthscales))])
smart_noise_scale = np.log(np.var(smart_y0))
gp_map['cov_params'] = np.append(cov_params[0],smart_lengthscales)
gp_map['x0'] = smart_x0
gp_map['y0'] = smart_y0
#gp_map['noise_scale'] = smart_noise_scale
smart_map[layer][unit] = gp_map
smart_params = pack_deep_params(smart_map)
return smart_params
def rbf_covariance(cov_params, x, xp):
output_scale = np.exp(cov_params[0])
lengthscales = np.exp(cov_params[1:])
diffs = np.expand_dims(x /lengthscales, 1)\
- np.expand_dims(xp/lengthscales, 0)
return output_scale * np.exp(-0.5 * np.sum(diffs**2, axis=2))
def pack_gp_params(gp_details):
params = np.append(gp_details['mean'],gp_details['noise_scale'])
params = np.concatenate([params,gp_details['cov_params']])
params = np.concatenate([params,np.ndarray.flatten(np.array(gp_details['x0']))])
params = np.concatenate([params,np.ndarray.flatten(np.array(gp_details['y0']))])
return params
def build_single_gp(cov_func, num_cov_params, num_pseudo_params, input_dimension):
"""Functions that perform Gaussian process regression.
cov_func has signature (cov_params, x, x')"""
def unpack_gp_params(params):
mean = params[0]
noise_scale = np.exp(params[1]) + 0.001
cov_params = params[2:2+num_cov_params]
pseudo_params = params[2+num_cov_params:]
x0, y0 = np.split(pseudo_params,[num_pseudo_params*input_dimension])
x0 = x0.reshape((num_pseudo_params,input_dimension))
return mean, cov_params, noise_scale, x0, y0
def create_gp_map(params):
mean, cov_params, noise_scale, x0, y0 = unpack_gp_params(params)
gp_map = {'mean': mean, 'noise_scale': noise_scale, 'cov_params': cov_params, 'x0': x0, 'y0': y0}
return gp_map
def predict(params, xstar, with_noise = False, FITC = False):
"""Returns the predictive mean and covariance at locations xstar,
of the latent function value f (without observation noise)."""
mean, cov_params, noise_scale, x0, y0 = unpack_gp_params(params)
cov_f_f = cov_func(cov_params, xstar, xstar)
cov_y_f = cov_func(cov_params, x0, xstar)
cov_y_y = cov_func(cov_params, x0, x0) + noise_scale * np.eye(len(y0))
pred_mean = mean + np.dot(solve(cov_y_y, cov_y_f).T, y0 - mean)
pred_cov = cov_f_f - np.dot(solve(cov_y_y, cov_y_f).T, cov_y_f)
if FITC:
pred_cov = np.diag(np.diag(pred_cov))
if with_noise:
pred_cov = pred_cov + noise_scale*np.eye(len(xstar))
return pred_mean, pred_cov
num_gp_params = 2 + num_cov_params + num_pseudo_params*input_dimension + num_pseudo_params
return num_gp_params, predict, create_gp_map
def pack_layer_params(layer_map):
params = np.array([])
for unit,gp_map in layer_map.iteritems():
params = np.concatenate([params,pack_gp_params(gp_map)])
return params
def build_single_layer(input_dimension, output_dimension, num_pseudo_params, covariance_function, random):
layer_details = [build_single_gp(covariance_function, input_dimension + 1, num_pseudo_params, input_dimension) for i in xrange(output_dimension)]
num_params_each_output, predict_layer_funcs, create_gp_map = zip(*layer_details)
total_params_layer = sum(num_params_each_output)
def unpack_layer_params(params):
gp_params = np.array_split(params, np.cumsum(num_params_each_output))
return gp_params
def create_layer_map(params):
gp_params = unpack_layer_params(params)
layer_map = {}
for unit in xrange(output_dimension):
layer_map[unit] = create_gp_map[unit](gp_params[unit])
return layer_map
def sample_from_mvn(mu, sigma,rs = npr.RandomState(0)):
return np.dot(np.linalg.cholesky(sigma+1e-6*np.eye(len(sigma))),rs.randn(len(sigma)))+mu if random == 1 else mu
def sample_mean_cov_from_layer(layer_params, xstar, with_noise = True, FITC = False):
gp_params = unpack_layer_params(layer_params)
samples = [predict_layer_funcs[i](gp_params[i],xstar,with_noise, FITC) for i in xrange(output_dimension)]
return samples
def sample_values_from_layer(layer_params, xstar, with_noise = True, rs = npr.RandomState(0), FITC = False):
samples = sample_mean_cov_from_layer(layer_params, xstar, with_noise, FITC)
outputs = [sample_from_mvn(mean,cov,rs) for mean,cov in samples]
return np.array(outputs).T
return total_params_layer, sample_mean_cov_from_layer, sample_values_from_layer, predict_layer_funcs, create_layer_map
def pack_deep_params(deep_map):
params = np.array([])
for layer,layer_map in deep_map.iteritems():
params = np.concatenate([params,pack_layer_params(layer_map)])
return params
def build_deep_gp(dimensions, covariance_function, num_pseudo_params, random):
deep_details = [build_single_layer(dimensions[i],dimensions[i+1],num_pseudo_params,covariance_function,random) for i in xrange(len(dimensions)-1)]
num_params_each_layer, sample_mean_cov_funcs, sample_value_funcs, predict_layer_funcs, create_layer_map = zip(*deep_details)
total_params_gp = sum(num_params_each_layer)
n_layers = len(dimensions)-1
def unpack_all_params(all_params):
all_layer_params = np.array_split(all_params,np.cumsum(num_params_each_layer))
return all_layer_params
def create_deep_map(all_params):
all_layer_params = unpack_all_params(all_params)
deep_map = {}
for layer in xrange(n_layers):
deep_map[layer] = create_layer_map[layer](all_layer_params[layer])
return deep_map
def sample_mean_cov_from_deep_gp(all_params, xstar, with_noise = True, rs=npr.RandomState(0), FITC = False):
xtilde = xstar
all_layer_params = unpack_all_params(all_params)
for layer in xrange(len(dimensions)-2):
layer_params = all_layer_params[layer]
xtilde = sample_value_funcs[layer](layer_params, xtilde, with_noise, rs, FITC)
final_layer = len(dimensions)-2
final_layer_params = all_layer_params[final_layer]
final_mean, final_cov = sample_mean_cov_funcs[final_layer](final_layer_params, xtilde, with_noise, FITC)[0] # index into 0 because final layer has one unit
return final_mean, final_cov
def evaluate_prior(all_params): # clean up code so we don't compute matrices twice
all_layer_params = unpack_all_params(all_params)
log_prior = 0
deep_map = create_deep_map(all_params)
for layer,layer_map in deep_map.iteritems():
for unit,gp_map in layer_map.iteritems():
cov_y_y = covariance_function(gp_map['cov_params'],gp_map['x0'],gp_map['x0']) + gp_map['noise_scale'] * np.eye(len(gp_map['y0']))
log_prior += mvn.logpdf(gp_map['y0'],np.ones(len(cov_y_y))*gp_map['mean'],cov_y_y + np.diag(np.diag(cov_y_y))*0) # CHANGE
##log_prior += mvn.logpdf(gp_map['y0'],np.ones(len(cov_y_y))*gp_map['mean'],cov_y_y + np.eye(len(cov_y_y))*tuning_param)
###log_prior += mvn.logpdf(gp_map['y0'],np.ones(len(cov_y_y))*gp_map['mean'],np.diag(np.diag(cov_y_y))*10)
return 0#log_prior
def log_likelihood(all_params, X, y, n_samples):
rs = npr.RandomState(0)
samples = [sample_mean_cov_from_deep_gp(all_params, X, True, rs, FITC = True) for i in xrange(n_samples)]
return logsumexp(np.array([mvn.logpdf(y,mean,var) for mean,var in samples])) - np.log(n_samples) \
+ evaluate_prior(all_params)
#return logsumexp(np.array([mvn.logpdf(y,mean,np.diag(np.diag(var))) for mean,var in samples])) - np.log(n_samples) \
# + evaluate_prior(all_params)
def squared_error(all_params, X, y, n_samples):
rs = npr.RandomState(0)
samples = np.array([sample_mean_cov_from_deep_gp(all_params, X, True, rs, FITC = True)[0] for i in xrange(n_samples)])
return np.mean((y - np.mean(samples,axis = 0)) ** 2)
return total_params_gp, log_likelihood, sample_mean_cov_from_deep_gp, predict_layer_funcs, squared_error, create_deep_map
if __name__ == '__main__':
random = 1
n_samples = 10
n_samples_to_plot = 5
n_data = 20
input_dimension = 1
num_pseudo_params = 10
X, y = build_step_function_dataset(D=input_dimension, n_data=n_data)
dimensions = [1,1]
n_layers = len(dimensions)-1
total_num_params, log_likelihood, sample_mean_cov_from_deep_gp, predict_layer_funcs, squared_error, create_deep_map = \
build_deep_gp(dimensions, rbf_covariance, num_pseudo_params, random)
def plot_single_gp(ax, params, layer, unit, plot_xs):
ax.cla()
rs = npr.RandomState(0)
deep_map = create_deep_map(params)
gp_details = deep_map[layer][unit]
gp_params = pack_gp_params(gp_details)
pred_mean, pred_cov = predict_layer_funcs[layer][unit](gp_params, plot_xs, with_noise = False, FITC = False)
x0 = deep_map[layer][unit]['x0']
y0 = deep_map[layer][unit]['y0']
noise_scale = deep_map[layer][unit]['noise_scale']
# Show samples from posterior.
sampled_funcs = rs.multivariate_normal(pred_mean, pred_cov*(random), size=n_samples_to_plot)
ax.plot(plot_xs, sampled_funcs.T)
ax.plot(x0, y0, 'ro')
ax.set_xticks([])
ax.set_yticks([])
def plot_deep_gp(ax, params, plot_xs):
ax.cla()
rs = npr.RandomState(0)
sampled_means_and_covs = [sample_mean_cov_from_deep_gp(params, plot_xs, rs = rs, with_noise = False, FITC = False) for i in xrange(n_samples_to_plot)]
sampled_funcs = np.array([rs.multivariate_normal(mean, cov*(random)) for mean,cov in sampled_means_and_covs])
ax.plot(plot_xs,sampled_funcs.T)
ax.plot(X, y, 'kx')
#ax.set_ylim([-1.5,1.5])
ax.set_xticks([])
ax.set_yticks([])
#ax.set_title("Full Deep GP, inputs to outputs")
def callback(params):
print("Log likelihood {}, Squared Error {}".format(-objective(params),squared_error(params,X,y,n_samples)))
rs = npr.RandomState(0)
npr.seed(0)
fig = plt.figure(figsize=(20,8), facecolor='white')
ax_large = fig.add_subplot(121, frameon=False)
ax_small = fig.add_subplot(122, frameon=False)
plt.show(block=False)
axes_set = [False, True] # Architecture of the GP. Last layer should always be 1
init_params = .1 * rs.randn(total_num_params)
deep_map = create_deep_map(init_params)
init_params = initialize(deep_map, X, num_pseudo_params)
print("Optimizing covariance parameters...")
objective = lambda params: -log_likelihood(params,X,y,n_samples)
params = minimize(value_and_grad(objective), init_params, jac=True,
method='BFGS', callback=callback,options={'maxiter':200})
params = params['x']
plot_xs = np.reshape(np.linspace(-5, 5, 300), (300,1))
deep_map = create_deep_map(params)
for axes in axes_set:
if axes:
ax = ax_small
title = "Close up"
else:
ax = ax_large
title = "Far"
plot_deep_gp(ax, params, plot_xs)
ax.plot(np.ndarray.flatten(deep_map[0][0]['x0']),deep_map[0][0]['y0'], 'ro')
if axes:
ax.set_ylim([-1.5,1.5])
else:
ax.set_ylim([-21,5])
#ax.set_title(title, fontsize = 20)
ax.set_xlabel(r'$x$',fontsize = 20)
ax.set_ylabel(r'$f(x)$',fontsize = 20)
print(deep_map[0][0]['cov_params'])
print(deep_map[0][0]['noise_scale'])
plt.savefig('step_without_prior.png', format='png', bbox_inches='tight',dpi=200)
plt.pause(80.0)