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explore_kernel.py
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# Copyright (c) 2008-2011, Jan Gasthaus
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this
# list of conditions and the following disclaimer.
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
from numpy import *
from pylab import *
import model
from utils import *
def gen_walk(themodel,start,num):
b = empty(num,dtype=object)
state = start
for i in range(num):
b[i] = state
state = themodel.walk(state)
return b
def plot_means(means):
plot(means[0,:],means[1,:],'.')
axis([-15,15,-15, 15])
def plot_lambdas(means):
plot(means[0,:],means[1,:],'.')
axis([0,40,0, 40])
def sample_prior(themodel,num):
b = empty(num,dtype=object)
for i in range(num):
b[i] = themodel.sample_prior()
return b
def get_means(walk):
N = walk.shape[0]
D = walk[0].mu.shape[0]
means = zeros((D,N))
for i in range(N):
means[:,i] = walk[i].mu
return means
def get_lambdas(walk):
N = walk.shape[0]
D = walk[0].lam.shape[0]
lams = zeros((D,N))
for i in range(N):
lams[:,i] = walk[i].lam
return lams
def get_probs(walk,themodel):
N = walk.shape[0]
ps = zeros(N)
for i in range(N):
ps[i] = themodel.p_prior_params(walk[i])
return ps
def get_cov(themodel,num,steps):
#samples = empty(num,dtype=object)
# for i in range(num):
# samples[i] = themodel.walk(start)
# means = get_means(samples)
# m = mean(means,1)
# print start.mu-m
# run num chains
means = zeros((num,steps))
start = themodel.sample_prior()
for i in range(num):
w = gen_walk(themodel,themodel.walk(start),steps)
m = get_means(w)
means[i,:] = m[0,:]
# print cov(means.T)
return cov(means,rowvar=0)
def compute_correlation(seq,diff):
m = mean(seq)
v = var(seq)
sm = seq - m
tmp = sm[:-diff]*sm[diff:]
return mean(tmp)/v
def compute_acf(seq,N):
tmp = zeros(N)
for n in range(1,N):
tmp[n] = compute_correlation(seq,n)
return tmp
def main():
params = model.DiagonalConjugateHyperParams(
a=4,
b=1,
mu0=0,
n0=0.1,
dims=2
)
# m = model.DiagonalConjugate(
# params,
# kernelClass=model.MetropolisWalk,
# kernelParams=(0.1,0.001)
# )
m = model.DiagonalConjugate(
hyper_params=params,
kernelClass=model.CaronIndependent,
kernelParams=tuple([100,0.01])
)
#diagnostic_plots(m,5000)
#plot_acf(m,10000,100)
#show()
figure(2)
sigmas = [(1,1),(10,1),(100,1),(1,0.1),(100,0.1),(1,10),(100,10)]
for l in sigmas:
print l
m = model.DiagonalConjugate(
hyper_params=params,
kernelClass=model.CaronIndependent,
kernelParams=tuple(l)
)
plot_acf(m,100000,100)
legend([r"$M=%i,\xi=%.2f$" % i for i in sigmas])
subplot(1,2,1)
F = gcf()
F.set_size_inches(6,3)
savefig("acf_caron.pdf")
#figure(3)
#diagnostic_plots(m,10000)
#show()
# print get_cov(m,1000,30)[:,0]
def plot_acf(m,walk_len,acf_len):
start = m.sample_prior()
mywalk = gen_walk(m,start,walk_len)
walk_means = get_means(mywalk)
walk_lambdas = get_lambdas(mywalk)
subplot(1,2,1)
acf = compute_acf(walk_means[0,:],acf_len)
plot(arange(1,acf.shape[0]+1),acf)
#acf = compute_acf(walk_means[1,:],acf_len)
#plot(arange(1,acf.shape[0]+1),acf)
axis([1,acf.shape[0]+1,0,1])
title(r"ACF of $\mu$")
xlabel(r"$\Delta t$")
ylabel("ACF")
grid()
subplot(1,2,2)
acf = compute_acf(walk_lambdas[0,:],acf_len)
plot(acf)
#acf = compute_acf(walk_lambdas[1,:],acf_len)
#plot(acf)
axis([1,acf.shape[0]+1,0,1])
title(r"ACF of $\lambda$")
xlabel(r"$\Delta t$")
grid()
#ylabel("ACF")
def diagnostic_plots(m,length):
start = m.sample_prior()
mywalk = gen_walk(m,start,length)
prior = sample_prior(m,length)
walk_means = get_means(mywalk)
walk_lambdas = get_lambdas(mywalk)
prior_means = get_means(prior)
prior_lambdas = get_lambdas(prior)
# print mywalk
subplot(3,2,1)
plot_means(walk_means)
subplot(3,2,2)
plot_means(prior_means)
subplot(3,2,3)
plot_lambdas(walk_lambdas)
subplot(3,2,4)
plot_lambdas(prior_lambdas)
subplot(3,2,5)
plot(walk_means[0,:],)
plot(walk_means[1,:],'r')
subplot(3,2,6)
plot(walk_lambdas[0,:],)
plot(walk_lambdas[1,:],'r')
#subplot(3,2,5)
#plot(get_probs(mywalk,m))
if __name__ == "__main__":
main()