def test_rkhs_dens_and_operators(D=1, nsamps=200):
targ = dist.mixt(D, [
dist.mvnorm(3 * np.ones(D),
np.eye(D) * 0.7**2),
dist.mvnorm(7 * np.ones(D),
np.eye(D) * 1.5**2)
], [0.5, 0.5])
out_samps = targ.rvs(nsamps)
gk_x = GaussianKernel(0.7)
de = RKHSDensityEstimator(out_samps, gk_x, 0.1)
x = np.linspace(-1, 12, 200)
pl.figure()
pl.plot(x, exp(targ.logpdf(x)), 'k-', label='truth')
pl.plot(x,
de.eval_rkhs_density_approx(x[:, None]),
'b--',
label='Density estimate')
pl.plot(x,
de.eval_kme(x[:, None]),
'r:',
label='KDE/Kernel mean embedding')
pl.legend(loc='best')
pl.savefig('Density_estimation_(preimage_of_KDE).pdf')
inp_samps = (out_samps - 5)**2 + np.random.randn(*out_samps.shape)
gk_y = GaussianKernel(1)
cme = ConditionMeanEmbedding(inp_samps, out_samps, gk_y, gk_x, 5)
cdo = ConditionDensityOperator(inp_samps, out_samps, gk_y, gk_x, 5, 5)
(fig, ax) = pl.subplots(3, 1, True, False, figsize=(10, 10))
ax[2].scatter(out_samps, inp_samps, alpha=0.3)
ax[2].axhline(0, 0, 8, color='r', linestyle='--')
ax[2].axhline(5, 0, 8, color='r', linestyle='--')
ax[2].set_title("Input: y, output: x, %d pairs" % nsamps)
ax[2].set_yticks((0, 5))
d = cdo.lhood(np.array([[0.], [5.]]), x[:, None]).T
e = cme.lhood(np.array([[0.], [5.]]), x[:, None]).T
assert (d.shape[0] == 2)
assert (np.allclose(d[0], cdo.lhood(0, x[:, None])))
assert (np.allclose(d[1], cdo.lhood(5, x[:, None])))
# assert()
ax[1].plot(x, d[1], '-', label='cond. density')
ax[1].plot(x, e[1], '--', label='cond. mean emb.')
ax[1].set_title("p(x|y=5)")
ax[0].plot(x, d[0], '-', label='cond. density')
ax[0].plot(x, e[0], '--', label='cond. mean emb.')
ax[0].set_title("p(x|y=0)")
ax[0].legend(loc='best')
fig.show()
fig.savefig("conditional_density_operator.pdf")
from numpy import exp, log, sqrt
from scipy.misc import logsumexp
from autograd import grad, hessian
import distributions as dist
#import seaborn as sns
import matplotlib as mpl
import matplotlib.pyplot as plt
x = np.linspace(-2, 8, 1000)
sp.random.seed(5)
targd = dist.mixt(1, [
dist.mvnorm(np.ones(1) + 1, np.ones(1)),
dist.mvnorm(np.ones(1) + 3.8, np.ones(1))
], [0.8, 0.2])
qrw = dist.mvnorm(np.zeros(1), np.ones(1) * 0.4)
qind = dist.mvnorm(np.ones(1) * 2, np.ones(1) * 0.2)
fig, ax = plt.subplots(figsize=(4, 2))
ax.plot(x,
exp(targd.logpdf(x)) / exp(targd.logpdf(x)).max(),
label=r'$\pi$',
linewidth=2)
for i in range(3):
current = targd.rvs().flatten()
ax.plot(x,
exp(qrw.logpdf(x - current)) / exp(qrw.logpdf(x - current)).max() /
2,
import scipy.stats as stats
from numpy import exp, log, sqrt
from scipy.misc import logsumexp
from autograd import grad, hessian
import distributions as dist
#import seaborn as sns
import matplotlib as mpl
import matplotlib.pyplot as plt
x = np.linspace(-2, 8, 1000)
targd = dist.mixt(1, [
dist.mvnorm(np.ones(1) + 2, np.ones(1)),
dist.mvnorm(np.ones(1) + 3.8, np.ones(1))
], [0.7, 0.3])
g = grad(targd.logpdf)
h = hessian(targd.logpdf)
res = sp.optimize.minimize_scalar(lambda x: -targd.logpdf(x))
#maximum = 3.44515
maximum = res['x']
print("Gradient at Maximum logpdf ", g(maximum))
#mpl.style.use('seaborn')
fig, ax = plt.subplots(figsize=(5, 3))
ax.plot(x, exp(targd.logpdf(x)), label='target density', linewidth=2)
ax.plot(x,
exp(dist.mvnorm(maximum, 1. / -h(maximum)).logpdf(x)),
'--',
label='Gaussian approx',
from numpy import exp, log, sqrt
from scipy.misc import logsumexp
from autograd import grad, hessian
import distributions as dist
#import seaborn as sns
import matplotlib as mpl
import matplotlib.pyplot as plt
x = np.linspace(-2, 8, 1000)
sp.random.seed(2)
targd = dist.mixt(1, [
dist.mvnorm(np.ones(1), np.ones(1)),
dist.mvnorm(np.ones(1) + 3.8, np.ones(1))
], [0.7, 0.3])
q0 = dist.mvnorm(np.ones(1) + 3, np.ones(1) * 2)
samps = q0.rvs(20)
lw = targd.logpdf(samps).flatten() - q0.logpdf(samps)
lw = lw - logsumexp(lw)
q1 = dist.mixt(1, [dist.mvnorm(mu, np.ones(1)) for mu in samps],
lw.flatten(),
comp_w_in_logspace=True)
fig, ax = plt.subplots(figsize=(6, 3))
ax.plot(x, exp(targd.logpdf(x)), label='target density', linewidth=2)
ax.plot(x, exp(q0.logpdf(x)), '-.', label='q0', linewidth=2)
ax.plot(x, exp(q1.logpdf(x)), '--', label='q1', linewidth=2)
ax.legend(loc='best')
ax.set_xticks([])
ax.set_yticks([])
from numpy import exp, log, sqrt
from scipy.misc import logsumexp
from autograd import grad, hessian
import distributions as dist
#import seaborn as sns
import matplotlib as mpl
import matplotlib.pyplot as plt
x = np.linspace(-2, 8, 1000)
sp.random.seed(2)
targd = dist.mixt(1, [
dist.mvnorm(np.ones(1) + 1, np.ones(1)),
dist.mvnorm(np.ones(1) + 3.8, np.ones(1))
], [0.8, 0.2])
q0 = dist.mvnorm(np.ones(1), np.ones(1) * 3)
q1 = dist.mvnorm(np.ones(1), np.ones(1) * 0.1)
fig, ax = plt.subplots(figsize=(6, 3))
ax.plot(x,
exp(targd.logpdf(x)) / exp(targd.logpdf(x)).max(),
label='target density',
linewidth=2)
ax.plot(x,
exp(q0.logpdf(x)) / exp(q0.logpdf(x)).max() / 2,
'-.',
label='q_0(.|1)',
linewidth=2)
ax.plot(x,