def test_contour_plot():
data = _setup_linear_regression()
bpplt.contour(data['B'],
np.linspace(1, 3, 1000),
np.linspace(1, 9, 1000),
n=10,
colors='k')
bpplt.plot(data['c'],
x=data['k'],
color='r',
marker='x',
linestyle='None',
markersize=10,
markeredgewidth=2)
def run():
k = 2
c = 5
s = 2
x = np.arange(10)
y = k * x + c + s * np.random.randn(10)
X=np.vstack([x,np.ones(len(x))]).T
B = GaussianARD(0, 1e-6, shape=(2,))
F = SumMultiply('i,i', B, X)
tau = Gamma(1e-3, 1e-3)
Y = GaussianARD(F, tau)
Y.observe(y)
from bayespy.inference import VB
Q = VB(Y, B, tau)
Q.update(repeat=1000)
xh = np.linspace(-5, 15, 100)
Xh = np.vstack([xh, np.ones(len(xh))]).T
Fh = SumMultiply('i,i', B, Xh)
bpplt.pyplot.figure()
bpplt.plot(Fh, x=xh, scale=2)
bpplt.plot(y, x=x, color='r', marker='x', linestyle='None')
bpplt.plot(k*xh+c, x=xh, color='r');
bpplt.pyplot.show()
import numpy
numpy.random.seed(1)
M = 20
N = 100
import numpy as np
x = np.random.randn(N, 2)
w = np.random.randn(M, 2)
f = np.einsum('ik,jk->ij', w, x)
y = f + 0.1 * np.random.randn(M, N)
D = 10
from bayespy.nodes import GaussianARD, Gamma, SumMultiply
X = GaussianARD(0, 1, plates=(1, N), shape=(D, ))
alpha = Gamma(1e-5, 1e-5, plates=(D, ))
C = GaussianARD(0, alpha, plates=(M, 1), shape=(D, ))
F = SumMultiply('d,d->', X, C)
tau = Gamma(1e-5, 1e-5)
Y = GaussianARD(F, tau)
Y.observe(y)
from bayespy.inference import VB
Q = VB(Y, X, C, alpha, tau)
C.initialize_from_random()
from bayespy.inference.vmp.transformations import RotateGaussianARD
rot_X = RotateGaussianARD(X)
rot_C = RotateGaussianARD(C, alpha)
from bayespy.inference.vmp.transformations import RotationOptimizer
R = RotationOptimizer(rot_X, rot_C, D)
Q.set_callback(R.rotate)
Q.update(repeat=1000)
import bayespy.plot as bpplt
bpplt.plot(F)
bpplt.plot(f, color='r', marker='x', linestyle='None')
#( 5 : Parameter expansion 収束が遅い時) # from bayespy.inference.vmp import transformations # rotX = transformations.RotateGaussianARD(X) # rotC = transformations.RotateGaussianARD(C, alpha) # R = transformations.RotationOptimizer(rotC, rotX, D) # R.rotate() # alpha.initialize_from_prior() # C.initialize_from_prior() # X.initialize_from_parameters(np.random.randn(1, 100, D), 10) # tau.initialize_from_prior() # Q = VB(Y, C, X, alpha, tau) # Q.callback = R.rotate # Q.update(repeat=1000, tol=1e-6) # -----Examining the results----- # Plotting the results bpplt.pyplot.figure() bpplt.pdf(Q['tau'], np.linspace(60, 140, num=100)) V = Gaussian([3, 5], [[4, 2], [2, 5]]) bpplt.pyplot.figure() bpplt.contour(V, np.linspace(1, 5, num=100), np.linspace(3, 7, num=100)) bpplt.pyplot.figure() bpplt.hinton(C) bpplt.pyplot.figure() bpplt.plot(X, axis=-2) bpplt.pyplot.show()
def test_contour_plot():
data = _setup_linear_regression()
bpplt.contour(data['B'], np.linspace(1,3,1000), np.linspace(1,9,1000),
n=10, colors='k')
bpplt.plot(data['c'], x=data['k'], color='r', marker='x', linestyle='None',
markersize=10, markeredgewidth=2)
from bayespy.inference import VB
Q = VB(X, C, gamma, A, alpha, tau, Y)
w = 0.3
a = np.array([[np.cos(w), -np.sin(w), 0, 0], [np.sin(w),
np.cos(w), 0, 0], [0, 0, 1, 0],
[0, 0, 0, 0]])
c = np.random.randn(M, 4)
x = np.empty((N, 4))
f = np.empty((M, N))
y = np.empty((M, N))
x[0] = 10 * np.random.randn(4)
f[:, 0] = np.dot(c, x[0])
y[:, 0] = f[:, 0] + 3 * np.random.randn(M)
for n in range(N - 1):
x[n + 1] = np.dot(a, x[n]) + [1, 1, 10, 10] * np.random.randn(4)
f[:, n + 1] = np.dot(c, x[n + 1])
y[:, n + 1] = f[:, n + 1] + 3 * np.random.randn(M)
from bayespy.utils import random
mask = random.mask(M, N, p=0.2)
Y.observe(y, mask=mask)
import bayespy.plot as bpplt
Q.update(repeat=10)
from bayespy.inference.vmp import transformations
rotC = transformations.RotateGaussianARD(C, gamma)
rotA = transformations.RotateGaussianARD(A, alpha)
rotX = transformations.RotateGaussianMarkovChain(X, rotA)
R = transformations.RotationOptimizer(rotX, rotC, D)
Q.callback = R.rotate
Q.update(repeat=1000)
bpplt.plot(F, center=True)
bpplt.pyplot.show()
import numpy
numpy.random.seed(1)
from bayespy.nodes import CategoricalMarkovChain
a0 = [0.6, 0.4] # p(rainy)=0.6, p(sunny)=0.4
A = [[0.7, 0.3], # p(rainy->rainy)=0.7, p(rainy->sunny)=0.3
[0.4, 0.6]] # p(sunny->rainy)=0.4, p(sunny->sunny)=0.6
N = 100
Z = CategoricalMarkovChain(a0, A, states=N)
from bayespy.nodes import Categorical, Mixture
P = [[0.1, 0.4, 0.5],
[0.6, 0.3, 0.1]]
Y = Mixture(Z, Categorical, P)
weather = Z.random()
activity = Mixture(weather, Categorical, P).random()
Y.observe(activity)
from bayespy.inference import VB
Q = VB(Y, Z)
Q.update()
import bayespy.plot as bpplt
bpplt.plot(Z)
bpplt.plot(1-weather, color='r', marker='x')
bpplt.pyplot.show()