Question

我正在尝试估计3个斑块高斯混合模型与PyMC3的协方差。均值和协方差完全未知，权重为[1,1,1]。对于平均估计，可以使用tt.stack([vx,vy])来建立适当的数量。但是对于协方差，我想使用[sigma_x, sigma_y, rho]作为随机变量。我尝试使用tt.stack用代码构建相应的协方差张量

import numpy as np, pandas as pd, matplotlib.pyplot as plt, seaborn as sns
import pymc3 as pm, theano.tensor as tt

k = 3 # number of patch
ndata = 500 # number of data

centers = np.array([[-10,-10], [0,0], [10,10]])
sigmax = [1,1,1]
sigmay = [1,1,1]
ro = [0,0,0]
cov = lambda sigmax, sigmay, ro: [[sigmax**2, ro*sigmax*sigmay],[ro*sigmax*sigmay, sigmay**2]]
v = np.random.choice([0,1,2], size=ndata, replace=True)

data = []
for i in v:
    data.append(np.random.multivariate_normal(centers[i], cov(sigmax[i], sigmay[i], ro[i])))

# plt.hist(data)
data = np.array(data)
# sns.distplot(data[:,1])
ax = plt.gca()
ax.scatter(data[:,0],data[:,1])

# setup model
vx_min, vx_max = -20, 20
vy_min, vy_max = -20, 20
Dx_min, Dx_max = 0.2, 3.0
Dy_min, Dy_max = 0.2, 3.0
ro_min, ro_max = 0.0, 0.9

with pm.Model() as model:
    # cluster sizes
    p = tt.constant(np.array([1.,1.,1.]))

    # cluster centers
    vx = pm.Uniform('vx', lower=vx_min, upper=vx_max, shape=3)
    vy = pm.Uniform('vy', lower=vx_min, upper=vx_max, shape=3)
    Dx1 = pm.Uniform('Dx', lower=Dx_min, upper=Dx_max, shape=3)
    Dy1 = pm.Uniform('Dy', lower=Dy_min, upper=Dy_max, shape=3)
    ro1 = pm.Uniform('ro', lower=ro_min, upper=ro_max, shape=3)    
    category = pm.Categorical('category',
                              p=p,
                              shape=ndata)

    means = tt.stack([vx, vy], axis=-1)
    m1 = [Dx1[category]*Dx1[category],ro1[category]*Dx1[category]*Dy1[category]]
    m2 = [ro1[category]*Dx1[category]*Dy1[category],Dy1[category]*Dy1[category]]

    cov = tt.stack([m1, m2], axis=-1)

    points = pm.MvNormal('obs',
                         mu=means[category],
                         cov=cov[category],
                         observed=data)

# sampling
with model:
    step1 = pm.Metropolis()
    step2 = pm.ElemwiseCategorical(vars=[category], values=[0, 1, 2])
    tr = pm.sample(100)

# plot results
pm.plots.traceplot(tr, ['vx']);
plt.show()

但是会引发错误：

Traceback (most recent call last):
      File "/Users/huox/Downloads/t1108.py", line 51, in <module>
        observed=data)
      File "/Users/huox/anaconda2/lib/python2.7/site-packages/pymc3/distributions/distribution.py", line 36, in __new__
        dist = cls.dist(*args, **kwargs)
      File "/Users/huox/anaconda2/lib/python2.7/site-packages/pymc3/distributions/distribution.py", line 47, in dist
        dist.__init__(*args, **kwargs)
      File "/Users/huox/anaconda2/lib/python2.7/site-packages/pymc3/distributions/multivariate.py", line 222, in __init__
        lower=lower, *args, **kwargs)
      File "/Users/huox/anaconda2/lib/python2.7/site-packages/pymc3/distributions/multivariate.py", line 57, in __init__
        raise ValueError('cov must be two dimensional.')
    ValueError: cov must be two dimensional.

该如何解决？还有其他有效的方法来估计协方差矩阵吗？

如何估算高斯混合的一般协方差

0 个答案: