我是PyMC3，Theano和numpy的新手。只是试图在Stan手册中复制第一个“隐藏的”Markov模型 - 实际观察状态的那个。但是，我一直遇到与Theano有关的错误，numpy，以及PyMC3发行版后面发生的事情，这对我来说似乎有些神秘。我的模型代码如下：
import pandas as pd
dat_hmm = pd.read_csv('hmmVals.csv')
emission=dat_hmm.emission.values
state=dat_hmm.state.values
from pymc3 import Model, Dirichlet, Categorical
import numpy as np
basic_model = Model()
with basic_model:
#Model constants:
#num unique hidden states, num unique emissions, num instances
K=3; V=9; T=10
alpha=np.ones(K); beta=np.ones(V)
# Priors for unknown model parameters
theta = np.empty(K, dtype=object) #theta=transmission
phi = np.empty(K, dtype=object) #phi=emission
#observed emission, state:
w=np.empty(T, dtype=object); z=np.empty(T, dtype=object);
for k in range(K):
theta[k]=Dirichlet('theta'+str(k), alpha)
phi[k]=Dirichlet('phi'+str(k), beta)
# Likelihood (sampling distribution) of observations
for t in range(T):
w[t]=Categorical('w'+str(t),theta[state[t]], shape=1, observed=emission[t])
for t in range(2, T):
z[t]=Categorical('z'+str(t),phi[state[t-1]], shape=1, observed=state[t])
行“w [t] =分类（'w'+ str（t），theta [state [t]]，shape = 1，observed = emission [t]）”生成错误，但不生成错误= 0，填充w0，但在t = 1时生成索引超出范围的错误。代码行本身没有索引超出范围，因为state [1]，theta [state [t]]和emission [t]都存在。错误消息是：
Traceback (most recent call last):
File "/usr/local/lib/python3.4/dist-packages/pymc3/distributions/distribution.py", line 25, in __new__
return model.Var(name, dist, data)
File "/usr/local/lib/python3.4/dist-packages/pymc3/model.py", line 306, in Var
var = ObservedRV(name=name, data=data, distribution=dist, model=self)
File "/usr/local/lib/python3.4/dist-packages/pymc3/model.py", line 581, in __init__
self.logp_elemwiset = distribution.logp(data)
File "/usr/local/lib/python3.4/dist-packages/pymc3/distributions/discrete.py", line 400, in logp
a = tt.log(p[value])
File "/usr/local/lib/python3.4/dist-packages/theano/tensor/var.py", line 532, in __getitem__
lambda entry: isinstance(entry, Variable)))
File "/usr/local/lib/python3.4/dist-packages/theano/gof/op.py", line 668, in __call__
required = thunk()
File "/usr/local/lib/python3.4/dist-packages/theano/gof/op.py", line 883, in rval
fill_storage()
File "/usr/local/lib/python3.4/dist-packages/theano/gof/cc.py", line 1707, in __call__
reraise(exc_type, exc_value, exc_trace)
File "/usr/local/lib/python3.4/dist-packages/six.py", line 686, in reraise
raise value
IndexError: index out of bounds
我不知道将Numpy对象粘贴到PyMC3发行版中的智慧，或者使用其结果来尝试参数化另一个发行版，但我在Web上看到了一些相似的代码，减去了最后一部分。是否有可能没有好的方法在PyMC3中编写这样一个隐藏的Markov模型呢？
答案 0 :(得分：2)
我找到了解决上述错误的方法。以下代码有效 - 没有错误，我至少可以使用Metropolis获得正确的参数估计值。
我犯了两个错误，并没有意识到他们是如此简单，因为我期待在Theano中发生一些复杂的事情。一个是我的数据是为Stan设置的，因此索引从1开始而不是0. Python将所有内容索引为0.我通过从每个值中减去1来更改数据文件。另一个错误是我使用theta（传输矩阵）来计算phi矩阵的单个发射，反之亦然。 Theta的排放时间太短了。
我希望我现在能理解的是，为什么NUTS采样器一直告诉我，我有一个非正定的缩放比例，即使我正在给它MAP估计。大都会工作，但很慢 - 这300个观察和1000个样本大约11分钟。另一个谜团是为什么PyMC3认为只花了几秒钟来计算样本。
import pandas as pd
dat_hmm = pd.read_csv('hmmVals.csv')
emission=dat_hmm.emission.values
state=dat_hmm.state.values
from pymc3 import Model, Dirichlet, Categorical
import numpy as np
basic_model = Model()
with basic_model:
#Model constants:
K=3; V=9; T=300 #num unique hidden states, num unique emissions, num instances
alpha=np.ones(K); beta=np.ones(V)
# Priors for unknown model parameters
theta = np.empty(K, dtype=object) #theta=transmission
phi = np.empty(K, dtype=object) #phi=emission
w=np.empty(T, dtype=object); z=np.empty(T, dtype=object); #observed emission, state
for k in range(K):
theta[k]=Dirichlet('theta'+str(k), alpha)
phi[k]=Dirichlet('phi'+str(k), beta)
#Likelihood (sampling distribution) of observationss
for t in range(2, T):
z[t]=Categorical('z'+str(t),theta[state[t-1]], shape=1, observed=state[t])
for t in range(T):
w[t]=Categorical('w'+str(t),phi[state[t]], shape=1, observed=emission[t])
答案 1 :(得分：1)
我还尝试在pymc3中实现HMM，但我遇到了类似的问题。我刚刚找到了一种以矢量化方式实现两级HMM的方法（说实话，我的模型不是隐藏的，但隐藏的部分可以轻松添加 - 我对状态变量的描述进行了矢量化）。我不确定这是否是最有效的方法，但我针对定义状态的简单for循环测试了此代码。下面的代码在不到一分钟的时间内运行1000个数据点，而for循环需要几个小时。
以下是代码：
import numpy as np
import theano.tensor as tt
import pymc3 as pm
class HMMStates(pm.Discrete):
"""
Hidden Markov Model States
Parameters
----------
P1 : tensor
probability to remain in state 1
P2 : tensor
probability to move from state 2 to state 1
"""
def __init__(self, PA=None, P1=None, P2=None,
*args, **kwargs):
super(HMMStates, self).__init__(*args, **kwargs)
self.PA = PA
self.P1 = P1
self.P2 = P2
self.mean = 0.
def logp(self, x):
PA = self.PA
P1 = self.P1
P2 = self.P2
# now we need to create an array with probabilities
# so that for x=A: PA=P1, PB=(1-P1)
# and for x=B: PA=P2, PB=(1-P2)
length = x.shape[0]
P1T = tt.tile(P1,(length-1,1)).T
P2T = tt.tile(P2,(length-1,1)).T
P = tt.switch(x[:-1],P1T,P2T).T
x_i = x[1:]
ou_like = pm.Categorical.dist(P).logp(x_i)
return pm.Categorical.dist(PA).logp(x[0]) + tt.sum(ou_like)
此类创建HMM的状态。要调用它，您可以执行以下操作：
theta = np.ones(2) # prior for probabilities
with pm.Model() as model:
# 2 state model
# P1 is probablility to stay in state 1
# P2 is probability to move from state 2 to state 1
P1 = pm.Dirichlet('P1', a=theta)
P2 = pm.Dirichlet('P2', a=theta)
PA = pm.Deterministic('PA',P2/(P2+1-P1))
states = HMMStates('states',PA,P1,P2, observed=data)
start = pm.find_MAP()
trace = pm.sample(5000, start=start)
只是为了展示旧代码的样子：
with pm.Model() as model:
# 2 state model
# P1 is probablility to stay in state 1
# P2 is probability to move from state 2 to state 1
P1 = pm.Dirichlet('P1', a=np.ones(2))
P2 = pm.Dirichlet('P2', a=np.ones(2))
PA = pm.Deterministic('PA',P2/(P2+1-P1))
state = pm.Categorical('state0',PA, observed=data[0])
for i in range(1,N_chain):
state = pm.Categorical('state'+str(i), tt.switch(data[i-1],P1,P2), observed=data[i])
start = pm.find_MAP()
trace = pm.sample(5000, start=start)