Python 将PyMC2代码移植到PyMC3-用于体育分析的分层模型

我尝试了以下代码，但遇到了问题。 我想。值是个问题，但我如何将其编码为Theano对象呢

以下是我的数据源

home_team,away_team,home_score,away_score
Wales,Italy,23,15
France,England,26,24
Ireland,Scotland,28,6
Ireland,Wales,26,3
Scotland,England,0,20
France,Italy,30,10
Wales,France,27,6
Italy,Scotland,20,21
England,Ireland,13,10
Ireland,Italy,46,7
Scotland,France,17,19
England,Wales,29,18
Italy,England,11,52
Wales,Scotland,51,3
France,Ireland,20,22

以下是PyMC2代码，它可以工作： 数据文件=数据目录+结果文件2014.csv

df = pd.read_csv(data_file, sep=',')
# Or whatever it takes to get this into a data frame.
teams = df.home_team.unique()
teams = pd.DataFrame(teams, columns=['team'])
teams['i'] = teams.index
df = pd.merge(df, teams, left_on='home_team', right_on='team', how='left')
df = df.rename(columns = {'i': 'i_home'}).drop('team', 1)
df = pd.merge(df, teams, left_on='away_team', right_on='team', how='left')
df = df.rename(columns = {'i': 'i_away'}).drop('team', 1)
observed_home_goals = df.home_score.values
observed_away_goals = df.away_score.values
home_team = df.i_home.values
away_team = df.i_away.values
num_teams = len(df.i_home.drop_duplicates())
num_games = len(home_team)
g = df.groupby('i_away')
att_starting_points = np.log(g.away_score.mean())
g = df.groupby('i_home')
def_starting_points = -np.log(g.away_score.mean())

#hyperpriors
home = pymc.Normal('home', 0, .0001, value=0)
tau_att = pymc.Gamma('tau_att', .1, .1, value=10)
tau_def = pymc.Gamma('tau_def', .1, .1, value=10)
intercept = pymc.Normal('intercept', 0, .0001, value=0)
#team-specific parameters
atts_star = pymc.Normal("atts_star", 
                        mu=0, 
                        tau=tau_att, 
                        size=num_teams, 
                        value=att_starting_points.values)
defs_star = pymc.Normal("defs_star", 
                        mu=0, 
                        tau=tau_def, 
                        size=num_teams, 
                        value=def_starting_points.values) 

# trick to code the sum to zero constraint
@pymc.deterministic
def atts(atts_star=atts_star):
    atts = atts_star.copy()
    atts = atts - np.mean(atts_star)
    return atts

@pymc.deterministic
def defs(defs_star=defs_star):
    defs = defs_star.copy()
    defs = defs - np.mean(defs_star)
    return defs

@pymc.deterministic
def home_theta(home_team=home_team, 
               away_team=away_team, 
               home=home, 
               atts=atts, 
               defs=defs, 
               intercept=intercept): 
    return np.exp(intercept + 
                  home + 
                  atts[home_team] + 
                  defs[away_team])

@pymc.deterministic
def away_theta(home_team=home_team, 
               away_team=away_team, 
               home=home, 
               atts=atts, 
               defs=defs, 
               intercept=intercept): 
    return np.exp(intercept + 
                  atts[away_team] + 
                  defs[home_team])   

home_points = pymc.Poisson('home_points', 
                          mu=home_theta, 
                          value=observed_home_goals, 
                          observed=True)
away_points = pymc.Poisson('away_points', 
                          mu=away_theta, 
                          value=observed_away_goals, 
                          observed=True)

mcmc = pymc.MCMC([home, intercept, tau_att, tau_def, 
                  home_theta, away_theta, 
                  atts_star, defs_star, atts, defs, 
                  home_points, away_points])
map_ = pymc.MAP( mcmc )
map_.fit()

mcmc.sample(200000, 40000, 20)

我尝试移植到PyMC3:） 我包括了争吵的代码。 我定义了自己的数据目录等

data_file = DATA_DIR + 'results_2014.csv'

df = pd.read_csv(data_file, sep=',')
# Or whatever it takes to get this into a data frame.
teams = df.home_team.unique()
teams = pd.DataFrame(teams, columns=['team'])
teams['i'] = teams.index
df = pd.merge(df, teams, left_on='home_team', right_on='team', how='left')
df = df.rename(columns = {'i': 'i_home'}).drop('team', 1)
df = pd.merge(df, teams, left_on='away_team', right_on='team', how='left')
df = df.rename(columns = {'i': 'i_away'}).drop('team', 1)
observed_home_goals = df.home_score.values
observed_away_goals = df.away_score.values
home_team = df.i_home.values
away_team = df.i_away.values
num_teams = len(df.i_home.drop_duplicates())
num_games = len(home_team)
g = df.groupby('i_away')
att_starting_points = np.log(g.away_score.mean())
g = df.groupby('i_home')
def_starting_points = -np.log(g.away_score.mean())

import theano.tensor as T
import pymc3 as pm3
#hyperpriors


x = att_starting_points.values
y = def_starting_points.values
model = pm.Model()
with pm3.Model() as model:
    home3 = pm3.Normal('home', 0, .0001)
    tau_att3 = pm3.Gamma('tau_att', .1, .1)
    tau_def3 = pm3.Gamma('tau_def', .1, .1)
    intercept3 = pm3.Normal('intercept', 0, .0001)
    #team-specific parameters
    atts_star3 = pm3.Normal("atts_star", 
                        mu=0, 
                        tau=tau_att3, 
                        observed=x)
    defs_star3 = pm3.Normal("defs_star", 
                        mu=0, 
                        tau=tau_def3,  
                        observed=y) 
    #Seems to be the error here. 
    atts = pm3.Deterministic('regression', 
    atts_star3 - np.mean(atts_star3))
    home_theta3 = pm3.Deterministic('regression', 
    T.exp(intercept3 + atts[away_team] + defs[home_team]))
atts = pm3.Deterministic('regression', atts_star3 - np.mean(atts_star3))
    home_theta3 = pm3.Deterministic('regression', T.exp(intercept3 +     atts[away_team] + defs[home_team]))
    # Unknown model parameters
    home_points3 = pm3.Poisson('home_points', mu=home_theta3, observed=observed_home_goals)
    away_points3 = pm3.Poisson('away_points', mu=home_theta3, observed=observed_away_goals)
    start = pm3.find_MAP()
    step = pm3.NUTS(state=start)
    trace = pm3.sample(2000, step, start=start, progressbar=True)

    pm3.traceplot(trace)

我得到一个错误，比如值不是Theano对象。 我想这就是上面的价值观部分。但我不知道如何把它转换成Theano张量。张量让我困惑：）

为了清楚起见，这个错误是因为我误解了PyMC3语法中的某些内容

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-71-ce51c1a64412> in <module>()
     23 
     24     #Seems to be the error here.
---> 25     atts = pm3.Deterministic('regression', atts_star3 - np.mean(atts_star3))
     26     home_theta3 = pm3.Deterministic('regression', T.exp(intercept3 + atts[away_team] + defs[home_team]))
     27 

/Users/peadarcoyle/anaconda/lib/python3.4/site-packages/numpy/core/fromnumeric.py in mean(a, axis, dtype, out, keepdims)
   2733 
   2734     return _methods._mean(a, axis=axis, dtype=dtype,
-> 2735                             out=out, keepdims=keepdims)
   2736 
   2737 def std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):

/Users/peadarcoyle/anaconda/lib/python3.4/site-packages/numpy/core/_methods.py in _mean(a, axis, dtype, out, keepdims)
     71         ret = ret.dtype.type(ret / rcount)
     72     else:
---> 73         ret = ret / rcount
     74 
     75     return ret

TypeError: unsupported operand type(s) for /: 'ObservedRV' and 'int'

---------------------------------------------------------------------------
TypeError回溯（最近一次调用上次）
在（）
23
24#似乎是这里的错误。
--->25 atts=pm3.确定性（'回归'，atts_star3-np.平均值（atts_star3））
26 home_theta3=pm3.Deterministic（'回归'，T.exp（截距3+atts[客场团队]+defs[主场团队]）
27
/Users/peadarcoyle/anaconda/lib/python3.4/site-packages/numpy/core/fromnumeric.py的平均值（a、axis、dtype、out、keepdims）
2733
2734返回方法。平均值（a，axis=axis，dtype=dtype，
->2735 out=out，keepdims=keepdims）
2736
2737 def std（a，轴=无，数据类型=无，输出=无，ddof=0，keepdims=假）：
/Users/peadarcoyle/anaconda/lib/python3.4/site-packages/numpy/core//u methods.py in\u mean（a、axis、dtype、out、keepdims）
71 ret=ret.dtype.type（ret/rcount）
72其他：
--->73 ret=ret/rcount
74
75返回ret
TypeError:/：“ObservedRV”和“int”的操作数类型不受支持

您的模型失败，因为您无法在无张量上使用NumPy函数。因此

np.mean(atts_star3)

会给你一个错误。您可以删除

atts\u star3=pm3.Normal（“atts\u star”，…）

并直接使用NumPy数组

atts\u star3=x

我认为您也不需要显式地建模

tau_att3

，

tau_def3

或

defs_star

---

或者，如果你想保留这些变量，你可以将

np.mean

替换为

theano.tensor.mean

，这应该是可行的。它不是我以前版本的直接端口，但它给了我一个答案。有人有任何反馈吗

import os
import math
import warnings
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import pymc3 as pm3# I know folks are switching to "as pm" but I'm just not there yet
%matplotlib inline
import seaborn as sns
from IPython.core.pylabtools import figsize
import seaborn as sns
import theano.tensor as T
figsize(12, 12)
DATA_DIR = os.path.join(os.getcwd(), 'data/')
data_file = DATA_DIR + 'results_2014.csv'

df = pd.read_csv(data_file, sep=',')
# Or whatever it takes to get this into a data frame.
teams = df.home_team.unique()
teams = pd.DataFrame(teams, columns=['team'])
teams['i'] = teams.index
df = pd.merge(df, teams, left_on='home_team', right_on='team', how='left')
df = df.rename(columns = {'i': 'i_home'}).drop('team', 1)
df = pd.merge(df, teams, left_on='away_team', right_on='team', how='left')
df = df.rename(columns = {'i': 'i_away'}).drop('team', 1)
observed_home_goals = df.home_score.values
observed_away_goals = df.away_score.values
home_team = df.i_home.values
away_team = df.i_away.values
num_teams = len(df.i_home.drop_duplicates())
num_games = len(home_team)
g = df.groupby('i_away')
att_starting_points = np.log(g.away_score.mean())
g = df.groupby('i_home')
def_starting_points = -np.log(g.away_score.mean())

import theano.tensor as T
import pymc3 as pm3
#hyperpriors

'''
def atts3(atts_star3=atts_star3):
    atts3 = atts_star.copy()
    atts3 = atts3 - np.mean(atts_star)
    return atts3
def defs3(defs_star3=defs_star3):
    defs3 = defs_star3.copy()
    defs3 = defs3 - np.mean(defs_star3)
    return defs
    '''
model = pm3.Model()
with pm3.Model() as model:
    home3 = pm3.Normal('home', 0, .0001)
    tau_att3 = pm3.Gamma('tau_att', .1, .1)
    tau_def3 = pm3.Gamma('tau_def', .1, .1)
    intercept3 = pm3.Normal('intercept', 0, .0001)
    #team-specific parameters
    atts_star3 = pm3.Normal("atts_star", 
                        mu=0, 
                        tau=tau_att3, 
                        shape=num_teams, 
                        observed=att_starting_points.values)
    defs_star3 = pm3.Normal("defs_star", 
                        mu=0, 
                        tau=tau_def3, 
                        shape=num_teams, 
                        observed=def_starting_points.values) 


    #home_theta3 = atts3 + defs3
    #away_theta3 = atts3 + defs3
    # Unknown model parameters
    home_points3 = pm3.Poisson('home_points', mu=1, observed=observed_home_goals)
    away_points3 = pm3.Poisson('away_points', mu=1, observed=observed_away_goals)
    start = pm3.find_MAP()
    step = pm3.NUTS(state=start)
    trace = pm3.sample(2000, step, start=start, progressbar=True)

    pm3.traceplot(trace)

---

以下是我对PyMC2模型的翻译：

model = pm.Model()
with pm.Model() as model:
    # global model parameters
    home        = pm.Normal('home',      0, .0001)
    tau_att     = pm.Gamma('tau_att',   .1, .1)
    tau_def     = pm.Gamma('tau_def',   .1, .1)
    intercept   = pm.Normal('intercept', 0, .0001)

    # team-specific model parameters
    atts_star   = pm.Normal("atts_star", 
                           mu   =0,
                           tau  =tau_att, 
                           shape=num_teams)
    defs_star   = pm.Normal("defs_star", 
                           mu   =0,
                           tau  =tau_def,  
                           shape=num_teams)

    atts        = pm.Deterministic('atts', atts_star - tt.mean(atts_star))
    defs        = pm.Deterministic('defs', defs_star - tt.mean(defs_star))
    home_theta  = tt.exp(intercept + home + atts[home_team] + defs[away_team]
    away_theta  = tt.exp(intercept + atts[away_team] + defs[home_team])

    # likelihood of observed data
    home_points = pm.Poisson('home_points', mu=home_theta, observed=observed_home_goals)
    away_points = pm.Poisson('away_points', mu=away_theta, observed=observed_away_goals)

在我看来，PyMC2和PyMC3模型构建之间的最大区别在于PyMC2中初始值的整个业务不包括在PyMC3的模型构建中。它被推入代码的模型拟合部分

---

这是一个笔记本，它将此模型与您的数据和一些拟合代码放在一起：

您能添加数据以便我重现您的错误吗？一个小的模拟示例就可以了，只要它引起与实际数据相同的错误。亚伯拉罕我修正了这个并添加了这个。谢谢你的提醒。不需要将数组转换成张量。我还是看不出你到底犯了什么错误。您正在运行最新的PyMC3吗？我只得到“NameError:name'defs'未定义”，这是有意义的，因为它未定义。此外，除非您缺少值或您真的关心“tau_att3”或“tau_def3”（但您不使用它们），否则我认为没有必要对“atts_star”和“defs_star”进行正态分布建模，你可以直接使用这些数据。谢谢你的回答。我试过了，我发现RV不能与int一起工作。我认为这个模型使用了atts_star3等的正态分布，因为这是我基于代码的论文中提到的。我想我需要对代码进行一些重构，然后看看接下来会发生什么。所以在遵循您的建议之后。但现在我得到了这个错误<代码>类型错误回溯（最近一次调用）in（）67 68--->69 home\u theta3=pm3.Deterministic（'regression'，T.exp（intercept3+atts3[way\u team]+defs3[home\u team]）70-way\u theta3=pm3.Deterministic（'regression'，T.exp（intercept3+atts3[way\u team]+defs3[home\u team]））71#未知模型参数TypeError:“function”对象不可下标看起来atts3或defs2实际上是一个函数。也许你运行了上面注释掉的代码？是的，我注释掉了代码，自己添加了一个mu，它为我运行。今天晚些时候我会再调查一下。但我认为它是PyMC3强大功能的一个“黑客”例子。你觉得怎么样？我会发布你的PyMC2代码的翻译，这有点不同。酷：）我很想看看。我接受了你的版本。我的话写得不太好：）谢谢亚伯拉罕。我会把这个添加到我在伦敦的PyData演讲中，但我一定会提到你：）。很好，你能发送幻灯片或演讲录音吗？听起来很有趣。我知道这很古老，但我尝试复制结果，Pymc3的后验概率非常不同（例如，主系数约为0.0）。注意，此代码中存在错误。home_theta的行必须读home_theta=tt.exp（intercept+home+atts[home_team]+defs[away_team]，如果没有修复，您会得到与pymc2不同的结果。我花了一段时间才找到这个！这可能也解释了fsocity的问题。