frequentism-and-bayesianism-chs-iv

频率主义与贝叶斯主义 IV:Python的贝叶斯工具

 

这个notebook出自Pythonic Perambulations博文。The content is BSD licensed.

 

这个系列共4个部分:中文版Part I Part II Part III Part IV,英文版Part I Part II Part III Part IV

 

我之前花了一堆时间来分享这两种思想。

这一篇文章,我打算撇开哪些争论,谈谈Python实现贝叶斯研究的工具。 现代贝叶斯主义的核心是马尔可夫链蒙特卡罗算法,MCMC,样本后验分布(sample posterior distributions)的高效算法。

下面我就用Python的三个包来演示MCMC:

  • emcee: the MCMC Hammer
  • pymc: Bayesian Statistical Modeling in Python
  • pystan: The Python Interface to Stan

我不会太关心它们的性能,也不会比较各自的API。这篇文章也不是教程;这三个包都有很完整的文档和教程。我要做的是比较一下三者的用法。用一个相对简单的例子,演示三个包的解法,希望对你有所帮助。

 

测试案例:线性拟合最优解

 

为了解决问题,我们做一个三参数模型来找数据的线性拟合解。参数是斜率,截距和相关性(scatter about the line);这个相关性可以当作冗余参数

 

数据

 

先来定义一些数据

In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np np.random.seed(42)
theta_true = (25, 0.5)
xdata = 100 * np.random.random(20)
ydata = theta_true[0] + theta_true[1] * xdata # add scatter to points
xdata = np.random.normal(xdata, 10)
ydata = np.random.normal(ydata, 10)
In [2]:
plt.plot(xdata, ydata, 'ok')
plt.xlabel('x')
plt.ylabel('y');
 
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tZMCDnh4yUlZc1O5ZxwFq6krNmpLEklYqeyJGnTTAiSJMCEIEmKTAiSJMCEIEmKTAiSJMCEIEmK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%0ASZIkSZKy9P9IrbyHX0e39QAAAABJRU5ErkJggg==" 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数据明显具有相关性,我们假设我们不知道误差。让我们构建一条直线来拟合。

 

模型:斜率,截距和未知相关系数

 

由贝叶斯定义可得

P(θ | D)∝P(D | θ)P(θ)

其中,D表示观察数据,θ表示模型

 

假设线性模型有斜率β,y轴截距α:

y^(xi | α,β)=α+βxi

假设y轴坐标具有正态分布误差, 那么模型下的任何数据点的概率为:

P(xi,yi | α,β,σ)=12πσ2−−−−√exp[−[yi−y^(xi | α,β)]22σ2]

其中,σ是未知测量误差,为冗余参数。

所以i的似然估计的乘积为:

P({xi},{yi} | α,β,σ)∝(2πσ2)−N/2exp[−12σ2∑i−1N[yi−y^(xi | α,β)]2]
 

先验条件

 

这里我们比之前的更仔细地选择先验条件。我们可以简单的认为α,β,和σ都是flat priors(扁平先验),但是我们必须记住扁平先验并非都无信息先验(uninformative priors)!Jeffreys先验可能是更好的选择,用对称的最大熵(symmetry and/or maximum entropy)来选择最大化的无信息先验(maximally noninformative priors)。虽然这种做法被频率论认为太主观,但是这么做是可以从信息理论中找到理论依据的。

为什么flat prior可能产生坏的选择?看看斜率就明白了。让我们来演示一下斜率从0-10的直线变化情况;

In [3]:
fig, ax = plt.subplots(subplot_kw=dict(aspect='equal'))
x = np.linspace(-1, 1) for slope in np.arange(0, 10, 0.1):
plt.plot(x, slope * x, '-k') ax.axis([-1, 1, -1, 1], aspect='equal');
 
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UFISAg8PT3RqVMnjB07Fv369YNUKsXChQvRvXt3DBs2DHPnzmVL0fPz87F48WLW6qitrUVgYCB2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%0ACRIkyPnk/wOq6WBV5NfJLQAAAABJRU5ErkJggg==" alt="" />
 

这些线按0.1的斜率间隔进行分布,高斜率区域的线十分密集。因为是扁平先验,你肯定会认为这些斜率彼此无差异。由上面的密集区域显然可以看出,斜率的扁平先验满足那些很陡的斜率。斜率的扁平先验不是一个最小化的无信息先验(minimally informative prior),可能是最终使你的结果有偏差(尽管有足够多的数据,结果可能几乎是0)。

你可能想动手做出一个更好的方案(可能在直线与x轴的夹角θ上用扁平先验),但是我们有更严谨的方案。这个问题在贝叶斯文献中已经有了答案;我找到的最佳方案来自Jaynes的论文直线拟合:贝叶斯方法(Straight Line Fitting: A Bayesian Solution) (pdf)

 

斜率和截距的先验

 

假设模型为

y=α+βx

那么构建参数空间(parameter-space),其概率元素为P(α,β) dα dβ

因为x和y是对称的,我们就可以进行参数交互

x=α′+β′y

其概率元素为Q(α′,β′)dα′dβ′,由此可得

(α′, β′)=(−β−1α, β−1).

通过雅可比变换(the Jacobian of the transformation),可得

Q(α′,β′)=β3P(α,β).

为了保持对称性,需要保证变量的改变不会影响先验概率,因此有:

β3P(α,β)=P(−β−1α,β−1).

此函数满足:

P(α,β)∝(1+β2)−3/2.

即α服从均匀分布,β服从参数为sinθ的均匀分布,其中,θ=tan−1β。

你可能会奇怪,斜率的分布服从参数为sinθ的均匀分布,而非θ。sinθ可以被认为是源自截距。如果把变量α改为α⊥=αcosθ,那么均匀分布就变为(α⊥, θ)。在用PyStan求解时我们会用这个。

 

σ的先验

 

同理,我们希望σ的先验与问题的规模变化无关(如,改变点的数据)。因此其概率必须满足

P(σ)dσ=P(σ/c)dσ/c.

方程等价于

P(σ)∝1/σ.

这就是Harold Jeffreys提出的Jeffreys先验

 

把先验放一起

 

把它们放到一起,我们用这些对称性参数推导出模型的最小无信息先验:

P(α,β,σ)∝1σ(1+β2)−3/2

综上所述,你可能用扁平先验做参数变换(α,β,σ)→(α⊥,θ,logσ),来解决这个问题, 但我认为对称/最大熵(symmetry/maximum entropy)方法更简洁明了——而且让我们能看到三个Python包演示这个先验的内涵。

 

用Python解决问题

 

现在有了数据,似然估计和先验,让我们用Python的emcee,PyMC和PyStan来演示。首先,让我们做一些辅助工作来可视化数据:

In [4]:
# Create some convenience routines for plotting

def compute_sigma_level(trace1, trace2, nbins=20):
"""From a set of traces, bin by number of standard deviations"""
L, xbins, ybins = np.histogram2d(trace1, trace2, nbins)
L[L == 0] = 1E-16
logL = np.log(L) shape = L.shape
L = L.ravel() # obtain the indices to sort and unsort the flattened array
i_sort = np.argsort(L)[::-1]
i_unsort = np.argsort(i_sort) L_cumsum = L[i_sort].cumsum()
L_cumsum /= L_cumsum[-1] xbins = 0.5 * (xbins[1:] + xbins[:-1])
ybins = 0.5 * (ybins[1:] + ybins[:-1]) return xbins, ybins, L_cumsum[i_unsort].reshape(shape) def plot_MCMC_trace(ax, xdata, ydata, trace, scatter=False, **kwargs):
"""Plot traces and contours"""
xbins, ybins, sigma = compute_sigma_level(trace[0], trace[1])
ax.contour(xbins, ybins, sigma.T, levels=[0.683, 0.955], **kwargs)
if scatter:
ax.plot(trace[0], trace[1], ',k', alpha=0.1)
ax.set_xlabel(r'$\alpha$')
ax.set_ylabel(r'$\beta$') def plot_MCMC_model(ax, xdata, ydata, trace):
"""Plot the linear model and 2sigma contours"""
ax.plot(xdata, ydata, 'ok') alpha, beta = trace[:2]
xfit = np.linspace(-20, 120, 10)
yfit = alpha[:, None] + beta[:, None] * xfit
mu = yfit.mean(0)
sig = 2 * yfit.std(0) ax.plot(xfit, mu, '-k')
ax.fill_between(xfit, mu - sig, mu + sig, color='lightgray') ax.set_xlabel('x')
ax.set_ylabel('y') def plot_MCMC_results(xdata, ydata, trace, colors='k'):
"""Plot both the trace and the model together"""
fig, ax = plt.subplots(1, 2, figsize=(10, 4))
plot_MCMC_trace(ax[0], xdata, ydata, trace, True, colors=colors)
plot_MCMC_model(ax[1], xdata, ydata, trace)
 

下面,就让我们来解决MCMC。

 

Emcee

 

emcee(就是Python历史上著名的MCMC Hammer)是天文学家Dan Foreman-Mackey写的纯Python包。这个简洁的包实现了复杂的仿射无关哈密顿(Affine-invariant Hamiltonian)MCMC。因为是纯Python,所以包很容易安装:

[~]$ pip install emcee

Emcee没有很多引用代码;只要传入Python函数就会返回与对数后验概率匹配的值和后验样本。下面用emcee演示一下:

In [5]:
import emcee
print(emcee.__version__)
 
2.1.0
In [6]:
# Define our posterior using Python functions
# for clarity, I've separated-out the prior and likelihood
# but this is not necessary. Note that emcee requires log-posterior # 用Python函数定义后验,我把先验和似然估计分开写了,其实没必要,主要是显得更简洁。
# 注意emcee需要对数后验证 def log_prior(theta):
alpha, beta, sigma = theta
if sigma < 0:
return -np.inf # log(0)
else:
return -1.5 * np.log(1 + beta ** 2) - np.log(sigma) def log_likelihood(theta, x, y):
alpha, beta, sigma = theta
y_model = alpha + beta * x
return -0.5 * np.sum(np.log(2 * np.pi * sigma ** 2) + (y - y_model) ** 2 / sigma ** 2) def log_posterior(theta, x, y):
return log_prior(theta) + log_likelihood(theta, x, y)
In [7]:
# Here we'll set up the computation. emcee combines multiple "walkers",
# each of which is its own MCMC chain. The number of trace results will
# be nwalkers * nsteps # 设置计算参数。emcee组合了多个"walkers",每个都有自己的MCMC链。
# 跟踪结果的数量为nwalkers * nsteps ndim = 3 # number of parameters in the model
nwalkers = 50 # number of MCMC walkers
nburn = 1000 # "burn-in" period to let chains stabilize
nsteps = 2000 # number of MCMC steps to take # set theta near the maximum likelihood, with
np.random.seed(0)
starting_guesses = np.random.random((nwalkers, ndim))
In [8]:
# Here's the function call where all the work happens:
# we'll time it using IPython's %time magic # 这就是所有调用内容。
# 这里用IPythn的%time方法计时。 sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[xdata, ydata])
%time sampler.run_mcmc(starting_guesses, nsteps)
print("done")
 
CPU times: user 4.38 s, sys: 1.09 ms, total: 4.38 s
Wall time: 4.38 s
done
In [9]:
# sampler.chain is of shape (nwalkers, nsteps, ndim)
# we'll throw-out the burn-in points and reshape: # sampler.chain返回数组维度为(nwalkers, nsteps, ndim) sampler.chain
emcee_trace = sampler.chain[:, nburn:, :].reshape(-1, ndim).T
plot_MCMC_results(xdata, ydata, emcee_trace)
 
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olOp+PSpUtoNJouFWj19fV89913fPjhh3h7e7NixQrc3d075dpCqHUwLa1Vt+q6vJk5bQkctVpN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%0ARERERERERGS2+X8A0fnNC5wm3wAAAABJRU5ErkJggg==" alt="" />
 

左图,我们演示了由冗余参数σ边缘化后的跟踪结果。在右侧显示了2-σ最佳拟合的不确定区域。这就是我们从MCMC得到的结果:边缘化的不确定轮廓提供了一个很好的拟合结果。

 

PyMC

 

PyMC包比emcee有更多的特征,有效的支持许多主流先验分布。 PyMC默认使用经典的Metropolis-Hastings取样器,最早的MCMC算法。性能方面,使用了Fortran库,因此用pip安装就有点复杂。先安装Fortran编译器,pip install pymc可以了。如果没装Fortran编译器,可以通过conda安装。

据说PyMC第三版要移除Fortran依赖,安装就容易了。而且PyMC 3的API更简洁,性能更好。但是目前仍是alpha版本,所以现在用就版本:

In [10]:
import pymc
print(pymc.__version__)
 
2.3.3
In [11]:
# Define the variables needed for the routine, with their prior distributions
alpha = pymc.Uniform('alpha', -100, 100) @pymc.stochastic(observed=False)
def beta(value=0):
return -1.5 * np.log(1 + value ** 2) @pymc.stochastic(observed=False)
def sigma(value=1):
return -np.log(abs(value)) # Define the form of the model and likelihood
@pymc.deterministic
def y_model(x=xdata, alpha=alpha, beta=beta):
return alpha + beta * x y = pymc.Normal('y', mu=y_model, tau=1. / sigma ** 2, observed=True, value=ydata) # package the full model in a dictionary
model1 = dict(alpha=alpha, beta=beta, sigma=sigma,
y_model=y_model, y=y)
In [12]:
# run the basic MCMC: we'll do 100000 iterations to match emcee above
S = pymc.MCMC(model1)
S.sample(iter=100000, burn=50000)
 
 [-----------------100%-----------------] 100000 of 100000 complete in 55.8 sec
In [13]:
# extract the traces and plot the results
pymc_trace = [S.trace('alpha')[:],
S.trace('beta')[:],
S.trace('sigma')[:]] plot_MCMC_results(xdata, ydata, pymc_trace)
 
aaarticlea/png;base64,iVBORw0KGgoAAAANSUhEUgAAAmoAAAEPCAYAAADyA+gLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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%0ASi8Y+xQVR8QAAAAASUVORK5CYII=" alt="" />
 

结果和emcee很相似。

 

PyStan

 

PyStan项目是C++实现的Stan概率编程语言的Python封装版。使用No U-Turn取样器,比Metropolis-Hastings和Gibbs取样更复杂。不考虑API,PyStan与emcee和PyMC的差异是,它要求在Python程序内编写并编译非Python编码

因为PyStan依赖Stan包,安装很困难。为了用Python封装版需要安装全部的Stan库。如果你有C/C++编译环境,直接pip install pystan就可以搞定。

好像Stan也提供已经编译版本,支持conda。因此,如果你没有C/C++编译环境,安装可能比较麻烦。

我用的PyStan 2.5版本:

In [14]:
import pystan
print(pystan.__version__)
 
2.5.0.0
 

还有一点诡异的是:PyStan在IPython notebook上运行容易崩溃,直接执行Python文件就没事。不明觉厉,但是这里可能是解法。所以,安全起见,我直接在命令行运行Python文件,结果写在盘里:

In [15]:
%%file pystan_example.py

import numpy as np
import pystan #---------------------------------------------
# Generate data (same as used in the notebook) np.random.seed(42)
theta_true = (25, 0.5)
xdata = 100 * np.random.random(20)
ydata = theta_true[0] + theta_true[1] * xdata # add scatter to points
xdata = np.random.normal(xdata, 10)
ydata = np.random.normal(ydata, 10) #----------------------------------------------
# Create the Stan model
# this is done by defining a string of Stan code. fit_code = """
data {
int<lower=0> N; // number of points
real x[N]; // x values
real y[N]; // y values
} parameters {
real alpha_perp;
real<lower=-pi()/2, upper=pi()/2> theta;
real log_sigma;
} transformed parameters {
real alpha;
real beta;
real sigma;
real ymodel[N]; alpha <- alpha_perp / cos(theta);
beta <- sin(theta);
sigma <- exp(log_sigma);
for (j in 1:N)
ymodel[j] <- alpha + beta * x[j];
} model {
y ~ normal(ymodel, sigma);
}
""" # perform the fit
fit_data = {'N': len(xdata), 'x': xdata, 'y': ydata}
fit = pystan.stan(model_code=fit_code, data=fit_data, iter=25000, chains=4) # extract the traces
traces = fit.extract()
pystan_trace = [traces['alpha'], traces['beta'], traces['sigma']] # save the traces with numpy
np.save("pystan_trace.npy", pystan_trace)
 
Writing pystan_example.py
In [16]:
# run the code we've created on the command-line
!python pystan_example.py
 
INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_c1dba2ed7f485b674d7ce5eb738ffe05 NOW.
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Iteration: 17500 / 25000 [ 70%] (Sampling) (Chain 1)
Iteration: 15000 / 25000 [ 60%] (Sampling) (Chain 3)
Iteration: 17500 / 25000 [ 70%] (Sampling) (Chain 2)
Iteration: 12500 / 25000 [ 50%] (Warmup) (Chain 0)
Iteration: 12501 / 25000 [ 50%] (Sampling) (Chain 0)
Iteration: 20000 / 25000 [ 80%] (Sampling) (Chain 1)
Iteration: 20000 / 25000 [ 80%] (Sampling) (Chain 2)
Iteration: 15000 / 25000 [ 60%] (Sampling) (Chain 0)
Iteration: 17500 / 25000 [ 70%] (Sampling) (Chain 3)
Iteration: 22500 / 25000 [ 90%] (Sampling) (Chain 1)
Iteration: 22500 / 25000 [ 90%] (Sampling) (Chain 2)
Iteration: 17500 / 25000 [ 70%] (Sampling) (Chain 0)
Iteration: 25000 / 25000 [100%] (Sampling) (Chain 1) # Elapsed Time: 0.608499 seconds (Warm-up)
# 0.684071 seconds (Sampling)
# 1.29257 seconds (Total) Iteration: 25000 / 25000 [100%] (Sampling) (Chain 2) # Elapsed Time: 0.620206 seconds (Warm-up)
# 0.72414 seconds (Sampling)
# 1.34435 seconds (Total) Iteration: 20000 / 25000 [ 80%] (Sampling) (Chain 3)
Iteration: 20000 / 25000 [ 80%] (Sampling) (Chain 0)
Iteration: 22500 / 25000 [ 90%] (Sampling) (Chain 3)
Iteration: 22500 / 25000 [ 90%] (Sampling) (Chain 0)
Iteration: 25000 / 25000 [100%] (Sampling) (Chain 3) # Elapsed Time: 0.610114 seconds (Warm-up)
# 0.657225 seconds (Sampling)
# 1.26734 seconds (Total) Iteration: 25000 / 25000 [100%] (Sampling) (Chain 0) # Elapsed Time: 0.616008 seconds (Warm-up)
# 0.687802 seconds (Sampling)
# 1.30381 seconds (Total)
 

可以看到,运行100,000样本约6秒。另外,在我的电脑上,模型运行前有约20秒准备时间。

In [17]:
# load the results from file; plot as above
pystan_trace = np.load('pystan_trace.npy')
plot_MCMC_results(xdata, ydata, pystan_trace)
 
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V8ihJpAcPXiag0DNpuNr776itWrVxMcHMwjjzzCpEmTrvh4vRFqnld8VoFTuJzQcRREkiDT6XRt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%0A02OYjGyZtN8AAAAASUVORK5CYII=" alt="" />
 

可见,结果和上面都差不多。

 

总结:结果比较

 

下面我们画图来比较一下三个结果:

In [18]:
fig, ax = plt.subplots(figsize=(8, 8))
plot_MCMC_trace(ax, xdata, ydata, emcee_trace, True,
colors='blue', linewidths=2)
plot_MCMC_trace(ax, xdata, ydata, pymc_trace,
colors='red', linewidths=2)
plot_MCMC_trace(ax, xdata, ydata, pystan_trace,
colors='green', linewidths=2)
ax.legend(ax.collections[::2], ['emcee', 'pymc', 'pystan'], fontsize=16);
 
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k7HREVFsXLlSo4dO8bXX39NxYoV6dWrF0eOHCn03IsWLaJhw4a899579OjRg8jISFq0aEF2dnYx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%0AiIiIiIiIiIiIiIiIiIiIiIiI1Ev/Dy9xJ2lx9qTIAAAAAElFTkSuQmCC" alt="" />
 

如我所料,结果都差不多!这表明我们定义的模型在这三个包都一致。另外,我们看到用来产生分布的“真”值(25, 0.5)落在1-σ的椭圆区域内。

 

三个包比较

 

哪个包好?因地制宜。下表是我自己的总结:

  复杂性 执行时间(100,000样本,包括准备阶段) 安装简易性 使用友好程度 特性丰富程度
emcee 轻量版 ~6秒 纯Python;pip安装简单 直截了当 & Pythonic 除了MCMC取样没太多功能
pymc2 大量功能 & 选项 ~17秒 要求fortran编译器; 可通过conda编译 Pythonic,但有大量的pymc引用文件 大量的内建Python功能
pystan 很多包; 要求Stan语言编写 ~20秒编译 + ~6秒计算 要求C编译器 + Stan安装; 没有编译好的文件 不是纯Python; 必须学习Stan建模语言 大量Stan功能
 

啰嗦几句:

emcee可谓短小精悍。你要做的所有工作就是Python对数后验,之后emcee就会从分布取样了。因为是纯Python而且没有许多常见的分布(如均匀分布,正态分布等)。我觉得它可能比另两个包慢,但是性能差的并不多。可能是取样算法相对简单,所以跑分不差。

pymc功能全面,一旦你明白了修饰器语法,分布函数,派生变量(derived quantities),那么还是容易用的。它的性能比其他两个都差:同样的查询花更多时间,尽管不同的先验取样都优化过。听说PyMC 3是完全重写,还是值得期待的。

pystan是最难用的,但那是因为不是真Python包。模型也不是Python的,是一种统计语言。这种语言很给力,但是有点难学。约20秒编译时间挺烦人,但我认为随着样本增大模型会更复杂,这点儿可以忽略。Stan是为这种工作设计的,模型都被编译成字节码,在做大case的时候是个不错的选择。

这里就不花太多时间了;前面说过,这些包用了不同的取样算法所以时间是不可比的。每种取样算法都有优缺点,你可以去看看。

希望我的比较是公正合理的。当然我不是这些包的大牛;只是简单读了一些文档,然后把教程的例子改改罢了。如果大牛碰巧读了这些,轻喷哈。再说两件事:

  1. 如果你用的更好,写点儿评论哈!
  2. 提醒一下那些想用这包解决问题的一般用户:读读教程,因地制宜。

感谢御览!

这篇博客是IPython notebook写的。可以[下载](http://jakevdp.github.io/downloads/notebooks/FreqBayes4.ipynb),或者看[nbviewer](http://nbviewer.ipython.org/url/jakevdp.github.io/downloads/notebooks/FreqBayes4.ipynb)静态网页。 十分感谢David W. Hogg对本文提出的建议。

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