加快内核估算的采样速度

Question

这是MWE我正在使用的更大的代码.基本上,它针对位于特定阈值以下的所有值对KDE(内核密度估计)执行蒙特卡洛积分(在该问题上建议积分方法BTW:积分2D核密度估计).

import numpy as np
from scipy import stats
import time

# Generate some random two-dimensional data:
def measure(n):
    "Measurement model, return two coupled measurements."
    m1 = np.random.normal(size=n)
    m2 = np.random.normal(scale=0.5, size=n)
    return m1+m2, m1-m2

# Get data.
m1, m2 = measure(20000)
# Define limits.
xmin = m1.min()
xmax = m1.max()
ymin = m2.min()
ymax = m2.max()

# Perform a kernel density estimate on the data.
x, y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
values = np.vstack([m1, m2])
kernel = stats.gaussian_kde(values)

# Define point below which to integrate the kernel.
x1, y1 = 0.5, 0.5

# Get kernel value for this point.
tik = time.time()
iso = kernel((x1,y1))
print 'iso: ', time.time()-tik

# Sample from KDE distribution (Monte Carlo process).
tik = time.time()
sample = kernel.resample(size=1000)
print 'resample: ', time.time()-tik

# Filter the sample leaving only values for which
# the kernel evaluates to less than what it does for
# the (x1, y1) point defined above.
tik = time.time()
insample = kernel(sample) < iso
print 'filter/sample: ', time.time()-tik

# Integrate for all values below iso.
tik = time.time()
integral = insample.sum() / float(insample.shape[0])
print 'integral: ', time.time()-tik

输出看起来像这样:

iso:  0.00259208679199
resample:  0.000817060470581
filter/sample:  2.10829401016
integral:  4.2200088501e-05

这显然意味着过滤器/样本调用几乎消耗了代码用于运行的所有时间.我必须迭代地运行这段代码几千次,这样才能耗费时间.

有没有办法加快过滤/采样过程？

---

加

这MWE是我用Ophion编写的多线程解决方案的实际代码更加逼真:

import numpy as np
from scipy import stats
from multiprocessing import Pool

def kde_integration(m_list):

    m1, m2 = [], []
    for item in m_list:
        # Color data.
        m1.append(item[0])
        # Magnitude data.
        m2.append(item[1])

    # Define limits.
    xmin, xmax = min(m1), max(m1)
    ymin, ymax = min(m2), max(m2)

    # Perform a kernel density estimate on the data:
    x, y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
    values = np.vstack([m1, m2])
    kernel = stats.gaussian_kde(values)

    out_list = []

    for point in m_list:

        # Compute the point below which to integrate.
        iso = kernel((point[0], point[1]))

        # Sample KDE distribution
        sample = kernel.resample(size=1000)

        #Create definition.
        def calc_kernel(samp):
            return kernel(samp)

        #Choose number of cores and split input array.
        cores = 4
        torun = np.array_split(sample, cores, axis=1)

        #Calculate
        pool = Pool(processes=cores)
        results = pool.map(calc_kernel, torun)

        #Reintegrate and calculate results
        insample_mp = np.concatenate(results) < iso

        # Integrate for all values below iso.
        integral = insample_mp.sum() / float(insample_mp.shape[0])

        out_list.append(integral)

    return out_list


# Generate some random two-dimensional data:
def measure(n):
    "Measurement model, return two coupled measurements."
    m1 = np.random.normal(size=n)
    m2 = np.random.normal(scale=0.5, size=n)
    return m1+m2, m1-m2

# Create list to pass.
m_list = []
for i in range(60):
    m1, m2 = measure(5)
    m_list.append(m1.tolist())
    m_list.append(m2.tolist())

# Call KDE integration function.
print 'Integral result: ', kde_integration(m_list)

Ophion提供的解决方案在我提供的原始代码上运行良好,但在此版本中失败并出现以下错误:

Integral result: Exception in thread Thread-3:
Traceback (most recent call last):
  File "/usr/lib/python2.7/threading.py", line 551, in __bootstrap_inner
    self.run()
  File "/usr/lib/python2.7/threading.py", line 504, in run
    self.__target(*self.__args, **self.__kwargs)
  File "/usr/lib/python2.7/multiprocessing/pool.py", line 319, in _handle_tasks
    put(task)
PicklingError: Can't pickle <type 'function'>: attribute lookup __builtin__.function failed

我尝试移动calc_kernel函数,因为这个问题中的一个答案多处理:如何在类中定义的函数上使用Pool.map？声明"你必须通过导入你的模块来访问你给map()的函数" ; 但我仍然无法使用此代码.

任何帮助将非常感谢.

---

加2

实现Ophion建议删除该calc_kernel功能并简单地使用:

results = pool.map(kernel, torun)

努力摆脱PicklingError但现在我看到,如果我创建一个m_list超过62-63项目的初始值我得到这个错误:

Traceback (most recent call last):
  File "~/gauss_kde_temp.py", line 67, in <module>
    print 'Integral result: ', kde_integration(m_list)
  File "~/gauss_kde_temp.py", line 38, in kde_integration
    pool = Pool(processes=cores)
  File "/usr/lib/python2.7/multiprocessing/__init__.py", line 232, in Pool
    return Pool(processes, initializer, initargs, maxtasksperchild)
  File "/usr/lib/python2.7/multiprocessing/pool.py", line 161, in __init__
    self._result_handler.start()
  File "/usr/lib/python2.7/threading.py", line 494, in start
    _start_new_thread(self.__bootstrap, ())
thread.error: can't start new thread

由于我在实际执行此代码中的实际列表最多可包含2000个项目,因此此问题会导致代码无法使用.线38是这一个:

pool = Pool(processes=cores)

显然它与我正在使用的核心数量有关？

Python中的这个问题"无法启动新线程错误"建议使用:

threading.active_count()

当我收到错误时检查我要去的线程数.我检查了它,当它到达374线程时它总是崩溃.我该如何编码这个问题？

---

这是处理这个最后一个问题的新问题:线程错误:无法启动新线程

Answer 1

也许加快速度的最简单方法是并行化kernel(sample)：

采取这个代码片段：

tik = time.time()
insample = kernel(sample) < iso
print 'filter/sample: ', time.time()-tik
#filter/sample:  1.94065904617

将此更改为使用multiprocessing：

from multiprocessing import Pool
tik = time.time()

#Create definition.
def calc_kernel(samp):
    return kernel(samp)

#Choose number of cores and split input array.
cores = 4
torun = np.array_split(sample, cores, axis=1)

#Calculate
pool = Pool(processes=cores)
results = pool.map(calc_kernel, torun)

#Reintegrate and calculate results
insample_mp = np.concatenate(results) < iso

print 'multiprocessing filter/sample: ', time.time()-tik
#multiprocessing filter/sample:  0.496874094009

仔细检查他们是否返回相同的答案：

print np.all(insample==insample_mp)
#True

4 核的性能提升了 3.9 倍。不确定您在什么上运行它，但在大约 6 个处理器之后，您的输入数组大小不足以获得可观的收益。例如，使用 20 个处理器，速度仅提高约 5.8 倍。