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POSpeed up sampling of kernel estimate
 

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  1. POSpeed up sampling of kernel estimate
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    <p>Here's a <code>MWE</code> of a much larger code I'm using. Basically, it performs a Monte Carlo integration over a KDE (<a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gaussian_kde.html" rel="nofollow noreferrer">kernel density estimate</a>) for all values located below a certain threshold (the integration method was suggested over at this question BTW: <a href="https://stackoverflow.com/questions/17822282/integrate-2d-kernel-density-estimate?rq=1">Integrate 2D kernel density estimate</a>).</p> <pre><code>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) &lt; 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 </code></pre> <p>The output looks something like this:</p> <pre><code>iso: 0.00259208679199 resample: 0.000817060470581 filter/sample: 2.10829401016 integral: 4.2200088501e-05 </code></pre> <p>which clearly means that the <em>filter/sample</em> call is consuming almost all of the time the code uses to run. I have to run this block of code iteratively several thousand times so it can get pretty time consuming.</p> <p>Is there any way to speed up the filtering/sampling process?</p> <hr> <h2>Add</h2> <p>Here's a slightly more realistic <code>MWE</code> of my actual code with Ophion's multi-threading solution written into it:</p> <pre><code>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) &lt; 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) </code></pre> <p>The solution presented by <em>Ophion</em> works great on the original code I presented, but fails with the following error in this version:</p> <pre><code>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 &lt;type 'function'&gt;: attribute lookup __builtin__.function failed </code></pre> <p>I tried moving the <code>calc_kernel</code> function around since one of the answers in this question <a href="https://stackoverflow.com/questions/3288595/multiprocessing-using-pool-map-on-a-function-defined-in-a-class">Multiprocessing: How to use Pool.map on a function defined in a class?</a> states that <em>"the function that you give to map() must be accessible through an import of your module"</em>; but I still can't get this code to work.</p> <p>Any help will be very much appreciated.</p> <hr> <h2>Add 2</h2> <p>Implementing <em>Ophion's</em> suggestion to remove the <code>calc_kernel</code> function and simply using:</p> <pre><code>results = pool.map(kernel, torun) </code></pre> <p>works to get rid of the <code>PicklingError</code> but now I see that if I create an initial <code>m_list</code> of anything more than around 62-63 items I get this error:</p> <pre><code>Traceback (most recent call last): File "~/gauss_kde_temp.py", line 67, in &lt;module&gt; 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 </code></pre> <p>Since my actual list in my real implementation of this code can have up to 2000 items, this issue renders the code unusable. Line <code>38</code> is this one:</p> <pre><code>pool = Pool(processes=cores) </code></pre> <p>so apparently it has something to do with the number of cores I'm using?</p> <p>This question <a href="https://stackoverflow.com/questions/10589766/cant-start-a-new-thread-error-in-python">&quot;Can&#39;t start a new thread error&quot; in Python</a> suggests using:</p> <pre><code>threading.active_count() </code></pre> <p>to check the number of threads I have going when I get that error. I checked and it always crashes when it reaches <code>374</code> threads. How can I code around this issue?</p> <hr> <p>Here's the new question dealing with this last issue: <a href="https://stackoverflow.com/questions/18602236/thread-error-cant-start-new-thread">Thread error: can&#39;t start new thread</a></p>
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    1. CORunning `kernel(sample) < iso` takes the 2 seconds in total, `kernel(sample)` is 99.99% of that time.
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    2. CO@Ophion yes that's my point. I need to find a way to optimize that process.
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    3. COYou might want to rephrase it as the `kernel(sample)` process is the most consuming part. Scipy routines are fairly optimized, unless there is some trickery to avoid that call all together there isnt much to be done.
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