## 1. A Nonparametric Density implementation in Spark

One of my previous blog post concerns about nonparametric density estimation. In this post i presented some Matlab code. An advantage of this Spark implementation is that the estimation is totally parallel since we only use build-in Spark procedures. Let be a random sample drawn from some distribution with an unknown density . The key is to use *data.cartesian(random_grid)* which creates pairs where is a predefined grid. Then using *map* together with an Epanechnikov kernel we get . The final is then evaluated using *reduceByKey*.

###A Spark-Function to derive a non-parametric kernel density from pyspark.mllib.regression import LabeledPoint from pyspark.mllib.feature import StandardScaler import matplotlib.pyplot as plt from numpy import * ##1.0 Simulated Data N=15000 mu, sigma = 2, 3 # mean and standard deviation rdd = sc.parallelize( random.normal(mu,sigma,N) ) ##2.0 The Function #2.1 Kernel Function def spark_density(data, Nout, bw): def epan_kernel(x,y,b): u=true_divide( (x-y), b) return max(0, true_divide( 1, b)*true_divide(3,4)*(1-u**2)) #derive the minia and maxi used for interpolation mini=data.takeOrdered(1, lambda x: x ) maxi=data.takeOrdered(1, lambda x: -1*x ) #create an interpolation grid (in fact NOT random this time) random_grid = sc.parallelize( linspace(mini, maxi, num=Nout) ) Nin=data.count() #compute K(x-xi) Matrix kernl=data.cartesian(random_grid).map(lambda x:( float(x[1]),true_divide(epan_kernel(array(x[0]),array(x[1]),bw),Nin) ) ) #sum up return kernl.reduceByKey( lambda y, x: y+x ) ##3.0 Results density= spark_density(rdd, 128, 0.8).collect() dens=array(density).transpose() anzahl=array(anz).transpose() #Plot the estimate plt.plot(dens[0], dens[1], 'bo') axis2=linspace(-10, 10, num=128) #plot the true density plt.plot(axis2, 1/(sigma * sqrt(2 * pi)) *exp( - (axis2 - mu)**2 / (2 * sigma**2) ),linewidth=2, color='r') plt.show()

UfoStupid question: can i just use R `density` for it?

Heiko WagnerPost authorSure, that is possible if you use R. In fact the R density function comes with some nice additional features like an automatich bandwith choice. However R has problems concerning big datasets, here Spark comes into play the algorithm shown above will is scalable and will able to handle a very large amount of data (if your Spark Cluster is powerful enough).

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