Using Existing Numerical Libraries on Spark
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1 Using Existing Numerical Libraries on Spark Brian Spector Chicago Spark Users Meetup June 24 th, 2015 Experts in numerical algorithms and HPC services
2 How to use existing libraries on Spark Call algorithm with data in-memory Sample If data is small enough Obtain estimates for parameters Reformulate the problem Map/Reduce existing functions across workers 2
3 Outline NAG Introduction Numerical Computing Linear Regression NAG Example on Spark Timings Problems Encountered MLlib Algorithms 3
4 Outline NAG Introduction Numerical Computing Linear Regression NAG Example on Spark Timings Problems Encountered MLlib Algorithms 4
5 The Numerical Algorithms Group Founded in 1970 as a cooperative project out of academia in UK Support and Maintain Numerical Library ~1700 Mathematical/Statistical Routines NAG s code is embedded in many vendor libraries (e.g. AMD, Intel) Numerical Services Numerical Library HPC Services 5
6 NAG Library Full Contents Root Finding Summation of Series Quadrature Ordinary Differential Equations Partial Differential Equations Numerical Differentiation Integral Equations Mesh Generation Interpolation Curve and Surface Fitting Optimization Approximations of Special Functions Dense Linear Algebra Sparse Linear Algebra Correlation & Regression Analysis Multivariate Methods Analysis of Variance Random Number Generators Univariate Estimation Nonparametric Statistics Smoothing in Statistics Contingency Table Analysis Survival Analysis Time Series Analysis Operations Research 6
7 Outline NAG Introduction Numerical Computing Linear Regression NAG Example on Spark Timings Problems Encountered MLlib Algorithms 7
8 Efficient Algorithms At NAG we have 40 years of algorithms Linear Algebra, Regression, Optimization Data is all in-memory call a compiled library LAPACK/BLAS MKL void nag_1d_spline_interpolant (Integer m, const double x[], const double y[], Nag_Spline *spline, NagError *fail); 8
9 Algorithms take advantage of AVX/AVX2 Multi-core Modern programming languages and compilers (hopefully) take care of some efficiencies for us Python numpy/scipy -O2 flag for compilers Efficient Algorithms Users worry less about efficient computing and more about solving their problem. 9
10 Big Data But what happens when it comes to Big Data? x = (double*) malloc(10,000,000 * 10,000 * sizeof(double)) Past efficient algorithms break down Need different ways of solving same problem How do we use our existing functions (libraries) on Spark? We must reformulate the problem An example 10
11 General Problem Linear Regression Example Given a set of input measurements x 1 x 2 x p and an outcome measurement y, fit a linear model y = X B + ε y = y 1 y p X = x 1,1 x 1,p x n,1 x n,p Three ways of solving the same problem 11
12 Linear Regression Example Solution 1 (Optimal Solution) X = x 1,1 x 1,p x n,1 x n,p = QR where R = R 0 R is p by p Upper Triangular, Q orthogonal R B = c 1 where c = Q T y lots of linear algebra, but we have an algorithm! 12
13 Linear Regression Example Solution 2 (Normal Equations) X T X B = X T y If we 3 independent variables X = , y =
14 Linear Regression Example X T X = = z 1,1 z 1,2 z 1,3 z 2,1 z 2,2 z 2,3 z 3,1 z 3,2 z 3,3 B = X T X 1 X T y This computation can be map out to slave nodes 14
15 Linear Regression Example Solution 3 (Optimization) min y X B 2 Iterative over the data Final answer is an approximate to the solution Can add constraints to variables (LASSO) MLlib Algorithms 15
16 MLlib Algorithms Machine Learning/Optimization MLlib uses solution #3 for many applications Classification Regression Gaussian Mixture Model Kmeans Slave nodes are used for callbacks to access data Map, Reduce, Repeat 16
17 MLlib Algorithms Master/Libraries Slaves Slaves 17
18 Outline NAG Introduction Numerical Computing Linear Regression NAG Example on Spark Timings Problems Encountered MLlib Algorithms 18
19 Use Normal Equations (Solution 2) to compute Linear Regression on large dataset. NAG Libraries were distributed across Master/Slave Nodes Steps: 1. Read in data 2. Call NAG routine to compute sum-of-squares matrix on partitions (chucks) NAG Example on Spark Default partition size is 64mb 3. Call NAG routine to aggregate SSQ matrix together 4. Call NAG routine to compute optimal coefficients 19
20 Linear Regression Example Master NAG Call NAG CALL NAG CALL 20
21 Linear Regression Example Data Label X1 X2 X3 X
22 The Data (in Spark) Slave Master Label X1 X2 X3 X rdd.parallelize(data).cache() Slave
23 The Data (in Spark) Slave Slave 2 NAG_CALL(data)
24 The Data (in Spark) Slave 1 Slave Slave 2 FlatMapFunction Slave
25 How it looks in Spark finalpt = data.mappartitions(new ComputeSSQ() ).reduce(new Function2()); static class ComputeSSQ implements FlatMapFunction<Iterator<LabeledPoint>, NAGData> public Iterable<NAGData> call(iterator<labeledpoint> iter) throws Exception { NAG CALL } 25
26 The Data (in Spark) Slave Master Slave
27 NAG Example Test 1 Test 2 Data ranges in size from 2 GB 64 GB on Amazon EC2 Cluster Used an 8 slave xlarge cluster (16 GB RAM) Varied the number of slave nodes from 2-16 Used 16 GB of data to see how algorithms scale 27
28 Cluster Utilization 28
29 NAG Results of Linear Regression 29
30 NAG Results of Scaling 30
31 NAG and MLlib Results 31
32 NAG on Spark NAG Functions that work on Spark Regression Linear regression (with constraints) Logistic regression (with constraints) Principal Component Analysis Statistics Summary information (mean, variance, etc) Correlation Probabilities and deviates for normal, student-t, chi-squared, beta, and many more distributions Random number generation Optimization including Linear, nonlinear, quadratic, and sum of squares for the objective function Constraints can be simple bounds, linear, or even nonlinear These require wrapping in specific environment (java/python) 32
33 Distributing libraries spark-ec2/copy-dir Setting environment variables LD_LIBRARY_PATH Needs to be set as you submit the job $./spark-submit --jars NAGJava.jar --conf "spark.executor.extralibrarypath= ${Path-to-Libraries-on-Worker-Nodes}" simplenagexample.jar Problems Encountered NAG_KUSARI_FILE (NAG license file) Can be set in code via sc.setexecutorenv Debugging slave nodes Partition sizes 33
34 Outline NAG Introduction Numerical Computing Linear Regression NAG Example on Spark Timings Problems Encountered MLlib Algorithms 34
35 MLlib Algorithms Basic statistics summary statistics correlations stratified sampling hypothesis testing random data generation Classification and regression linear models (SVMs, logistic regression, linear regression) naive Bayes decision trees ensembles of trees (Random Forests and Gradient-Boosted Trees) isotonic regression Collaborative filtering alternating least squares (ALS) Clustering k-means Gaussian mixture power iteration clustering (PIC) latent Dirichlet allocation (LDA) streaming k-means Dimensionality reduction singular value decomposition (SVD) principal component analysis (PCA) Feature extraction and transformation Frequent pattern mining FP-growth Optimization (developer) stochastic gradient descent limited-memory BFGS (L-BFGS) 35
36 DataFrames MLlib pipeline SparkR More and better optimizers Improved APIs Contains all the components for better numerical computations Use existing R code on Spark! Free Other Improvements Huge open source community 36
37 How to use existing libraries on Spark Call algorithm with data in-memory Sample If data is small enough Obtain estimates for parameters Reformulate the problem Map/Reduce existing functions across slaves 37
38 NAG and Apache Spark Thanks! For more information: Check out The NAG Blog 38
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