large scale machine earning with the simsql system · 2015-11-14 · 1 large scale machine learning...

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LARGE SCALE MACHINE LEARNING WITH THE SIMSQL SYSTEM

Chris JermaineRice University

Current/Recent SimSQL team member: Zhuhua Cai, Jacob Gao, Michael Gubanov, Shangyu Luo, Luis Perez

Also, Peter J. Haas at IBM Almaden

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The Last Few Years...

• Have seen huge interest in large-scale data-processing systems• OptiML, GraphLab, SystemML, MLBase, HBase, MongoDB, BigTable, Pig, Impala,

ScalOps, Pregel, Giraph, Hadoop, TupleWare, Hama, Spark, Flink, Ricardo, Nyad, Dra-dLinq, and many others...

• Many have had significant industrial impact...• Why now?

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Until the Mid-2000’s

• If you had a large-scale data-processing problem, you:1. Rolled your own

2. Bought an SQL-based database system

3. Used a niche (often industry-specific) solution

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Available to very few people

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SQL Databases

• What were the complaints?— Poor performance

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SQL Databases

• What were the complaints?— Poor performance This is misleading...

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SQL Databases

• What were the complaints?— Poor price/performance (Teradata costs a lot)

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SQL Databases


— No open-source solution with good scale out

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SQL Databases



— Frustration with cost to load data into relations

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SQL Databases




— SQL has never played nicely with other tools (software packages, other PLs)

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SQL Databases




— SQL has never played nicely with other tools (software packages, other PLs)

A Lot Of Pain in the Analytics Space

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Then, Suddenly We Had Hadoop

• Our salvation! Right??

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import java.util.*;

import org.apache.hadoop.mapreduce.lib.input.TextInputFormat;import org.apache.hadoop.mapreduce.lib.output.TextOutputFormat;import org.apache.hadoop.mapreduce.Job;import org.apache.hadoop.conf.Configuration;import org.apache.hadoop.fs.Path;import org.apache.hadoop.io.Text;import org.apache.hadoop.io.IntWritable;

public class WordCount { public static int main(String[] args) throws Exception { // if we got the wrong number of args, then exit if (args.length != 4 || !args[0].equals ("-r")) { System.out.println("usage: WordCount -r <num reducers> <input> <output>"); return -1; } // Get the default configuration object Configuration conf = new Configuration (); // now create the MapReduce job Job job = new Job (conf); job.setJobName ("WordCount"); // we'll output text/int pairs (since we have words as keys and counts as values) job.setMapOutputKeyClass (Text.class); job.setMapOutputValueClass (IntWritable.class); // again we'll output text/int pairs (since we have words as keys and counts as values) job.setOutputKeyClass (Text.class); job.setOutputValueClass (IntWritable.class); // tell Hadoop the mapper and the reducer to use job.setMapperClass (WordCountMapper.class); job.setCombinerClass (WordCountReducer.class); job.setReducerClass (WordCountReducer.class); // we'll be reading in a text file, so we can use Hadoop's built-in TextInputFormat job.setInputFormatClass (TextInputFormat.class); // we can use Hadoop's built-in TextOutputFormat for writing out the output text file job.setOutputFormatClass (TextOutputFormat.class);

// set the input and output paths TextInputFormat.setInputPaths (job, args[2]); TextOutputFormat.setOutputPath (job, new Path (args[3])); // set the number of reduce paths try { job.setNumReduceTasks (Integer.parseInt (args[1])); } catch (Exception e) { System.out.println("usage: WordCount -r <num reducers> <input> <output>"); return -1; } // force the mappers to handle one megabyte of input data each TextInputFormat.setMinInputSplitSize (job, 1024 * 1024); TextInputFormat.setMaxInputSplitSize (job, 1024 * 1024); // this tells Hadoop to ship around the jar file containing "WordCount.class" to all of the different // nodes so that they can run the job job.setJarByClass(WordCount.class); // submit the job and wait for it to complete! int exitCode = job.waitForCompletion (true) ? 0 : 1; return exitCode;


Here’s the main program forWord Count...

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import java.util.*;

import org.apache.hadoop.mapreduce.lib.input.TextInputFormat;import org.apache.hadoop.mapreduce.lib.output.TextOutputFormat;import org.apache.hadoop.mapreduce.Job;import org.apache.hadoop.conf.Configuration;import org.apache.hadoop.fs.Path;import org.apache.hadoop.io.Text;import org.apache.hadoop.io.IntWritable;

public class WordCount { public static int main(String[] args) throws Exception { // if we got the wrong number of args, then exit if (args.length != 4 || !args[0].equals ("-r")) { System.out.println("usage: WordCount -r <num reducers> <input> <output>"); return -1; } // Get the default configuration object Configuration conf = new Configuration (); // now create the MapReduce job Job job = new Job (conf); job.setJobName ("WordCount"); // we'll output text/int pairs (since we have words as keys and counts as values) job.setMapOutputKeyClass (Text.class); job.setMapOutputValueClass (IntWritable.class); // again we'll output text/int pairs (since we have words as keys and counts as values) job.setOutputKeyClass (Text.class); job.setOutputValueClass (IntWritable.class); // tell Hadoop the mapper and the reducer to use job.setMapperClass (WordCountMapper.class); job.setCombinerClass (WordCountReducer.class); job.setReducerClass (WordCountReducer.class); // we'll be reading in a text file, so we can use Hadoop's built-in TextInputFormat job.setInputFormatClass (TextInputFormat.class); // we can use Hadoop's built-in TextOutputFormat for writing out the output text file job.setOutputFormatClass (TextOutputFormat.class);

// set the input and output paths TextInputFormat.setInputPaths (job, args[2]); TextOutputFormat.setOutputPath (job, new Path (args[3])); // set the number of reduce paths try { job.setNumReduceTasks (Integer.parseInt (args[1])); } catch (Exception e) { System.out.println("usage: WordCount -r <num reducers> <input> <output>"); return -1; } // force the mappers to handle one megabyte of input data each TextInputFormat.setMinInputSplitSize (job, 1024 * 1024); TextInputFormat.setMaxInputSplitSize (job, 1024 * 1024); // this tells Hadoop to ship around the jar file containing "WordCount.class" to all of the different // nodes so that they can run the job job.setJarByClass(WordCount.class); // submit the job and wait for it to complete! int exitCode = job.waitForCompletion (true) ? 0 : 1; return exitCode;


Plus, often not that fast... No pretty!

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Data load engineering $$

Dat

a qu

ery

engi

neer

ing

$$

SQL

MapReduce(Hadoop)

Complexity of Computation

Que

ry R

espo

nse

Tim

eSQL

MapReduce(Hadoop)


Not a clear win...

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Data load engineering $$

Dat

a qu

ery

engi

neer

ing

$$

SQL

DryadLinq,Spark, Flink, others

Complexity of Computation

Que

ry R

espo

nse

Tim

eSQL

Next Generation “DataFlow” Platforms

DryadLinq,Spark, Flink, others

Cleaner programming interface

Better Implementation TechniquesSo people worked at improvingthe situation...

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Next Generation “DataFlow” Platforms

• “Dataflow” platforms (such as Spark) are effectively RA engines— Human being strings together (simple) bulk ops to form a computation

— But DB people have recognized imperative data access is bad for nearly 40 years

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One Step Forward, Two Steps Back



Dept (Name, Supervisor, Address)

Affiliation (PercentEffort)

Employee (EName, Age, Salary)

Works (Duration)

Project (PName, Director, Customer)

CODASYL Data Model (1969)

“Which employees supervised byChris worked on the Plinyproject?”

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Works (Duration)




Good if few employees per project

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Works (Duration)




Good if few people supervised by Chris

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Works (Duration)




Good if few people supervised by Chris

Such Issues Led Directly to Widespread Adoption ofthe Relational Model

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Deja Vu, All Over Again

• I’m teaching a data science class this semester at Rice— Assignment 3: Use Spark to analyze NYC taxi GPS data

— One task: find drop-off anomalies and geographic points-of-interest nearby

— “Prof. Chris: My last join hasn’t finished in two hours!!”

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Deja Vu, All Over Again #Map the above to CellDayHour, ratio numDrop/avgDrops, numDrops then #take the top 20 ratios

output3 = output2.map(lambda p:(p[0], (p[1]/p[2], p[1]))).takeOrdered

(20, lambda (key, value): -value[0])

#Turn back into RDD

output4 = sc.parallelize(output3)

#Change formatting of the output

output5 = output4.map(lambda p: (str(p[0].split(":")[0]), [p[0].split(":")[1].split("")[1],p[0].split(":")[1].split(" ")[0], p[1]])).keyBy(lambda p: p[0])

#Map locations to grid cells

mappedData = mappings.map(lambda m: (str(changeValToCell (float(m.split("||")[1]))) + str(changeValToCell (float(m.split("||")[0]))), (m.split("||")[2]))).keyBy(lambda p: p[0]).reduceByKey(lambda t1, t2: (t1))

#Join the mappings to the data together

final_output = output5.leftOuterJoin(mappedData).map(lambda p: (p[0], p[1][0][1][0], p[1][0][1][1],p[1][0][1][2][0] ,p[1][0][1][2][1]))

Here’s a fast solution

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Deja Vu, All Over Again # Now that it's sorted, put it back to (grid_cell,

# (hour, date, fraction, number))

grid_cell_combined = grid_cell_combined.map(lambda t: (t[1][0].split

(":")[0], (t[1][0].split(":")[1], t[1][1],t[0], t[1][2])))

# now let's grab the POI data

lines = sc.textFile(sys.argv[2], 1)

poi_lines = lines.map(lambda x: x.split('||')).map(lambda l:

(get_cell_id(l[0], l[1]), [l[2]])).reduceByKey(lambda list1,

list2: list1 + list2)

grid_with_poi = grid_cell_combined.leftOuterJoin(poi_lines).map(

lambda t: (t[1][0][2], (t[0], t[1][0][0], t[1][0][1], t[1][0][3],

t[1][1]))).sortByKey(ascending=False).map(

lambda t: (t[1][0], t[1][1], t[1][2], t[0], t[1][3], t[1][4]))

test_taxi_rows = sc.parallelize(grid_with_poi.take(20))

test_taxi_rows.saveAsTextFile(sys.argv[3])

And here’s a slow one

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Is This Progress?

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Is This Progress?

• Dataflow engine: not the right platform for complicated analytics— Throwing away the optimizer radically increases programmer burden

— 100% host language code: significant portion of program opaque to system-Means system cannot optimize

— Loss of control of data format/layout: big performance hit

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The Ideal Analytics Ecosystem

Unstructured data store

(HDFS)Long-term storage

Dataflowplatform

Structured data storeLong-term storage (hot data)

Short-term storage (cool data)

Simple/one-off analytics

Dataintake

SQL

DSL1

DSL2

DSL3

Complexanalytics

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Our Research

• What should this system look like?• Design principals:

— RDBMS/declarative = GOOD

— Incremental, not revolutionary

— No need to throw out 40 years of tech.

— Statistical processing: esp. important



SQL

DSL1

DSL2

DSL3

Complexanalytics

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Our Research



SQL

DSL1

DSL2

DSL3

Complexanalytics

• What should this system look like?• Design principals:

— RDBMS/declarative = GOOD

— Incremental, not revolutionary

— No need to throw out 40 years of tech.

— Statistical processing: esp. important

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How Must DBMS Change?

• More extensive support for recursion• Fancier table functions (“VG functions”)• Add native support for vectors/matrices (as att types)• Support for executing huge “query” plans (1000’s of operations)• New logical/physical operators• Additional DSLs (SQL not enough)

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SimSQL’s Version of SQL

• Most fundamental SQL addition is “VG Function” abstraction• Called via a special CREATE TABLE statement• Example; assuming:

— SBP(MEAN, STD, GENDER)

— PATIENTS(NAME, GENDER)

• To create a derived table, we might have:CREATE TABLE SBP_DATA(NAME, GENDER, SBP) ASFOR EACH p in PATIENTS WITH Res AS Normal ( SELECT s.MEAN, s.STD FROM SPB s WHERE s.GENDER = p.GENDER) SELECT p.NAME, p.GENDER, r.VALUE FROM Res r

We like randomized algs(MCMC) but not limited to that

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How Does This Work?

CREATE TABLE SBP_DATA(NAME, GENDER, SBP) ASFOR EACH p in PATIENTS WITH Res AS Normal ( SELECT s.MEAN, s.STD FROM SPB s WHERE s.GENDER = p.GENDER) SELECT p.NAME, p.GENDER, r.VALUE FROM Res r

PATIENTS (NAME, GENDER)(Joe, Male) “p”(Tom, Male)(Jen, Female)(Sue, Female)(Jim, Male)

SBP(MEAN, STD, GENDER)(150, 20, Male)(130, 25, Female)

Loop through PATIENTS

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How Does This Work?




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How Does This Work?




Normal(150,20)

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How Does This Work?




Res(VALUE)(162)

Normal(150,20)

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How Does This Work?




Res(VALUE)(162)

SBP_DATA (NAME, GENDER, SPB)(Joe, Male, 162)

Normal(150,20)

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How Does This Work?


PATIENTS (NAME, GENDER)(Joe, Male)(Tom, Male) “p”(Jen, Female)(Sue, Female)(Jim, Male)


Res(VALUE)(135)

SBP_DATA (NAME, GENDER, SPB)(Joe, Male, 162)

Normal(150,20)

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How Does This Work?


PATIENTS (NAME, GENDER)(Joe, Male)(Tom, Male) “p”(Jen, Female)(Sue, Female)(Jim, Male)


Res(VALUE)(135)

SBP_DATA (NAME, GENDER, SPB)(Joe, Male, 162)(Tom, Male, 135)

Normal(150,20)

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How Does This Work?


PATIENTS (NAME, GENDER)(Joe, Male)(Tom, Male) (Jen, Female) “p”(Sue, Female)(Jim, Male)


Res(VALUE)(112)

Normal(130,25)

SBP_DATA (NAME, GENDER, SPB)(Joe, Male, 162)(Tom, Male, 135)

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How Does This Work?


PATIENTS (NAME, GENDER)(Joe, Male)(Tom, Male) (Jen, Female) “p”(Sue, Female)(Jim, Male)


Res(VALUE)(112)

Normal(130,25)

SBP_DATA (NAME, GENDER, SPB)(Joe, Male, 162)(Tom, Male, 135)(Jen, Female, 112)

and so on...

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More Complicated Computations

• Previous allows (for example) table-valued RVs• But Markov chains are easy in SimSQL, so Bayesian ML easy• Here’s a silly Markov chain. We have:

— PERSON (pname)

— PATH (fromCity, toCity, prob)

— RESTAURANT (city, rname, prob)

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Markov Chain Simulation

• To select an initial starting position for each person:CREATE TABLE POSITION[0] (pname, city) ASFOR EACH p IN PERSON WITH City AS DiscreteChoice ( SELECT r DISTINCT toCity FROM PATH) SELECT p.pname, City.value FROM City

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• And then randomly select a restaurant:CREATE TABLE VISITED[i] (pname, rname) ASFOR EACH p IN PERSON WITH Visit AS Categorical ( SELECT r.rname, r.prob FROM RESTAURANT r, POSITION[i] l WHERE r.city = l.city AND l.pname = p.pname) SELECT p.pname, Visit.val FROM Visit

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• And transition the person:CREATE TABLE POSITION[i] (pname, city) ASFOR EACH p IN PERSON WITH Next AS Categorical ( SELECT PATH.tocity, PATH.prob FROM PATH, POSITION[i - 1] l WHERE PATH.fromcity = l.city AND l.pname = p.pname) SELECT p.pname, Next.val FROM Next

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• And transition the person:CREATE TABLE POSITION[i] (pname, city) ASFOR EACH p IN PERSON WITH Next AS Categorical ( SELECT PATH.tocity, PATH.prob FROM PATH, POSITION[i - 1] l WHERE PATH.fromcity = l.city AND l.pname = p.pname) SELECT p.pname, Next.val FROM Next

• Fully spec’ed a distributed Markov chain!

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Native Vector and Matrix Support

• Vectors and matrices fundamental to analytics

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• Vectors and matrices fundamental to analytics• Can be difficult to write code/expensive without it

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data (pointID INTEGER, dimID INTEGER, value DOUBLE)matrixA (row INTEGER, col INTEGER, value DOUBLE)

CREATE VIEW xDiff (pointID, value) AS SELECT x2.pointID, x1.value - x2.value FROM data AS x1, data AS x2 WHERE x1.pointID = i and x1.dim = x2.dim

SELECT x.pointID, SUM (firstPart.value * x.value)FROM (SELECT x.pointID, a.colID, SUM (a.value, x.value) AS value FROM xDiff as X, matrixA AS a WHERE x.dimID = a.rowID GROUP BY x.pointID, a.colID) AS firstPart, xDiff AS xWHERE firstPart.colID = x.dimID AND firstPart.pointID = x.pointIDGROUP BY x.pointID

Classical SQL

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data (pointID INTEGER, val VECTOR [])matrixA (val MATRIX [][])

SELECT x2.pointID, inner_product ( matrix_vector_multiply ( x1.val - x2.val, a.val), x1.val - x2.val) AS valueFROM data AS x1, data AS x2, matrixA AS aWHERE x1.pointID = i

SimSQL

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• Another example: linear regression• Goal is to compute

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• Another example: linear regression• Goal is to compute

CREATE TABLE X ( i INTEGER, x_i VECTOR []);

CREATE TABLE y ( i INTEGER, y_i DOUBLE);

SELECT matrix_vector_multiply (matrix_inverse ( SUM (outer_product (X.x_i, X.x_i))), SUM (X.x_i * y_i))FROM X, yWHERE X.i = y.i

Easy in SimSQL!

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Promotion and Demotion

• Start with pure, tuple-based encoding

mat (row INTEGER, col INTEGER, value DOUBLE)

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• Start with pure, tuple-based encoding• Move to a set of (vector, rowID) pairs


CREATE VIEW vecs (vec, row) AS SELECT VECTORIZE (label_scalar (val, col)) AS vec, row FROM mat GROUP BY row

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• Start with pure, tuple-based encoding• Move to a set of (vector, rowID) pairs• Then create a matrix...



SELECT ROWMATRIX (label_vector (vec, row))FROM vecs

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• Start with pure, tuple-based encoding• Move to a set of (vector, rowID) pairs• Then create a matrix... or move back to tuples



SELECT ROWMATRIX (label_vector (vec, row))FROM vecs

SELECT v.row, c.cnt AS col, get_scalar (v.vec, c.cnt) AS v.valueFROM vecs AS v, counts AS c

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Additional DSLs: BUDS

• SQL might not be most natural declarative interface for analytics

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Additional DSLs: BUDS

• SQL might not be most natural declarative interface for analytics• Math for the Bayesian Lasso, lifted from original paper

1.

2.

3.

— where ,

r Normal A 1– XTy σ2A 1–,( )∼

σ2 InvGamma n 1–( ) p+2

-------------------------- y Xr–( )T y Xr–( )T rTD 1– r+2

---------------------------------------------------------------------,⎝ ⎠⎛ ⎞∼

τj2– InvGaussian λσ

rj------- λ2,⎝ ⎠⎛ ⎞∼

A XTX D 1–+= D 1– diag τ12– τ2

2– …, ,( )=

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SQL Is Not TrivialCREATE TABLE tau[0](tauValue) AS WITH ig AS InvGaussian_VM(SELECT invGaussianMean, invGaussianShape FROM prior)

SELECT ig.outValue FROM ig;

CREATE TABLE A[i](AValue) AS SELECT MATRIX_INVERSE(xtx.val + DIAG_MATRIX(t.tauValue)) FROM tau[i] t, regressorGram xtx;

CREATE TABLE beta[i](betaValue) AS WITH mvn AS MultiNormal_VM( (SELECT MATRIX_VECTOR_MULTIPLY(a.AValue, rs.sumValue), (a.AValue * s.sigmaValue)

FROM A[i] a, regressorSum rs, sigma[i] s)) SELECT mvn.out_mean FROM mvn;

CREATE TABLE sigma[i](sigmaValue) AS WITH g as InvGamma( (SELECT (pr.numResponses - 1)/2.0 + (pr.numRegressors/2.0) FROM prior pr), (SELECT sb.sumBetas + st.sumTaus FROM (SELECT SUM(((res.respValue - xb.sumValue) * (res.respValue - xb.sumValue)) / 2.0) AS sumBetas

FROM centeredResponse res, (SELECT reg.respID as respID, INNER_PRODUCT(reg.regValue, b1.betaValue) as sumValue

FROM regressor reg, beta[i-1] b1) AS xb WHERE res.respID = xb.respID) AS sb, (SELECT (INNER_PRODUCT(b2.betaValue * b2.betaValue, t.tauValue) / 2.0) AS sumTaus

FROM tau[i-1] t, beta[i-1] b2) AS st)) SELECT g.outValue FROM g;

CREATE TABLE tau[i](tauValue) AS WITH ig AS InvGaussian_VM( (SELECT SQRT_VECTOR((pr1.lambdaValue * pr1.lambdaValue * s.sigmaValue) / (b.betaValue * b.betaValue))

FROM prior pr1, sigma[i] s, beta[i-1] b), (SELECT (pr2.lambdaValue * pr2.lambdaValue) FROM prior pr2)), SELECT ig.outValue FROM ig;

CREATE TABLE response( respID INTEGER, respValue DOUBLE, PRIMARY KEY (respID));CREATE TABLE regressor( respID INTEGER, regValue VECTOR[], PRIMARY KEY (respID));CREATE TABLE prior( numResponses INTEGER, numRegressors INTEGER, lambdaValue DOUBLE, invGammaShape DOUBLE, invGammaScale DOUBLE, invGaussianMean VECTOR[], invGaussianShape DOUBLE);

CREATE VIEW centeredResponse(respID, respValue) AS SELECT r1.respID, (r1.respValue - m.meanRespValue) FROM response r1, (SELECT AVG(r2.respValue) AS meanRespValue FROM response r2) AS m;

CREATE VIEW regressorGram(val) AS SELECT SUM(OUTER_PRODUCT(r.regValue, r.regValue)) FROM regressor r;

CREATE VIEW regressorSum(sumValue) AS SELECT SUM(reg.regValue * res.respValue) FROM regressor reg, centeredResponse res WHERE reg.respID = res.respID;

CREATE TABLE sigma[0](sigmaValue) AS WITH g AS InvGamma (SELECT invGammaShape, invGammaScale FROM prior)

SELECT g.outValue

FROM g;

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BUDS Is Much Simpler!

• Write code that looks just like the math...data { n: range (responses); p: range (regressors); X: array[n, p] of real; y: array[n] of real; lam: real}

var { sig: real; r, t: array[p] of real; yy, Z: array[n] of real;}

A <- inv(X ‘* X + diag(t));yy <- (y[i] - mean(y) | i in 1:n);Z <- yy - X * r;

init { sig ~ InvGamma (1, 1); t ~ (InvGauss (1, lam) | j in 1:p);} r ~ Normal (A *’ X * yy, sig * A);sig ~ InvGamma(((n-1) + p)/2, (Z ‘* Z + (r * diag(t) ‘* r)) / 2);for (j in 1:p) { t[j] ~ InvGauss (sqrt((lam * sig) / r[j]), lam);}

Truly declarative;Programmer only lists dependencies

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BUDS Is Much Simpler!

• Write code that looks just like the math...data { n: range (responses); p: range (regressors); X: array[n, p] of real; y: array[n] of real; lam: real}

var { sig: real; r, t: array[p] of real; yy, Z: array[n] of real;}

A <- inv(X ‘* X + diag(t));yy <- (y[i] - mean(y) | i in 1:n);Z <- yy - X * r;

init { sig ~ InvGamma (1, 1); t ~ (InvGauss (1, lam) | j in 1:p);} r ~ Normal (A *’ X * yy, sig * A);sig ~ InvGamma(((n-1) + p)/2, (Z ‘* Z + (r * diag(t) ‘* r)) / 2);for (j in 1:p) { t[j] ~ InvGauss (sqrt((lam * sig) / r[j]), lam);}



-------------------------- y Xr–( )T y Xr–( )T rTD 1– r+2

---------------------------------------------------------------------,⎝ ⎠⎛ ⎞∼


rj------- λ2,⎝ ⎠⎛ ⎞∼

A XTX D 1–+=

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How Well Does All of This Work?

• SimSQL is great in theory...— Many will buy the “data independence” argument

— Will appreciate being able to specify algs at a very high level

• But can it scale? Isn’t the DB approach gonna be slow?• Yes, it’s slow, compared to C/Fortran + MPI

— But zero data independence with MPI

• But does it compete well with other “Big Data” ML platforms?— After all, are many that count ML as the primary (or a motivating) application

— OptiML, GraphLab, SystemML, MLBase, ScalOps, Pregel, Giraph, Hama, Spark, Ricardo, Nyad, DradLinq

— How might those compare?

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How Well Does All of This Work?

• We’ve done a LOT of comparisons with other mature platforms— Specifically, GraphLab, Giraph, Spark

— More than 70,000 hours of Amazon EC2 time ($100,000 @on-demand price)

— I’d wager that few groups have a better understanding of how well these platforms work in practice!

• Note: point is not to show SimSQL is the fastest (it is not)— Only to argue that it can compete well

— If it competes, it’s a strong argument for the DB approach to ML

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Example One: Bayesian GMM

Generative process:

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Generative process:(1) Pick a cluster

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Generative process:(1) Pick a cluster(2) Use it to generate point

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70



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Then given this

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Infer this

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• Implemented relevant MCMC simulation on all four platforms— SimSQL, GraphLab, Spark, Giraph

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• Philosophy: be true to the platform— Ex: avoid “Hadoop abuse” [Smola & Narayanamurthy, VLDB 2010]

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• Philosophy: be true to the platform— Ex: avoid “Hadoop abuse” [Smola & Narayanamurthy, VLDB 2010]

• Ran on 10 dimensional data, 10 clusters, 10M points per machine— Full (non-diagonal) covariance matrix

— Also on 100 dimensional data, 1M points per machine

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• Some notes:— Times are HH:MM:SS per iteration (time in parens is startup/initialization)

— Amount of data is kept constant per machine in all tests

— “Fail” means that even with much effort and tuning, it crashed

(a) GMM: Initial Implementations10 dimensions 100 dimensions

lines of code 5 machines 20 machines 100 machines 5 machines

SimSQL 197 27:55 (13:55) 28:55 (14:38) 35:54 (18:58) 1:51:12 (36:08)GraphLab 661 Fail Fail Fail FailSpark (Python) 236 26:04 (4:10) 37:34 (2:27) 38:09 (2:00) 47:40 (0:52)Giraph 2131 25:21 (0:18) 30:26 (0:15) Fail Fail

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• Not much difference!— But SimSQL was slower in 100 dims. Why?

-Experiments didn’t use support for vectors/matrices




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• Spark is surprisingly slow— Is Spark slower due to Python vs. Java?




(b) GMM: Alternative Implementations10 dimensions 100 dimensions


Spark (Java) 737 12:30 (2:01) 12:25 (2:03) 18:11 (2:26) 6:25:04 (36:08)

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• What about GraphLab?— GraphLab failed every time. Why?




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n data points

k clusters

mixing proportionvertex

GraphLab/Giraph graph model

1 billion data points by10 clusters by1KB = 10TB RAM (6TB RAM in 100-machine cluster)

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m “super vertices”

k clusters

mixing proportionvertex

GraphLab/Giraph graph model

10,000 super vertices10 clusters by1KB = 100 MB RAM (insignificant!)

To Fix...

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• Super vertex results— GraphLab super vertex screams!


lines of code 5 machines 20 machines 100 machines 5 machinesSpark (Java) 737 12:30 (2:01) 12:25 (2:03) 18:11 (2:26) 6:25:04 (36:08)GraphLab (Super Vertex) 681 6:13 (1:13) 4:36 (2:47) 6:09 (1:21)∗ 33:32 (0:42)

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• Super vertex results— GraphLab super vertex screams!

— But to be fair, others can benefit from super vertices as well....


lines of code 5 machines 20 machines 100 machines 5 machinesSpark (Java) 737 12:30 (2:01) 12:25 (2:03) 18:11 (2:26) 6:25:04 (36:08)GraphLab (Super Vertex) 681 6:13 (1:13) 4:36 (2:47) 6:09 (1:21)∗ 33:32 (0:42)

(c) GMM: Super Vertex Implementations10 dimensions, 5 machines 100 dimensions, 5 machines

w/o super vertex with super vertex w/o super vertex with super vertex

SimSQL 27:55 (13:55) 6:20 (12:33) 1:51:12 (36:08) 7:22 (14:07)GraphLab Fail 6:13 (1:13) Fail 33:32 (0:42)Spark (Python) 26:04 (4:10) 29:12 (4:01) 47:40 (0:52) 47:03 (2:17)Giraph 25:21 (0:18) 13:48 (0:03) Fail 6:17:32 (0:03)

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Example Two: Bayesian Lasso

• Bayesian LR model— Due to Park and Casella [JASA 2008]

— With Laplace prior on regression coefs (good regularization)

— Clever Markov chain derivation means all updates from standard dist families

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• Bayesian LR model— Due to Park and Casella [JASA 2008]

— With Laplace prior on regression coefs (good regularization)

— Clever Markov chain derivation means all updates from standard dist families

• Gibbs sampler is:

1.

2.

3.

— where , , and is the regul’z’n param



-------------------------- y Xr–( )T y Xr–( )T rTD 1– r+2

---------------------------------------------------------------------,⎝ ⎠⎛ ⎞∼


rj------- λ2,⎝ ⎠⎛ ⎞∼

A XTX D 1–+= D 1– diag τ12– τ2

2– …, ,( )= λ

Gram matrix computationmakes it interesting for high-D data

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• Experimental setup— 1K regressors (dense)

— 100K points per machine

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• ResultsBayesian Lasso

lines of code 5 machines 20 machines 100 machines

SimSQL 100 7:09 (2:40:06) 8:04 (2:45:28) 12:24 (2:54:45)GraphLab (Super Vertex) 572 0:36 (0:37) 0:26 (0:35) 0:31 (0:50)Spark (Python) 168 0:55 (1:26:59) 0:59 (1:33:13) 1:12 (2:06:30)Giraph 1871 Fail Fail FailGiraph (Super Vertex) 1953 0:58 (1:14) 1:03 (1:14) 2:08 (6:31)

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• Results

• Interesting points— SimSQL slow (again, lack of support for vectors/matrices is brutal here)...

— But Spark is almost as slow for startup (computation of Gram matrix)

— Check out GraphLab: super fast!

Bayesian Lassolines of code 5 machines 20 machines 100 machines

SimSQL 100 7:09 (2:40:06) 8:04 (2:45:28) 12:24 (2:54:45)GraphLab (Super Vertex) 572 0:36 (0:37) 0:26 (0:35) 0:31 (0:50)Spark (Python) 168 0:55 (1:26:59) 0:59 (1:33:13) 1:12 (2:06:30)Giraph 1871 Fail Fail FailGiraph (Super Vertex) 1953 0:58 (1:14) 1:03 (1:14) 2:08 (6:31)

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Example Three: LDA

• Sort of a Bayesian variant on PCA (for dimensionality reduction)• Experimental setup

— Run over a document database, dictionary size of 10K words

— 100 “topics” (components) were learned

— Constant 2.5M documents per machine

• Note: didn’t do collapsed simulation, since hard to parallelize

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Example Three: LDA

• First we considered a “word based” implementation— Arguably the most natural

— One vertex for each word in corpus in graph-based

— Separate Multnomial call for each word in each doc in SimSQL/Spark

• And a “document based” implementation— One vertex for each document in graph-based

— Update membership for all words at once in SimSQL/Spark (faster ‘cause you broadcast the model, do join with words in doc in user code)

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Example Three: LDA

• Results

• Interesting findings— Only SimSQL can handle word-based imp, but really slow

— Only Giraph gives reasonable performance!

— Spark unable to join words-in-doc with topic-probs, hence an NA

— Giraph unable to load up word-based graph, hence an NA

(a) LDA: Word-based and document-based implementations

Word-based, 5 machines Document-based, 5 machines

lines of code running time lines of code running time

SimSQL 126 16:34:39 (11:23:22) 129 4:52:06 (4:34:27)Spark (Python) NA NA 188 ≈15:45:00 (≈2:30:00)Giraph NA NA 1358 22:22 (5:46)

(b) LDA: Super Vertex Implementations

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Example Three: LDA

• Results

• Interesting findings— Only SimSQL can handle word-based imp, but really slow

— Only Giraph gives reasonable performance!

— Spark unable to join words-in-doc with topic-probs, hence an NA

— Giraph unable to load up word-based graph, hence an NA

• How about super vertex? (handle thousands of docs in a batch)

(a) LDA: Word-based and document-based implementations

Word-based, 5 machines Document-based, 5 machines

lines of code running time lines of code running time

SimSQL 126 16:34:39 (11:23:22) 129 4:52:06 (4:34:27)Spark (Python) NA NA 188 ≈15:45:00 (≈2:30:00)Giraph NA NA 1358 22:22 (5:46)


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Example Three: LDA

• Super vertex results

• Interesting findings— Only SimSQL can scale to 250M docs on 100 machines



Giraph 1406 18:49 (2:35) 20:02 (2:46) FailGraphLab 517 39:27 (32:14) Fail FailSpark (Python) 220 ≈3:56:00 (≈2:15:00) ≈3:57:00 (≈2:15:00) FailSimSQL 117 1:00:17 (3:09) 1:06:59 (3:34) 1:13:58 (4:28)

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Example Three: LDA



— Even super vertex can’t help GraphLab here...




-10K super vertices on 100 machines -each broadcasts 100 different 10K vectors to each topic node-10K by 10K by 100 is 10 billion numbers... -what if a machine gets 2 or three topic nodes?

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Example Three: LDA




— Spark does quite poorly... might this be due to Python?




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Example Three: LDA




— Spark does quite poorly... might this be due to Python?




GMM experiments,ing. For each datah gave us a proba-e. Each of the tenensored by flipping

LDA Spark Java Implementationlines of code 5 machines 20 machines 100 machines

377 9:47 (0:53) 19:36 (1:15) Fail

Figure 6: Average time per iteration (and startup time).

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Summary of Findings

• Giraph can be made very fast— Mostly ‘cause of distributed aggregation facilities

— But it is still brittle, perhaps due to reliance on main memory

98

Summary of Findings



• GraphLab codes are small and nice, especially considering C++— And it can be very fast

— But lack of distributed agg is a killer... what does this even mean in asynch env?

99

Summary of Findings





• Spark codes (Python) are startlingly beautiful. Wow!— But Spark was brittle, hard to tune, and often slow

100

Summary of Findings





• Spark codes (Python) are startlingly beautiful. Wow!— But Spark was brittle, hard to tune, and often slow

• SimSQL codes fully declarative, and often competitive in speed— Only platform to run everything we threw at it

— But lack of matrices and vectors really hurts

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Summary of Talk

• I’ve motivated a relational approach to large-scale ML— All about data independence!

— Same code works for any data set, compute platform

— Just drop in a new physical optimizer and runtime, keep application stack

102

Summary of Talk




• I’ve briefly described SimSQL, our realization of the approach

103

Summary of Talk




• I’ve briefly described SimSQL, our realization of the approach• And I’ve given experimental evidence the approach is practical

— Our Hadoop targeted optimizer and runtime competes well

— And its the only platform to handle everything we threw at it

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That’s It. Questions?

• Download SimSQL today— http://cmj4.web.rice.edu/SimSQL/SimSQL.html

• This presentation at— http://cmj4.web.rice.edu/SimSQLNew.pdf

large scale machine earning with the simsql system · 2015-11-14 · 1 large scale machine learning...

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