Talk about how you normally would use the Normal equation, notes from Andrew Ng
“Unlikely optimization algorithms such as stochastic gradient descent show amazing performance for large-scale problems.“Bottou, 2010SGD has been around for decadesyet recently Langford, Bottou, others have shown impressive speed increasesSGD has been shown to train multiple orders of magnitude faster than batch style learnerswith no loss on model accuracy
“Unlikely optimization algorithms such as stochastic gradient descent show amazing performance for large-scale problems.“Bottou, 2010SGD has been around for decadesyet recently Langford, Bottou, others have shown impressive speed increasesSGD has been shown to train multiple orders of magnitude faster than batch style learnerswith no loss on model accuracy
The most important additions in Mahout’s SGD are:confidence weighted learning rates per termevolutionary tuning of hyper-parametersmixed ranking and regressiongrouped AUCImplications of it being local is that you are limited to the compute capacity of the local machine as opposed to even a single machine on the cluster.
At current disk bandwidth and capacity (2TB at 100MB/s throughput) 6 hours to read the content of a single HD
Bottou similar to Xu2010 in the 2010 paper
Benefits of data flow: runtime can decide where to run tasks and can automatically recover from failuresAcyclic data flow is a powerful abstraction, but is not efficient for applications that repeatedly reuse a working set of data:Iterative algorithms (many in machine learning)• No single programming model or framework can excel atevery problem; there are always tradeoﬀs between simplicity, expressivity, fault tolerance, performance, etc.
Performance still largely dependent on implementation of algo
POLR: Parallel Online Logistic RegressionTalking points:wanted to start with a known tool to the hadoop community, with expected characteristicsMahout’s SGD is well known, and so we used that as a base point
Transcript of "Hadoop Summit EU 2013: Parallel Linear Regression, IterativeReduce, and YARN"
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Josh Patterson Email: Past Published in IAAI-09: josh@floe.tv “TinyTermite: A Secure Routing Algorithm” Twitter: Grad work in Meta-heuristics, Ant-algorithms Tennessee Valley Authority (TVA) @jpatanooga Hadoop and the Smartgrid Github: Cloudera Principal Solution Architect https://github.com/jp Today atanooga Independent Consultant
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Sections1. Modern Data Analytics2. Parallel Linear Regression3. Performance and Results
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The World as Optimization Data tells us about our model/engine/product We take this data and evolve our product towards a state of minimal market error WSJ Special Section, Monday March 11, 2013 Zynga changing games based off player behavior UPS cut fuel consumption by 8.4MM gallons Ford used sentiment analysis to look at how new car features would be received
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The Modern Data Landscape Apps are coming but they need Platforms Components Workflows Lots of investment in Hadoop in this space Lots of ETL pipelines Lots of descriptive Statistics Growing interest in Machine Learning
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Hadoop as The Linux of Data Hadoop has won the Cycle “Hadoop is the kernel of a Gartner: Hadoop will be in distributed operating 2/3s of advanced analytics products by 2015 [1] system, and all the other components around the kernel are now arriving on this stage” ---Doug Cutting
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Today’s Hadoop ML Pipeline Data cleansing / ETL performed with Hive or Pig Data In Place Processed Mahout R Custom MapReduce Algorithm Or Externally Processed SAS SPSS KXEN Weka
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As Focus Shifts to Applications Data rates have been climbing fast Speed at Scale becomes the new Killer App Companies will want to leverage the Big Data infrastructure they’ve already been working with Hadoop HDFS as main storage system A drive to validate big data investments with results Emergence of applications which create “data products”
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Patterson’s Law“As the percent of your total data heldin a storage system approaches 100%the amount of in-system processingand analytics also approaches 100%”
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Tools Will Move onto Hadoop Already seeing this with Vendors Who hasn’t announced a SQL engine on Hadoop lately? Trend will continue with machine learning tools Mahout was the beginning More are following But what about parallel iterative algorithms?
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Distributed Systems Are Hard Lots of moving parts Especially as these applications become more complicated Machine learning can be a non-trivial operation We need great building blocks that work well together I agree with Jimmy Lin [3]: “keep it simple” “make sure costs don’t outweigh benefits” Minimize “Yet Another Tool To Learn” (YATTL) as much as we can!
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To Summarize Data moving into Hadoop everywhere Patterson’s Law Focus on hadoop, build around next-gen “linux of data” Need simple components to build next-gen data base apps They should work cleanly with the cluster that the fortune 500 has: Hadoop Also should be easy to integrate into Hadoop and with the hadoop-tool ecosystem Minimize YATTL
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Linear Regression In linear regression, data is modeled using linear predictor functions unknown model parameters are estimated from the data. We use optimization techniques like Stochastic Gradient Descent to find the coeffcients in the model Y = (1*x0) + (c1*x1) + … + (cN*xN)
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17 Stochastic Gradient Descent Hypothesis about data Cost function Update function Andrew Ng’s Tutorial: https://class.coursera.org/ml/lecture/preview_view /11
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18 Stochastic Gradient Descent Training Data Training Simple gradient descent procedure Loss functions needs to be convex (with exceptions) Linear Regression SGD Loss Function: squared error of prediction Prediction: linear combination of coefficients and input variables Model
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19 Mahout’s SGD Currently Single Process Multi-threaded parallel, but not cluster parallel Runs locally, not deployed to the cluster Tied to logistic regression implementation
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20 Current Limitations Sequential algorithms on a single node only goes so far The “Data Deluge” Presents algorithmic challenges when combined with large data sets need to design algorithms that are able to perform in a distributed fashion MapReduce only fits certain types of algorithms
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21 Distributed Learning Strategies McDonald, 2010 Distributed Training Strategies for the Structured Perceptron Langford, 2007 Vowpal Wabbit Jeff Dean’s Work on Parallel SGD DownPour SGD Sandblaster
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23 YARN Yet Another Resource Negotiator Node Manager Framework for scheduling Container App Mstr distributed applications Client Resource Node Manager Manager Allows for any type of parallel Client application to run natively on App Mstr Container hadoop MRv2 is now a distributed MapReduce Status Node Manager application Job Submission Node Status Resource Request Container Container
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24 IterativeReduce Designed specifically for parallel iterative algorithms on Hadoop Implemented directly on top of YARN Intrinsic Parallelism Easier to focus on problem Not focusing on the distributed application part
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26 SGD Master Collects all parameter vectors at each pass / superstep Produces new global parameter vector By averaging workers’ vectors Sends update to all workers Workers replace local parameter vector with new global parameter vector
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27 SGD Worker Each given a split of the total dataset Similar to a map task Performs local SGD pass Local parameter vector sent to master at superstep Stays active/resident between iterations
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28 SGD: Serial vs Parallel Split 1 Split 2 Split 3 Training Data Worker N Worker 1 Worker 2 … Partial Partial Model Partial Model Model Master Model Global Model
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Parallel Linear Regression with IterativeReduce Based directly on work we did with Knitting Boar Parallel logistic regression Scales linearly with input size Can produce a linear regression model off large amounts of data Packaged in a new suite of parallel iterative algorithms called Metronome 100% Java, ASF 2.0 Licensed, on github
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Unit Testing and IRUnit Simulates the IterativeReduce parallel framework Uses the same app.properties file that YARN applications do Examples https://github.com/jpatanooga/Metronome/blob/master/src/test/jav a/tv/floe/metronome/linearregression/iterativereduce/TestSimulat eLinearRegressionIterativeReduce.java https://github.com/jpatanooga/KnittingBoar/blob/master/src/test/j ava/com/cloudera/knittingboar/sgd/iterativereduce/TestKnittingB oar_IRUnitSim.java
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Running the Job via YARN Build with Maven Copy Jar to host with cluster access Copy dataset to HDFS Run job Yarn jar iterativereduce-0.1-SNAPSNOT.jar app.properties
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Results Linear Regression - Parallel vs Serial 200 Total Processing Time 150 100 Parallel Runs 50 Serial Runs 0 64 128 192 256 320 Megabytes Processed Total
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Lessons Learned Linear scale continues to be achieved with parameter averaging variations Tuning is critical Need to be good at selecting a learning rate YARN still experimental, has caveats Container allocation is still slow Metronome continues to be experimental
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Special Thanks Michael Katzenellenbollen Dr. James Scott University of Texas at Austin Dr. Jason Baldridge University of Texas at Austin
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Future Directions More testing, stability Cache vectors in memory for speed Metronome Take on properties of LibLinear Plugable optimization, general linear models YARN-centric first class Hadoop citizen Focus on being a complement to Mahout K-means, PageRank implementations
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References1. http://www.infoworld.com/d/business- intelligence/gartner-hadoop-will-be-in-two-thirds-of- advanced-analytics-products-2015-2114752. https://cwiki.apache.org/MAHOUT/logistic- regression.html3. MapReduce is Good Enough? If All You Have is a Hammer, Throw Away Everything That’s Not a Nail! • http://arxiv.org/pdf/1209.2191.pdf
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