1 什么是线性回归
线性回归是另一个传统的有监督机器学习算法。在这个问题中,每个实体与一个实数值的标签 (而不是一个像在二元分类的0,1标签),和我们想要预测标签尽可能给出数值代表实体特征。MLlib支持线性回归以及L2(ridge)和L1（lasso）正则化参数调整。Mllib还有一个回归算法,原始梯度下降(在下面描述),和上面描述的有相同的参数二元分类算法。
可用线性回归算法:
LinearRegressionWithSGD
RidgeRegressionWithSGD
LassoWithSGD。
注意：
(1)因为是线性回归，所以学习到的函数为线性函数，即直线函数；
(2)因为是单变量，因此只有一个x；
我们能够给出单变量线性回归的模型：
我们常称x为feature，h(x)为hypothesis；
2. Gradient Descent（梯度下降）
但是又一个问题引出了，虽然给定一个函数，我们能够根据cost function知道这个函数拟合的好不好，但是毕竟函数有这么多，总不可能一个一个试吧？
因此我们引出了梯度下降：能够找出cost function函数的最小值；
梯度下降原理：将函数比作一座山，我们站在某个山坡上，往四周看，从哪个方向向下走一小步，能够下降的最快；
当然解决问题的方法有很多，梯度下降只是其中一个，还有一种方法叫Normal Equation；
方法：
(1)先确定向下一步的步伐大小，我们称为Learning rate；
(2)任意给定一个初始值：；
(3)确定一个向下的方向，并向下走预先规定的步伐，并更新；
(4)当下降的高度小于某个定义的值，则停止下降；
算法：
特点：
(1)初始点不同，获得的最小值也不同，因此梯度下降求得的只是局部最小值；
(2)越接近最小值时，下降速度越慢；
3.线性回归代码
下面的示例演示如何加载训练数据,把它解析成 LabeledPoint的RDD对象（弹性分布式数据集）。这个例子然后使用LinearRegressionWithSGD构建一个简单的线性模型来预测标签值。最后我们计算均方误差对拟合优度进行评估。
执行结果如下：
root@master scala]# sbt/sbt package run
[info] Set current project to scala (in build file:/root/sample/scala/)
[success] Total time: 2 s, completed Feb 17, 2014 9:53:53 PM
[info] Running SimpleApp
log4j:WARN No appenders could be found for logger (akka.event.slf4j.Slf4jLogger).
log4j:WARN Please initialize the log4j system properly.
log4j:WARN See #noconfig for more info.
14/02/17 21:53:55 INFO SparkEnv: Using Spark's default log4j profile: org/apache/spark/log4j-defaults.properties
14/02/17 21:53:55 INFO SparkEnv: Registering BlockManagerMaster
14/02/17 21:53:55 INFO DiskBlockManager: Created local directory at /tmp/spark-local-20140217215355-b441
14/02/17 21:53:55 INFO MemoryStore: MemoryStore started with capacity 580.0 MB.
14/02/17 21:53:55 INFO ConnectionManager: Bound socket to port 45162 with id = ConnectionManagerId(master,45162)
14/02/17 21:53:55 INFO BlockManagerMaster: Trying to register BlockManager
14/02/17 21:53:55 INFO BlockManagerMasterActor$BlockManagerInfo: Registering block manager master:45162 with 580.0 MB RAM
14/02/17 21:53:55 INFO BlockManagerMaster: Registered BlockManager
14/02/17 21:53:55 INFO HttpServer: Starting HTTP Server
14/02/17 21:53:56 INFO HttpBroadcast: Broadcast server started at :54817
14/02/17 21:53:56 INFO SparkEnv: Registering MapOutputTracker
14/02/17 21:53:56 INFO HttpFileServer: HTTP File server directory is /tmp/spark-b1b6ca47-4f04-4a60-8cb5-4b7151c6e9a2
14/02/17 21:53:56 INFO HttpServer: Starting HTTP Server
14/02/17 21:53:56 INFO SparkUI: Started Spark Web UI at :4040
14/02/17 21:53:57 WARN NativeCodeLoader: Unable to load native-Hadoop library for your platform... using builtin-Java classes where applicable
14/02/17 21:53:57 INFO SparkContext: Added JAR target/scala-2.10/scala_2.10-0.1-SNAPSHOT.jar at :47898/jars/scala_2.10-0.1-SNAPSHOT.jar with timestamp 1392645237384
14/02/17 21:53:57 INFO AppClient$ClientActor: Connecting to master spark://192.168.159.129:7077...
14/02/17 21:53:58 WARN SizeEstimator: Failed to check whether UseCompressedOops is set; assuming yes
14/02/17 21:53:58 INFO MemoryStore: ensureFreeSpace(132636) called with curMem=0, maxMem=608187187
14/02/17 21:53:58 INFO MemoryStore: Block broadcast_0 stored as values to memory (estimated size 129.5 KB, free 579.9 MB)
14/02/17 21:53:59 INFO SparkDeploySchedulerBackend: Connected to Spark cluster with app ID app-20140217215359-0003
14/02/17 21:53:59 INFO AppClient$ClientActor: Executor added: app-20140217215359-0003/0 on worker-20140217214342-master-54909 (master:54909) with 1 cores
14/02/17 21:53:59 INFO SparkDeploySchedulerBackend: Granted executor ID app-20140217215359-0003/0 on hostPort master:54909 with 1 cores, 512.0 MB RAM
14/02/17 21:53:59 INFO AppClient$ClientActor: Executor added: app-20140217215359-0003/1 on worker-20140217214339-slaver02-52414 (slaver02:52414) with 1 cores
14/02/17 21:53:59 INFO SparkDeploySchedulerBackend: Granted executor ID app-20140217215359-0003/1 on hostPort slaver02:52414 with 1 cores, 512.0 MB RAM
14/02/17 21:53:59 INFO AppClient$ClientActor: Executor added: app-20140217215359-0003/2 on worker-20140217214341-slaver01-34119 (slaver01:34119) with 1 cores
14/02/17 21:53:59 INFO SparkDeploySchedulerBackend: Granted executor ID app-20140217215359-0003/2 on hostPort slaver01:34119 with 1 cores, 512.0 MB RAM
14/02/17 21:53:59 INFO AppClient$ClientActor: Executor updated: app-20140217215359-0003/1 is now RUNNING
14/02/17 21:53:59 INFO AppClient$ClientActor: Executor updated: app-20140217215359-0003/2 is now RUNNING
14/02/17 21:53:59 INFO AppClient$ClientActor: Executor updated: app-20140217215359-0003/0 is now RUNNING
14/02/17 21:54:02 INFO SparkDeploySchedulerBackend: Registered executor: Actor[akka.tcp://sparkExecutor@slaver02:42172/user/Executor#1991133218] with ID 1
14/02/17 21:54:03 INFO FileInputFormat: Total input paths to process : 1
14/02/17 21:54:03 INFO SparkContext: Starting job: first at GeneralizedLinearAlgorithm.scala:121
14/02/17 21:54:03 INFO DAGScheduler: Got job 0 (first at GeneralizedLinearAlgorithm.scala:121) with 1 output partitions (allowLocal=true)
14/02/17 21:54:03 INFO DAGScheduler: Final stage: Stage 0 (first at GeneralizedLinearAlgorithm.scala:121)
14/02/17 21:54:03 INFO DAGScheduler: Parents of final stage: List()
14/02/17 21:54:03 INFO DAGScheduler: Missing parents: List()
14/02/17 21:54:03 INFO DAGScheduler: Computing the requested partition locally
14/02/17 21:54:03 INFO HadoopRDD: Input split: hdfs://master:9000/mllib/lpsa.data:0+5197
14/02/17 21:54:03 INFO BlockManagerMasterActor$BlockManagerInfo: Registering block manager slaver02:33696 with 297.0 MB RAM
14/02/17 21:54:04 INFO SparkContext: Job finished: first at GeneralizedLinearAlgorithm.scala:121, took 0.703681387 s
14/02/17 21:54:04 INFO SparkContext: Starting job: count at GradientDescent.scala:137
14/02/17 21:54:04 INFO DAGScheduler: Got job 1 (count at GradientDescent.scala:137) with 2 output partitions (allowLocal=false)
14/02/17 21:54:04 INFO DAGScheduler: Final stage: Stage 1 (count at GradientDescent.scala:137)
14/02/17 21:54:04 INFO DAGScheduler: Parents of final stage: List()
14/02/17 21:54:04 INFO DAGScheduler: Missing parents: List()
14/02/17 21:54:04 INFO DAGScheduler: Submitting Stage 1 (MappedRDD[3] at map at GeneralizedLinearAlgorithm.scala:139), which has no missing parents
14/02/17 21:54:04 INFO DAGScheduler: Submitting 2 missing tasks from Stage 1 (MappedRDD[3] at map at GeneralizedLinearAlgorithm.scala:139)
14/02/17 21:54:04 INFO TaskSchedulerImpl: Adding task set 1.0 with 2 tasks
14/02/17 21:54:04 INFO TaskSetManager: Starting task 1.0:0 as TID 0 on executor 1: slaver02 (NODE_LOCAL)
14/02/17 21:54:04 INFO TaskSetManager: Serialized task 1.0:0 as 1749 bytes in 24 ms
14/02/17 21:54:32 INFO DAGScheduler: Got job 14 (reduce at GradientDescent.scala:150) with 2 output partitions (allowLocal=false)
14/02/17 21:54:32 INFO DAGScheduler: Final stage: Stage 14 (reduce at GradientDescent.scala:150)
14/02/17 21:54:32 INFO DAGScheduler: Parents of final stage: List()
14/02/17 21:54:33 INFO DAGScheduler: Missing parents: List()
14/02/17 21:54:33 INFO DAGScheduler: Submitting Stage 14 (MappedRDD[29] at map at GradientDescent.scala:145), which has no missing parents
14/02/17 21:54:33 INFO DAGScheduler: Submitting 2 missing tasks from Stage 14 (MappedRDD[29] at map at GradientDescent.scala:145)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Adding task set 14.0 with 2 tasks
14/02/17 21:54:33 INFO TaskSetManager: Starting task 14.0:0 as TID 26 on executor 2: slaver01 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 14.0:0 as 2419 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Starting task 14.0:1 as TID 27 on executor 1: slaver02 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 14.0:1 as 2419 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 26 in 35 ms on slaver01 (progress: 0/2)
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(14, 0)
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 27 in 85 ms on slaver02 (progress: 1/2)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Remove TaskSet 14.0 from pool
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(14, 1)
14/02/17 21:54:33 INFO DAGScheduler: Stage 14 (reduce at GradientDescent.scala:150) finished in 0.082 s
14/02/17 21:54:33 INFO SparkContext: Job finished: reduce at GradientDescent.scala:150, took 0.098827167 s
14/02/17 21:54:33 INFO SparkContext: Starting job: reduce at GradientDescent.scala:150
14/02/17 21:54:33 INFO DAGScheduler: Got job 15 (reduce at GradientDescent.scala:150) with 2 output partitions (allowLocal=false)
14/02/17 21:54:33 INFO DAGScheduler: Final stage: Stage 15 (reduce at GradientDescent.scala:150)
14/02/17 21:54:33 INFO DAGScheduler: Parents of final stage: List()
14/02/17 21:54:33 INFO DAGScheduler: Missing parents: List()
14/02/17 21:54:33 INFO DAGScheduler: Submitting Stage 15 (MappedRDD[31] at map at GradientDescent.scala:145), which has no missing parents
14/02/17 21:54:33 INFO DAGScheduler: Submitting 2 missing tasks from Stage 15 (MappedRDD[31] at map at GradientDescent.scala:145)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Adding task set 15.0 with 2 tasks
14/02/17 21:54:33 INFO TaskSetManager: Starting task 15.0:0 as TID 28 on executor 2: slaver01 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 15.0:0 as 2421 bytes in 1 ms
14/02/17 21:54:33 INFO TaskSetManager: Starting task 15.0:1 as TID 29 on executor 1: slaver02 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 15.0:1 as 2421 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 28 in 68 ms on slaver01 (progress: 0/2)
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(15, 0)
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 29 in 80 ms on slaver02 (progress: 1/2)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Remove TaskSet 15.0 from pool
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(15, 1)
14/02/17 21:54:33 INFO DAGScheduler: Stage 15 (reduce at GradientDescent.scala:150) finished in 0.082 s
14/02/17 21:54:33 INFO SparkContext: Job finished: reduce at GradientDescent.scala:150, took 0.317842176 s
14/02/17 21:54:33 INFO SparkContext: Starting job: reduce at GradientDescent.scala:150
14/02/17 21:54:33 INFO DAGScheduler: Got job 16 (reduce at GradientDescent.scala:150) with 2 output partitions (allowLocal=false)
14/02/17 21:54:33 INFO DAGScheduler: Final stage: Stage 16 (reduce at GradientDescent.scala:150)
14/02/17 21:54:33 INFO DAGScheduler: Parents of final stage: List()
14/02/17 21:54:33 INFO DAGScheduler: Missing parents: List()
14/02/17 21:54:33 INFO DAGScheduler: Submitting Stage 16 (MappedRDD[33] at map at GradientDescent.scala:145), which has no missing parents
14/02/17 21:54:33 INFO DAGScheduler: Submitting 2 missing tasks from Stage 16 (MappedRDD[33] at map at GradientDescent.scala:145)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Adding task set 16.0 with 2 tasks
14/02/17 21:54:33 INFO TaskSetManager: Starting task 16.0:0 as TID 30 on executor 2: slaver01 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 16.0:0 as 2420 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Starting task 16.0:1 as TID 31 on executor 1: slaver02 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 16.0:1 as 2420 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 31 in 52 ms on slaver02 (progress: 0/2)
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(16, 1)
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 30 in 60 ms on slaver01 (progress: 1/2)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Remove TaskSet 16.0 from pool
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(16, 0)
14/02/17 21:54:33 INFO DAGScheduler: Stage 16 (reduce at GradientDescent.scala:150) finished in 0.050 s
14/02/17 21:54:33 INFO SparkContext: Job finished: reduce at GradientDescent.scala:150, took 0.071822529 s
14/02/17 21:54:33 INFO SparkContext: Starting job: reduce at GradientDescent.scala:150
14/02/17 21:54:33 INFO DAGScheduler: Got job 17 (reduce at GradientDescent.scala:150) with 2 output partitions (allowLocal=false)
14/02/17 21:54:33 INFO DAGScheduler: Final stage: Stage 17 (reduce at GradientDescent.scala:150)
14/02/17 21:54:33 INFO DAGScheduler: Parents of final stage: List()
14/02/17 21:54:33 INFO DAGScheduler: Missing parents: List()
14/02/17 21:54:33 INFO DAGScheduler: Submitting Stage 17 (MappedRDD[35] at map at GradientDescent.scala:145), which has no missing parents
14/02/17 21:54:33 INFO DAGScheduler: Submitting 2 missing tasks from Stage 17 (MappedRDD[35] at map at GradientDescent.scala:145)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Adding task set 17.0 with 2 tasks
14/02/17 21:54:33 INFO TaskSetManager: Starting task 17.0:0 as TID 32 on executor 2: slaver01 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 17.0:0 as 2417 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Starting task 17.0:1 as TID 33 on executor 1: slaver02 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 17.0:1 as 2417 bytes in 1 ms
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 33 in 45 ms on slaver02 (progress: 0/2)
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(17, 1)
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 32 in 58 ms on slaver01 (progress: 1/2)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Remove TaskSet 17.0 from pool
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(17, 0)
14/02/17 21:54:33 INFO DAGScheduler: Stage 17 (reduce at GradientDescent.scala:150) finished in 0.055 s
14/02/17 21:54:33 INFO SparkContext: Job finished: reduce at GradientDescent.scala:150, took 0.067749084 s
14/02/17 21:54:33 INFO SparkContext: Starting job: reduce at GradientDescent.scala:150
14/02/17 21:54:33 INFO DAGScheduler: Got job 18 (reduce at GradientDescent.scala:150) with 2 output partitions (allowLocal=false)
14/02/17 21:54:33 INFO DAGScheduler: Final stage: Stage 18 (reduce at GradientDescent.scala:150)
14/02/17 21:54:33 INFO DAGScheduler: Parents of final stage: List()
14/02/17 21:54:33 INFO DAGScheduler: Missing parents: List()
14/02/17 21:54:33 INFO DAGScheduler: Submitting Stage 18 (MappedRDD[37] at map at GradientDescent.scala:145), which has no missing parents
14/02/17 21:54:33 INFO DAGScheduler: Submitting 2 missing tasks from Stage 18 (MappedRDD[37] at map at GradientDescent.scala:145)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Adding task set 18.0 with 2 tasks
14/02/17 21:54:33 INFO TaskSetManager: Starting task 18.0:0 as TID 34 on executor 2: slaver01 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 18.0:0 as 2419 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Starting task 18.0:1 as TID 35 on executor 1: slaver02 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 18.0:1 as 2419 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 35 in 40 ms on slaver02 (progress: 0/2)
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(18, 1)
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 34 in 97 ms on slaver01 (progress: 1/2)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Remove TaskSet 18.0 from pool
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(18, 0)
14/02/17 21:54:33 INFO DAGScheduler: Stage 18 (reduce at GradientDescent.scala:150) finished in 0.092 s
14/02/17 21:54:33 INFO SparkContext: Job finished: reduce at GradientDescent.scala:150, took 0.105965063 s
14/02/17 21:54:33 INFO SparkContext: Starting job: reduce at GradientDescent.scala:150
14/02/17 21:54:33 INFO DAGScheduler: Got job 19 (reduce at GradientDescent.scala:150) with 2 output partitions (allowLocal=false)
14/02/17 21:54:33 INFO DAGScheduler: Final stage: Stage 19 (reduce at GradientDescent.scala:150)
14/02/17 21:54:33 INFO DAGScheduler: Parents of final stage: List()
14/02/17 21:54:33 INFO DAGScheduler: Missing parents: List()
14/02/17 21:54:33 INFO DAGScheduler: Submitting Stage 19 (MappedRDD[39] at map at GradientDescent.scala:145), which has no missing parents
14/02/17 21:54:33 INFO DAGScheduler: Submitting 2 missing tasks from Stage 19 (MappedRDD[39] at map at GradientDescent.scala:145)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Adding task set 19.0 with 2 tasks
14/02/17 21:54:33 INFO TaskSetManager: Starting task 19.0:0 as TID 36 on executor 2: slaver01 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 19.0:0 as 2418 bytes in 1 ms
14/02/17 21:54:33 INFO TaskSetManager: Starting task 19.0:1 as TID 37 on executor 1: slaver02 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 19.0:1 as 2418 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 36 in 39 ms on slaver01 (progress: 0/2)
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(19, 0)
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 37 in 52 ms on slaver02 (progress: 1/2)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Remove TaskSet 19.0 from pool
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(19, 1)
14/02/17 21:54:33 INFO DAGScheduler: Stage 19 (reduce at GradientDescent.scala:150) finished in 0.042 s
14/02/17 21:54:33 INFO SparkContext: Job finished: reduce at GradientDescent.scala:150, took 0.060941515 s
14/02/17 21:54:33 INFO SparkContext: Starting job: reduce at GradientDescent.scala:150
14/02/17 21:54:33 INFO DAGScheduler: Got job 20 (reduce at GradientDescent.scala:150) with 2 output partitions (allowLocal=false)
14/02/17 21:54:33 INFO DAGScheduler: Final stage: Stage 20 (reduce at GradientDescent.scala:150)
14/02/17 21:54:33 INFO DAGScheduler: Parents of final stage: List()
14/02/17 21:54:33 INFO DAGScheduler: Missing parents: List()
14/02/17 21:54:33 INFO DAGScheduler: Submitting Stage 20 (MappedRDD[41] at map at GradientDescent.scala:145), which has no missing parents
14/02/17 21:54:33 INFO DAGScheduler: Submitting 2 missing tasks from Stage 20 (MappedRDD[41] at map at GradientDescent.scala:145)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Adding task set 20.0 with 2 tasks
14/02/17 21:54:33 INFO TaskSetManager: Starting task 20.0:0 as TID 38 on executor 2: slaver01 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 20.0:0 as 2418 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Starting task 20.0:1 as TID 39 on executor 1: slaver02 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 20.0:1 as 2418 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 38 in 33 ms on slaver01 (progress: 0/2)
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(20, 0)
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 39 in 71 ms on slaver02 (progress: 1/2)
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(20, 1)
14/02/17 21:54:33 INFO DAGScheduler: Stage 20 (reduce at GradientDescent.scala:150) finished in 0.064 s
14/02/17 21:54:33 INFO SparkContext: Job finished: reduce at GradientDescent.scala:150, took 0.080835519 s
14/02/17 21:54:33 INFO TaskSchedulerImpl: Remove TaskSet 20.0 from pool
14/02/17 21:54:33 INFO SparkContext: Starting job: reduce at GradientDescent.scala:150
14/02/17 21:54:33 INFO DAGScheduler: Got job 21 (reduce at GradientDescent.scala:150) with 2 output partitions (allowLocal=false)
14/02/17 21:54:33 INFO DAGScheduler: Final stage: Stage 21 (reduce at GradientDescent.scala:150)
14/02/17 21:54:33 INFO DAGScheduler: Parents of final stage: List()
14/02/17 21:54:33 INFO DAGScheduler: Missing parents: List()
14/02/17 21:54:33 INFO DAGScheduler: Submitting Stage 21 (MappedRDD[43] at map at GradientDescent.scala:145), which has no missing parents
14/02/17 21:54:33 INFO DAGScheduler: Submitting 2 missing tasks from Stage 21 (MappedRDD[43] at map at GradientDescent.scala:145)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Adding task set 21.0 with 2 tasks
14/02/17 21:54:33 INFO TaskSetManager: Starting task 21.0:0 as TID 40 on executor 2: slaver01 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 21.0:0 as 2422 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Starting task 21.0:1 as TID 41 on executor 1: slaver02 (NODE_LOCAL)
14/02/17 21:54:33 INFO TaskSetManager: Serialized task 21.0:1 as 2422 bytes in 0 ms
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 40 in 40 ms on slaver01 (progress: 0/2)
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(21, 0)
14/02/17 21:54:33 INFO TaskSetManager: Finished TID 41 in 45 ms on slaver02 (progress: 1/2)
14/02/17 21:54:33 INFO TaskSchedulerImpl: Remove TaskSet 21.0 from pool
14/02/17 21:54:33 INFO DAGScheduler: Completed ResultTask(21, 1)
14/02/17 21:54:33 INFO DAGScheduler: Stage 21 (reduce at GradientDescent.scala:150) finished in 0.041 s
14/02/17 21:54:33 INFO SparkContext: Job finished: reduce at GradientDescent.scala:150, took 0.051875321 s