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MET CS 777 - Big Data Analytics

创建日期：2024-08-03 15:30:04

所属分类：数学mathematics

标签： MET CS 777

Big Data Analytics

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MET CS 777 - Big Data Analytics

Gradient Descent

(20 points)

GitHub Classroom Invitation Link

1 Description

In this assignment you will implement Batch Gradient Descent to fit a line into a two dimensional

data set. You will implement a set of Spark jobs that will learn parameters for such line from the

New York City Taxi trip reports in the Year 2013. The dataset was released under the FOIL (The

Freedom of Information Law) and made public by Chris Whong. See the Assignment 1 for details about this data set.

We would like to train a linear model between travel distance in miles and fare amount (the

money that is paid to the taxis).

2 Taxi Data Set - Same data set as Assignment 1

This is the same data set as use for the Assignment 1. Please have a look on the table description

there.

The data set is in Comma Separated Volume Format (CSV). When you read a line and split it

by comma sign ”,” you will the an string array with length of 17. With index number started from

zero, we need for this assignment to get index 5 trip distance (trip distance in miles) and index 11

fare amount ( fare amount in dollars) as stated on the following table.

index 5 (this our X-axis) trip distance trip distance in miles

index 11 (this our Y-axis) fare amount fare amount in dollars

Table 1: Taxi Data Set fields

Data Clean-up Step

? Remove all taxi rides that are less than 2 min or more than 1 hours.

? Remove all taxi rides that have ”fare amount” less than 3 dollar or more than 200 dollar

? Remove all taxi rides that have ”trip distance” less than 1 mile or more than 50 miles

? Remove all taxi rides that have ”tolls amount” less than 3 dollar.

You can also preprocess the data and store it in your own cluster storage.

3 Obtaining the Dataset

Small data set. (93 MB compressed, uncompressed 384 MB) for implementation and testing purposes

(roughly 2 million taxi trips). This is available at Amazon S3:

https://s3.amazonaws.com/metcs777/taxi-data-sorted-small.csv.bz2

You can download or access the data sets using the following internal URLs:

Google Cloud

Small Data Set gs://metcs777/taxi-data-sorted-small.csv.bz2

Large Data Set gs://metcs777/taxi-data-sorted-large.csv.bz2

Table 2: Data set on Google Cloud Storage - URLs

Amzon AWS

Small Data Set s3://metcs777/taxi-data-sorted-small.csv.bz2

Large Data Set s3://metcs777/taxi-data-sorted-large.csv.bz2

Table 3: Data set on Amazon AWS - URLs

4 Assignment Tasks

4.1 Task 1 : Simple Linear Regression (4 points)

We want to find a simple line to our data (distance, ”fare amount”) and use it to predict ”fare amount”

from the travel distance.

Consider a Simple Linear Regression model given in equation (1). What are the regression

coefficient for your model?

The solutions for m slope of the line and y-intercept is calculated based on the equations (2)

and (3).

(3)

Implement a PySpark Job that calculates the exact answers for the parameters m and b. The

slope of the line is the parameter m and b is the y-intercept of the line.

Run your implementation on the large data set and report the computation time for your Spark

Job for this task. You can find the time for the completion of your Job on the Cloud System. You

find there a place that reports the time for you.

Note on Task 1: Execution of this task on Large data set depending on your implementation

can take longer time, for example on a cluster with 12 cores in total, it takes more than 40 min

computation time.

4.2 Task 2 - Find the Parameters using Gradient Descent (8 Points)

In this task, you should implement the batch gradient descent to find the optimal parameters for our

Simple Linear Regression model.

? You should load the data into spark cluster memory as RDD or Dataframe

? Start with all parameters set to 0.1 and do 100 iterations.

Cost function will be then

Here is a list of important setup parameters:

? Initialize all of your model parameters with zeros

? Set your initial learning rate to be learningRate=0.0001 and change it if needed.

? You can implement the bold driver to improve your learning rate.

? Maximum number of iteration should be 100 iterations, num iteration=100

Run your implementation on the large data set and report the computation time for your Spark

Job for this task. Compare the computation time with the previous tasks.

? Print out the costs in each iteration

? Print out the model parameters in each iteration

Note: You might write some code for the iteration of gradient descent in PySpark that can work

perfect on your laptop but does not run on the clusters (AWS/Google Cloud). The main reason is

that on your laptop it is running in single process while on a cluster it runs on multiple processes

(shared-nothing processes). You need to be careful to reduce all of jobs/processes to be able to

update the variables, otherwise each processes will have its own variables.

4.3 Task 3 - Fit Multiple Linear Regression using Gradient Descent (8 Points)

We would like to learn a linear model with 4 variables to predict total paid amounts of Taxi rides.

The following table describes the variables that we want to use.

index 4 (1st independent variable) trip time in secs duration of the trip

index 5 (2nd independent variable) trip distance trip distance in miles

index 11 (3rd independent variable) fare amount fare amount in dollars

index 12 (4th independent variable) tolls amount bridge and tunnel tolls in dollars

index 16 (y-axis, dependent variable) total amount total paid amount in dollars

Table 4: Taxi Data Set fields

? Initialize all parameters with 0.1

? Set your learning rate to be learningRate=0.001

? Maximum number of iteration should be 100, num iteration=100

? Use Vectorizatoin for this task. We will not accept your solution when you write duplicated

code. It should include vectorization.

? Implement ”Bold Driver” technique to dynamically change the learning rate. (2 points

of 8 points)

? Print out the costs in each iteration

? Print out the model parameters in each iteration

5 Important Considerations

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关键词一关键词二关键词三关键词四关键词五和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 EMESTER1 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1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 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