Introduction to Data Science - University of Illinois at ... › ... › public › ...Data_Science_Slides.pdf · Interdisciplinary Product Innovation Center Development BMW USA 2

Innovation Center Interdisciplinary Product Development BMW USA 1

Interdisciplinary Product Development CS 491, DES 430, IE 444, ME 444, MKTG 477 UIC Innovation Center Fall 2017 and Spring 2018 Instructors: Charles Frisbie, Marco Susani, Michael Scott

and Ugo Buy Author: Ugo Buy

Introduction to Data Science


•  Discipline seeking to extract knowledge and insights from large amounts of raw data

−  Examples: Predict income level from age; predict gender of Twitter user from colors chosen in tweets, etc.

•  Multidisciplinary in nature, mostly borrowing from:

−  Statistics

−  Computer Science (databases, machine learning, data mining, parallel computing)

−  Data Visualization

What is data science?

•  AKA “Data Analytics”

•  Wide array of applications

−  Medical sciences (healthcare)

−  Finance (market predictions)

−  Logistics, etc.


•  Multidisciplinary convergence:

! Math and statistics

! Domain knowledge

! Computer science

•  Detailed descriptions make it explicit the role of HCI and UX in data science

! HCI = Human Computer Interaction

! UX = User Experience

Drew Conway’s Venn diagram


Overarching pedagogical goal:

•  Learn how to extract knowledge from mobility and transportation datasets

!  Public datasets: UIC library, Bureau of Transportation Statistics, Chicago Data Portal, etc.

!  BMW datasets (hopefully)

Our learning objectives

Specific learning objectives:

•  Learn the basics of statistical learning

!  Input variables (aka features or predictors) vs. responses (aka outcomes or output variables)

!  Distinguish different prediction methods: regression and classification

!  Regression = predicted variable is continuous (e.g., predict vehicle value based on family income, etc.)

!  Classification = predicted variable is discrete (e.g., fraudulent vs. legit transaction, male vs.female user )

•  Learn how to visualize analysis results (Professor Susani)

!  Box plots, Scatter plots, Histograms, etc.)


Statistical learning: An Introduction to Statistical Learning

•  PDF available from http://www-bcf.usc.edu/~gareth/ISL/

Resources

Computer Science: Various languages with built-in support for statistical analysis, e.g.,

•  R – https://www.r-project.org/

•  Hadoop – http://hadoop.apache.org/


1.  SimplyAnalytics database(UIC Library)

!  EASI " Census Data " Employment

!  EASI " Census Data " Vehicles

2.  Chicago Data Portal (public)

!  https://data.cityofchicago.org/

!  Transportation data

!  Similar sites for NYC, LA, SFO, etc.

!  Counties sometimes have similar sites

3.  National transit database (public)

!  https://www.transit.dot.gov/ntd

!  Asset Inventory Module (aka vehicles)

Public and UIC datasets

4.  Reference USA database (public)

!  http://resource.referenceusa.com/

!  Use advanced search

!  Location and number of gas stations, car rental companies, etc.

5.  Bureau of transportation statistics (BTS)

!  https://data.cityofchicago.org/

!  Intermodal transportation database

!  Data on commercial aviation

!  Data on transportation economics


•  We extract information by means of statistical analysis

•  Paradigm

1.  Formulate a hypothesis (i.e. ask a question)

!  Examples: Is there a correlation between urban traffic density and air pollution?

2.  Apply statistical learning methods to dataset

!  Compute correlation indices between input and output variable, e.g., using regression analysis

3.  Analyze statistical data to validate or refute initial hypothesis

!  Null hypothesis: No significant correlation between input and output variables (variables are independent of each other)

!  Alternative hypothesis: Variables are in fact correlated (e.g., when input is high, output is likely to be low)

What we do with datasets of interest


•  Ultimate goal of correlation analysis: Establish causal relationships between different variables

!  If two variables are correlated, there could be a causal relationship between the variables…

!  ... or not

•  Analysis of beach communities shows high correlation between ice cream sales and shark attacks

!  But nobody is suggesting cutting ice cream sales as a way of preventing shark attacks

!  Ice cream sales and shark attacks are correlated but not causally related

Correlation ≠ Causality

?

Source:h*ps://m.xkcd.com/552/


•  Average (aka mean value): Given a set of n values, their average μ is the sum of the values divided by the number n of values that were added together

!  Assume dataset = (15, 18, 6, 20, 24), then average μ = 16 = (12+18+6+20+24)/5

•  Median: Given a set of n values, median M is the “value in the middle”

!  Dataset above " M = 18

!  Often more useful than average, because average sometimes affected by outliers

Basic statistics definitions

•  Variance: Average of the squared differences of the values from the mean, denoted by σ2

!  Indication of “how spread out” values are around the average

!  Sets (5, 10, 10, 15) and (9, 10, 10, 11) have the same μ=10, but their variances are different (12.5 vs. 0.5)

•  Standard deviation: The square root of the variance, denoted by σ

!  How much you should expect random value to differ from mean

!  σ = 3.535 and σ = 0.707 for two sets above


Plotting wage data (response variable) with respect to age (input variable) or year (input variable) Blue lines represent averages for each age and year value – Help make sense of data!

Source: ISLR, page 2

How do statistics help us?


Given an input variable X, estimate response variable Y as a function of X + some error ε See how f may help understand relation between input and output variables Population = 30 people with different incomes and education


The key goal: Express output as a function of input + some error


•  Given a response variable Y, and a set of input variables Xi

!  Which input variables will affect the response?

!  What is the relationship between the response and each input variable?

!  Can the relationship be modeled as a linear function or is it more complex?

•  We will consider linear relationships first

•  Example: different advertising markets


The inference problem


Simple linear regression

•  Statistical model assuming that a single input variable is linearly related to response variable

•  Basic assumption: The relation between input and output is arranged as a line

!  Actual relation drawn as a line

!  Could be true or false, but a good starting point for analyzing CAT datasets

!  Linear prediction from n observations

!  Goal: Try to get predicted values as close as possible to actual values


Drawing the line

•  What is the line that best fits our observations?

!  Must come up with predicted slope and intercept values β0 and β1

•  Least squares method: Minimize the square of the errors between observed and predicted values

!  Residual (error of one observation is difference between observed and predicted value):

!  Minimize RSS = Residual Sum of Squares when choosing β0 and β1

!  Good news: You’ll never have to do calculation of β0 and β1 yourself


The numbers for TV ad problem

•  Advertising dataset (From http://www-bcf.usc.edu/~gareth/ISL/data.html)

•  Predicted slope β1 = 0.0475

!  Sales to increase by 47.5 units of product for every $1,000 spent in TV advertising

•  Predicted intercept β0 = 7.03

!  Sales without TV advertising predicted to be 7,030 units


How good of a prediction?

•  Must validate linear model assumption, but how?

1. Residual Standard Error (RSE): Ratio of RSS and number of observations n:

•  RSE is absolute value of lack of fit of linear prediction (= 3.26 for TV ad data; prediction off by 3,260 units on average)

2. R2 statistic: Normalized version of RSE (values between 0 and 1): Proportion of variability of Y that is explained by X

where

Values close to 1 indicate high correlation; close to 0 indicate low correlation


Analyzing public datasets

•  Decide whether certain features may affect each other (e.g., urban pollution vs. population density)

•  Select features of interest (X and Y)

•  Regress one feature over the other, using R or other analysis system

•  Do regression analysis (e.g., using R or other statistical analysis package)

•  Check the null hypothesis (X and Y are not correlated)

!  If null hypothesis is true, slope β1 will be zero or close to zero

!  How close to zero?

!  t-statistic: Normalized value of slope β1 relative to zero

!  p-value: Probability that given t-value be consistent with null hypothesis; reject null hypothesis for p-value less than 5%


The values for the TV ad dataset

•  Source: ISLR, Pages 68 and 69


The language R

•  Programming language for statistical computing and graphics

•  Named after initial letter of founders’ names, Ross Ihaka and Robert Gentleman

•  Relatively easy syntax

•  Lots of built-in analysis methods (both for regression and classification)

•  Basic language has command line interface; various GUI-based systems exist (e.g., Rattle, R Studio, etc.)

!  GUI tools usually include command-line window

•  Target platform: standalone computer (vs. Hadoop)

•  Freely available on MS Windows, Linux, and Mac OS X platforms (GNU GPL terms)

!  Quite extensible " Packages

•  Software, documentation and reference materials available at https://cran.r-project.org/


R: Basic commands

•  Most commands execute built-in and user-defined functions

•  Syntax: function_name(arg1, arg2, …)

!  Example: sqrt is a 1-argument function returning the argument’s square root

!  sqrt(9) " 3

•  Values returned by functions can be saved with variables

!  x = sqrt(9)

!  Now x equals 3

•  Function c() concatenates args into a vector of values, e.g.,

!  c(10, 20, 30, 40) ! 10 20 30 40

•  Functions length(), mean(), median(), var(), sd() take a vector of values and return the obvious


R: Matrix commands

•  Matrix: A table of numbers (2-dimensional matrix)

!  R representation of CAT spreadsheets

•  Create matrix with function:

matrix(elements, row_number, column_number)

•  Typically assign matrix to a variable to “remember” it

•  Matrix element access by values or sets of values for row and column

!  Use name of matrix + row index and column index in square brackets, e.g.,

!  y[3,2] returns second element in the third row of y

!  Ranges possible for row and column index


R: Read data from spreadsheets

•  Function read.csv() loads spreadsheet into R

!  Input: Comma-Separated Values (csv) spreadsheet

!  Output: A 2-dimensional matrix

•  Function dim() returns dimensions

•  Function names() returns column names

•  Function cor() returns correlation index (= sqrt of R2)

•  Use dollar sign $ to denote column by symbolic name

!  Syntax: matrix_name$column_name

•  Alternatively,

!  Use attach() function (sets default matrix)

!  Use numeric indices


R: Graphic display tools

Function plot() opens window with scatter plot of 2 features

Function hist() shows histogram of 1 feature


R: Statistical learning tools

•  Function lm() computes linear model

!  Funny syntax uses tilde character

var = lm(response_var~input1+input2)

•  Function summary(var) returns summary data

•  Function abline(var) returns column names (use after plot())

!  Beware of switching response and predictors order between lm and plot()


R: Statistical outputs


R: Some of your friends… use wisely

•  Help: Type function name preceded by question mark to get function documentation (e.g., ?lm, ?read.csv, etc.)

•  Function write.csv() saves an object to a file – Syntax: write.csv(object.name,”file.name”)

•  Function subset() allows you to select rows and columns based on conditions on values stored, e.g.,

!  selected.data = subset(original.data, RunTime >= 10 | RunTime < 5, select=c(RunTime, …))

!  See http://www.statmethods.net/management/subset.html

•  Function merge() allows you to perform database JOIN operations on multiple spreadsheets

•  All the functions shown in the previous slides


References

•  ISLR: http://www-bcf.usc.edu/~gareth/ISL/

•  R Language System: https://www.r-project.org/

•  Hadoop Language System: http://hadoop.apache.org/

•  Advertising dataset: http://www-bcf.usc.edu/~gareth/ISL/data.html

•  Nice R GUI #1: https://rattle.togaware.com (Rattle – runs on Windows or Linux)

•  Nice R GUI #2: https://www.rstudio.com

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Introduction to Data Science - University of Illinois at ... › ... › public › ...Data_Science_Slides.pdf · Interdisciplinary Product Innovation Center Development BMW USA 2