README

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# README FILE
# Introduction to Machine Learning
# Assignment 3
#
# After completing the assignment, fill in this README file.  It asks you to duplicate
# your answer to several questions.  Be certain that your answers in this README file
# (which will be used for auto-grading) match the answers in your PDF writeup.
#
# This README file is formatted in YAML to allow it to be machine readable.  Please
# be very careful with how you edit it, being careful to following the formatting.
# Make certain not to change any text in all UPPERCASE.  After editing, you can make 
# certain that your README file follows proper YAML syntax by running it through an
# online YAML checker, such as http://yaml-online-parser.appspot.com/
# 
# The most frequent error is multi-line strings, such as "SOURCESCONSULTED" and 
# "FEEDBACK_ERRORS".  Make certain that the previous line ends with a | followed by a 
# newline.  Then, make certain that the subsequent lines are indented one level in 
# (4 spaces).  This sounds complex, but just follow the existing format of this file.
# If you run into any problems that you can't fix easily in listing your sources or 
# providing feedback on the assignment, just include your multi-line string answers to
# these parts as comments.  Everything else (all simple one-word or numeric answers) must
# be properly formatted YAML.
# 
# Assignment Version 20151012a
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# Personal information  (BE SURE TO CHANGE THIS!)
FIRSTNAME: Eric
LASTNAME:  Eaton
PENNKEY:   eeaton
PENNID:    123456

# Which course are you enrolled in?  (enter 419 or 519)
COURSE:  419 


# List all sources of help that you consulted while completing this assignment 
# (other students, colleagues, textbooks, websites, etc.).  This includes anyone you 
# briefly discussed the homework with.  If you received help from the following sources, 
# you do not need to cite it: course instructor, course teaching assistants, course 
# lecture notes, course textbooks or other readings.
# 
# If you didn't receive help from anyone, write "none".

SOURCESCONSULTED: |
    While completing the assignment, I consulted the following sources: 
    http://web.stanford.edu/~hastie/Papers/samme.pdf


 
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# Answers to Problem 1:  Probability decision boundary
#
# Please list your final answers below for auto-grading.
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# Problem 1b: what is the threshold for the loss matrix?  (only your final numeric answer)
PROB_PROBDECISIONBOUNDARY_THRESHOLD: 2



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# Answers to Problem 2:  Double counting the evidence
#
# Please list your final answers below for auto-grading.
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# Problem 2a: what is the expected error rate for only X1?  (only your final numeric answer)
PROB_DOUBLECOUNTINGEVIDENCE_ERRORX1: 0.25

# Problem 2a: what is the expected error rate for only X2?  (only your final numeric answer)
PROB_DOUBLECOUNTINGEVIDENCE_ERRORX2: 0.30

# Problem 2c: what is the expected error rate adding X3?  (only your final numeric answer)
PROB_DOUBLECOUNTINGEVIDENCE_ERRORWITHX3: 0.13

# Problem 2e: does logistic regression suffer from the same problem?  (answer either YES or NO)
PROB_DOUBLECOUNTINGEVIDENCE_LOGREGPROBLEM: NO



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# Answers to Problem 3:  Reject Option (CIS 519 ONLY)
# 
# (Students in 419 can leave this section unchanged)
#
# Please list your final answers below for auto-grading.
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# Problem 3a: which decision minimizes expected loss?  (enter only 0 or 1 or REJECT)
PROB_REJECTOPTION_P20: 9

# Problem 3b: which decision minimizes expected loss?  (enter only 0 or 1 or REJECT)
PROB_REJECTOPTION_P40: 9

# Problem 3d: what is the threshold for theta_0?  (only your final numeric answer)
PROB_REJECTOPTION_THETA0: 123.45

# Problem 3d: what is the threshold for theta_1?  (only your final numeric answer)
PROB_REJECTOPTION_THETA1: 123.45




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# Answers to Implementation Exercise 1.1:  BoostedDT on Unknown Data
#
# Please list your final answers below for auto-grading.
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# Copy and Paste the list of predicted labels below  (one very long line of text without spaces)
# Make sure it is all on one line
CHALLENGE_BOOSTEDDT_PREDICTIONS: 7,7,8,5,5,5,3,6,3,5,1,5,0,3,0,2,1,5,4,7,5,0,7,5,3,5,3,7,7,7,1,7,1,7,8,6,3,2,0,4,7,1,6,0,0,8,5,3,2,8,1,7,5,1,7,1,6,1,0,3,5,5,0,1,1,3,6,3,8,7,1,5,7,6,2,4,0,0,1,1,1,7,7,1,0,5,4,7,1,1,7,3,8,8,6,2,7,4,7,2,1,3,7,5,3,2,3,0,2,6,2,1,4,0,4,5,2,1,6,2,3,4,3,7,7,0,2,5,8,0,0,5,5,8,7,0,1,1,0,1,0,5,4,5,3,8,0,0,5,8,1,5,0,1,7,0,1,8,0,2,7,5,0,7,2,7,2,5,7,7,0,5,1,6,0,5,1,0,7,1,5,5,6,8,1,0,5,7,2,0,2,5,0,3,2,3,6,6,0,6,8,5,5,0,7,1,0,1,7,1,4,1,1,7,0,2,2,3,1,0,2,8,6,7,5,7,2,3,0,8,7,8,8,5,5,3,7,5,3,3,0,0,0,7,3,6,0,2,0,0,4,2,1,7,0,1,7,5,2,5,7,0,2,7,6,7,0,5,1,3,7,7,1,5,2,3,1,1,5,5,4,7,2,1,5,7,5,2,2,8,0,8,7,6,7,2,6,0,8,5,5,8,7,7,5,5,7,0,2,3,1,3,0,4,8,0,0,6,8,0,7,1,5,5,1,2,7,1,1,2,7,0,6,6,2,3,0,5,8,0,2,1,8,3,7,5,0,8,1,3,2,1,7,0,0,7,0,8,0,5,5,0,1,4,5,1,7,7,2,3,7,1,7,3,8,2,7,0,2,5,7,6,8,7,3,1,0,2,5,0,3,1,3,7,1,1,1,1,3,1,0,7,7,2,7,2,1,5,8,7,1,3,2,0,3,1,7,8,0,0,1,5,0,7,8,0,1,1,0,3,7,8,2,4,6,0,1,0,5,7,8,8,5,0,8,6,3,3,0,1,0,0,7,7,1,5,0,0,0,5,8,5,1,1,7,4,2,3,7,0,1,3,4,3,0,1,8,0,3,8,0,7,7,2,0,2,2,3,8,0,4,2,7,5,7,2,6,1,8,1,7,0,4,5,7,3,3,1,8,0,1,6,0,2,0,1,0,1,2,2,0,0,5,3,7,0,5,7,8,5,5,7,0,2,1,1,0,8,8,0,7,1,1,0,2,2,6,1,0,3,5,5,1,2,7,5,6,3,8,1,1,7,0,2,2,0,2,1,5,0,8,0,7,7,7,0,0,3,0,1,0,1,0,1,0,5,1,5,0,7,2,7,1,1,0,7,2,6,7,5,4,5,8,5,7,7,7,5,2,3,0,5,8,1,5,8,8,5,7,0,6,5,7,3,5,0,7,5,5,4,5,2,8,3,4,7,0,3,8,3,1,0,0,2,6,2,1,6,7,7,5,2,0,3,7,0,3,7,7,3,7,0,7,3,5,3,5,1,8,0,8,0,7,5,2,6,3,1,7,2,3,7,5,7,8,2,8,8,0,5,3,1,8,0,1,1,7,1,8,1,2,0,1,8,0,3,8,7,1,1,3,0,1,7,5,8,1,1,6,0,5,1,1,7,0,0,3,8,7,6,7,7,3,3,2,7,5,3,8,3,1,0,0,2,3,6,7,0,0,0,5,3,1,1,5,2,8,1,3,5,2,7,0,5,0,7,5,6,0,7,4,2,7,3,5,4,8,1,3,3,2,8,2,2,1,0,0,1,2,6,5,7,5,7,7,7,5,1,0,0,5,3,7,4,2,1,5,7,6,2,6,0,1,3,8,0,5,2,1,8,7,2,2,0,0,0,6,7,2,1,2,3,7,1,5,0,2,7,7,1,8,3,2,5,2,5,2,7,1,2,0,5,1,6,4,0,3,5,2,4,3,0,8,2,8,1,6,5,1,0,6,7,7,3,2,8,4,0,2,1,8,0,7,1,1,8,5,1,1,2,7,6,5,1,0,8,8,0,1,7,0,5,6,3,0,7,0,7,4,6,5,0,8,0,7,7,3,7,0,3,5,2,8,4,3,1,0,7,1,1,6,1,8,1,7,1,7,0,5,5,5,5,8,0,8,2,3,3,6,1,5,8,2,3,0,0,4,3,8,0,5,3,3,7,3,1,6,0,5,5,3,7,7,1,6,2,5,0,3,5,7,5,1,3,1,0,0,1,1,2,8,1,7,1,2,2,6,7,0,1,1,5,1,0,6,7,1,4,4,0,7,5,8,3,2,7,2,3,3,3,1,2,0,3,5,7,8,3,8,1,0,1,0,4,6,8,0,5,6,7,0,2,6,5,0,3,5,1,5,1,7,0,4,7,7,1,7,5,0,1,7,6,1,3,6,5,2,5,0,7,5,0,1,7,5,0,3,7,1,7,3,5,5,4,7,1,7,5,2,0,7,0,3,3,6,1,1,0,1,0,7,8,0,7,3,2,0,3,1,1,7,1,0,0,3,5,7,2,1,5,3,7,1,3,0,4,1,0,6,7,3,5,4,8,8,5,2,7,0,7,5,1,6,7,2,7,2,1,7,5,3,0,3,5,5,2,0,0,2,6,8,5,4,0,0,4,1,7,0,3,1,7,5,7,0,3,5,2,1,7,2,0,1,0,7,2,5,6,2,3,3,0,1,1,1,0,6,0,1,2,0,7,0,0,1,1,6,7,7,6,8,0,5,8,8,5,7,8,3,2,2,5,0,7,0,1,2,0,5,0,3,7,7,0,2,7,1,2,7,8,7,7,8,5,1,3,0,0,6,2,1,4,7,2,3,0,3,1,3,7,5,1,1,1,6,1,5,0,1,7,3,2,6,2,0,1,0,6,7,0,0,2,6,7,8,5,3,1,5,2,0,0,0,8,5,7,0,7,0,7,2,2,4,3,7,0,2,3,7,8,3,0,5,8,0,7,1,3,8,3,3,3,7,4,7,0,5,0,8,7,1,1,6,0,0,1,0,2,8,7,0,2,1,4,0,7,5,7,0,5,2,0,6,6,1,0,2,3,3,8,3,4,1,7,7,7,1,3,1,4,5,0,7,5,2,5,3,1,1,8,0,5,8,2,8,3,7,7,6,7,5,0,7,5,0,6,1,1,0,7,8,8,5,1,6,5,2,7,0,1,8,3,1,3,0,1,3,1,3,7,1,8,5,5,0,0,2,0,7,5,5,2,0,5,2,4,3,6,4,0,1,3,1,1,1,1,2,2,0,3,5,3,3,0,7,1,1,1,7,1,0,0,5,8,0,8,2,5,6,6,3,8,2,2,2,0,0,6,5,7,6,1,1,2,1,0,7,0,7,1,4,0,2,5,8,7,3,6,8,2,8,1,4,2,3,7,0,2,0,3,0,3,6,1,0,7,5,5,0,2,1,2,3,6,7,0,3,1,2,7,3,1,0,0,0,5,3,4,2,1,2,0,0,0,1,1,7,7,1,5,1,2,2,7,2,3,5,2,8,6,5,1,8,5,8,5,0,6,7,1,3,6,0,0,7,2,8,0,0,0,7,0,1,7,7,0,1,5,7,5,2,3,1,1,7,6,0,8,8,2,7,2,0,3,1,0,1,0,0,7,7,3,1,3,7,1,0,5,1,7,3,8,1,4,5,4,3,7,1,2,7,2,5,0,0,0,6,1,1,0,7,3,0,6,5,0,7,8,1,7,6,1,0,2,0,0,7,8,0,5,5,5,0,5,8,3,7,5,6,7,7,7,4,2,2,4,0,3,7,5,1,7,0,0,1,7,1,2,1,7,2,2,8,7,7,1,1,5,7,0,4,8,0,8,7,7,0,0,5,2,0,0,2,0,8,3,7,2,0,3,1,1,7,6,2,3,3,0,0,0,7,2,7,3,5,7,8,7,7,1,5,1,3,7,0,8,1,5,5,5,3,8,1,0,4,0,0,7,1,7,8,5,0,7,3,0,8,1,1,3,5,7,7,5,1,7,5,2,2,0,3,0,3,2,2,1,3,5,8,1,6,0,0,1,3,3,5,7,7,5,8,7,1,7,1,7,3,0,7,0,3,7,4,8,7,6,4,1,7,5,1,7,0,1,3,6,2,7,2,8,5,5,8,5,5,3,7,2,5,8,1,1,8,5,5,2,6,3,1,7,1,0,6,1,1,1,2,5,5,2,7,1,7,8,3,7,2,0,7,7,7,0,0,5,5,2,5,3,8,1,5,2,5,6,7,4,7,7,1,0,0,0,4,7,0,7,0,0,1,7,5,5,7,0,1,8,2,6,3,0,7,7,2,2,5,0,5,1,0,6,7,1,8,7,1,2,1,0,1,7,7,2,2,3,2,8,7,7,8,7,7,7,0,3,6,2,8,1,3,0,1,0,5,7,0,7,2,0,4,1,8,0,7,8,7,7,5,4,3,0,3,7,6,5,1,1,3,7,3,0,0,7,1,2,8,0,1,6,5,2,0,8,7,5,7,7,2,3,1,8,7,5,0,1,1,2,5,7,3,1,7,2,2,1,2,3,7,0,3,3,0,5,1,1,5,8,7,5,2,8,6,1,2,2,8,7,2,2,3,1,8,8,8,0,2,7,8,0,2,7,1,3,3,4,1,1,5,7,7,6,7,8,0,7,8,5,0,7,6,3,3,1,7,7,6,7,0,3,8,1,4,0,5,2,5,4,3,0,0,1,6,5,2,6,5,4,7,0,7,4,7,0,8,5,7,3,5,5,7,1,0,0,3,1,8,1,7,1,2,6,4,7,2,2,8,0,8,2,1,5,0,0,6,1,3,4,2,1,3,2,0,0,5,2,8,1,7,7,3,5,6,7,1,2,8,7,7,5,0,3,0,4,6,5,3,2,2,3,2,7,5,8,0,4,7,1,0,7,8,7,7,7,4,5,3,7,2,1,2,2,1,0,5,3,1,0,5,5,0,0,5,5,1,3,3,7,1,8,5,2,1,8,0,3,8,7,0,1,6,7,2,0,1,6,1,7,5,7,7,2,1,1,5,1,1,8,0,2,1,0,0,5,3,5,3,7,0,8,5,7,5,0,3,1,7,2,5,3,5,1,4,3,1,8,8,5,7,0,3,0,5,2,0,3,6,1,2,7,2,1,3,7,0,7,7,1,7,2,0,3,1,8,1,5,2,8,7,8,5,3,7,7,7,6,1,1,8,8,2,3,1,0,5,3,0,5,8,3,6,7,7,3,0,8,3,7,1,7,7,2,2,2,1,5,0,1,6,1,8,5,7,1,1,0,0,5,6,3,1,6,7,0,7,4,5,5,2,2,3,3,3,7,7,5,8,3,3,8,4,6,6,3,1,5,8,5,4,0,8,7,7,1,0,7,5,5,1,7,6,2,1,5,5,1,8,5,2,3,4,1,4,6,4,2,0,6,0,1,3,4,2,0,0,1,7,7,5,7,0,5,0,5,2,1,7,5,8,1,2,7,0,7,1,7,0,7,7,6,7,0,7,1,0,0,8,6,6,5,7,7,8,8,5,5,3,0,1,7,2,1,2,2,3,5,6,4,0,0,7,1,5,7,2,1,3,0,3,7,7,3,7,7,1,0,4,1,7,0,7,7,2,5,7,2,2,3,0,3,1,3,0,7,7,0,0,1,7,8,3,7,0,0,1,4,0,0,1,6,0,7,7,8,6,8,2,1,6,5,2,2,7,3,3,0,3,3,2,4,1,1,4,3,1,2,0,0,3,1,0,7,2,2,5,2,3,5,7,2,3,5,1,7,7,3,2,3,1,6,3,4,2,0,3,3,3,3,8,7,3,2,3,5,0,7,1,1,2,0,0,6,0,1,0,0,8,7,7,5,0,7,5,6,0,4,8,7,1,2,1,5,7,5,1,4,7,2,7,7,7,2,7,3,7,7,7,0,8,0,1,0,5,3,7,2,2,0,1,4,7,0,8,1,7,8,1,0,7,0,0,1,3,1,0,3,3,3,7,3,2,0,5,0,7,2,0,0,0,7,7,8,1,0,1,4,2,5,0,3,2,7,7,1,5,0,1,5,6,4,1,5,4,8,4,7,3,0,5,1,4,5,5,7,3,7,0,0,8,3,1,0,0,0,2,3,7,7,8,3,7,7,1,2,4,2,2,1,1,7,7,6,0,0,0,1,0,8,0,2,6,6,2,3,7,3,7,2,7,2,7,2,0,1,0,1,1,1,5,5,8,2,7,6,3,0,7,8,0,5,1,8,8,5,5,7,3,5,0,0,1,5,6,3,1,7,6,6,4,5,0,7,7,4,1,2,7,3,5,1,7,3,1,1,3,2,7,1,5,1,1,7,5,8,2,8,4,3,1,3,0,3,5,7,6,5,1,8,1,8,3,1,1,7,8,5,3,7,5,7,8,7,7,7,5,7,5,8,8,0,7,2,1,1,7,2,2,2,1,8,0,7,3,0,3,7,5,1,0,7,2,3,0,7,3,0,6,2,6,6,3,0,7,7,2,5,2,2,4,1,1,7,3,3,3,6,2,5,1,0,2,0,3,2,1,0,2,6,5,3,3,0,3,8,1,4,2,7,0,1,5,7,0,2,5,7,7,5,1,8,3,5,5,5,4,6,0,0,7,8,5,5,7,0,2,6,2,6,7,0,6,7,5,7,5,0,8,5,2,1,1,3,3,1,2,6,1,0,7,8,7,8,2,7,7,1,0,5,7,7,5,0,2,4,1,7,7,2,1,6,1,0,1,0,5,0,0,1,0,3,1,2,3,1,1,2,2,3,8,2,7,6,5,5,6,5,0,0,1,8,1,7,2,7,1,8,7,1,1,1,1,5,0,1,8,6,5,0,5,0,7,0,1,7,5,3,5,0,6,3,3,2,5,3,1,7,7,2,2,0,3,7,0,1,0,1,1,7,1,5,1,5,0,0,7,5,1,7,5,2,0,8,8,1,7,5,5,7,0,3,5,3,7,1,3,0,3,8,1,1,7,0,5,7,3,6,0,2,2,6,8,0,1,3,3,7,3,5,3,1,7,5,2,6,0,7,3,1,7,3,1,0,2,7,1,0,5,7,0,7,0,8,7,5,0,3,7,7,3,2,7,0,0,3,7,6,1,0,0,1,0,5,5,5,7,6,5,6,1,6,3,1,6,8,5,2,7,0,7,0,7,6,2,0,8,1,0,1,6,7,0,3,3,2,1,2,5,1,8,8,2,7,6,2,1,8,0,5,3,0,6,1,1,3,0,1,7,7,3,4,4,0,2,6,6,0,2,0,8,1,0,4,7,3,0,4,3,5,5,0,2,3,0,2,8,0,8,8,1,0,7,1,7,8,2,7,0,1,1,4,2,0,5,5,1,0,3,5,8,2,2,2,5,0,8,7,2,0,1,3,7,8,8,7,5,7,1,1,7,3,7,2,3,2,2,1,1,2,0,1,0,2,3,0,6,2,7,7,5,7,7,1,6,3,3,1,1,7,2,8,4,1,5,7,5,8,8,3,1,5,3,0,0,2,5,3,7,5,2,7,0,0,5,1,8,7,7,2,8,4,2,5,0,5,6,0,2,5,3,0,5,0,0,6,3,2,3,7,5,7,5,5,7,8,1,1,7,0,0,0,1,0,5,3,5,3,3,3,7,5,7,8,3,7,1,1,6,7,8,1,0,1,0,2,5,7,5,5,3,1,7,0,8,2,7,1,6,5,1,6,5,1,5,5,8,7,3,1,5,2,5,8,3,2,7,5,0,7,2,8,6,0,6,7,3,6,1,6,3,8,8,8,8,5,5,5,1,8,1,7,2,8,1,1,6,2,7,2,5,8,0,3,2,2,2,2,4,5,7,7,7,2,3,6,2,3,7,8,6,6,2,5,1,7,5,4,5,0,0,1,5,3,7,7,5,8,3,7,5,3,2,1,7,2,4,8,1,1,3,7,8,0,3,6,1,3,1,7,7,1,1,2,7,5,2,8,3,5,2,7,2,4,1,6,6,1,2,1,0,3,5,1,3,5,5,7,5,8,0,0,2,0,0,7,6,5,6,8,8,0,3,0,5,2,8,8,3,4,8,5,5,8,1,8,2,5,5,1,1,0,2,3,0,5,5,2,0,2,5,1,5,0,0,8,3,0,0,1,0,7,6,0,0,6,2,2,0,1,0,3,3,3,1,2,1,0,2,0,2,3,7,2,6,3,5,1,6,0,6,8,7,0,1,2,2,2,1,7,8,8,1,2,7,3,5,0,5,6,5,1,1,6,5,7,5,1,0,8,1,0,2,0,1,0,0,8,1,7,0,6,7,7,1,0,0,0,1,5,0,7,5,1,3,5,8,6,8,7,2,2,2,8,3,7,8,2,7,5,5,1,0,7,7,6,5,2,1,0,5,4,2,1,2,0,7,0,0,7,0,6,2,5,5,0,2,2,2,6,5,7,8,7,3,7,4,0,1,3,5,7,8,5,7,0,0,1,8,8,8,2,3,7,0,8,5,0,3,6,0,7,8,8,3,0,2,7,7,5,5,7,7,2,0,3,3,7,3,5,0,1,2,5,6,1,3,5,0,1,5,1,0,1,2,1,1,5,7,1,8,1,3,7,2,2,6,3,5,2,0,2,7,1,1,3,4,1,0,2,8,7,8,7,7,3,5,1,3,4,8,6,5,8,6,3,7,1,3,7,4,3,1,5,3,1,8,3,5,7,6,8,7,0,5,1,1,5,7,7,8,5,0,6,7,0,8,5,1,7,1,5,6,0,5,6,7,2,5,6,0,7,5,7,3,5,1,3,2,2,1,5,7,2,5,8,5,0,2,5,8,8,0,7,5,1,1,8,7,1,5,3,3,1,5,6,6,1,0,5,7,6,4,0,1,6,6,5,5,1,5,6,1,3,8,5,8,6,5,0,1,8,1,3,2,1,8,8,6,0,8,4,7,1,7,6,1,5,8,2,4,5,6,2,1,5,7,0,0,3,1,4,0,5,8,2,8,1,2,7,2,5,7,2,0,0,2,7,7,4,7,5,3,0,7,1,5,8,7,5,8,1,5,7,0,1,1,2,2,2,3,6,6,0,5,4,0,4,0,8,0,5,5,5,5,7,0,1,8,6,1,1,6,0,5,3,8,2,7,7,1,3,8,7,3,6,2,7,5,1,2,6,7,2,4,6,5,6,7,2,3,0,7,0,1,5,7,1,1,0,0,4,7,5,5,7,5,7,7,0,2,2,7,8,7,5,2,2,6,0,1,1,0,7,1,3,7,8,0,8,5,1,8,0,8,3,2,1,0,0,7,4,8,1,7,4,8,7,0,5,0,6,6,5,8,7,8,6,0,2,0,5,2,1,3,5,5,2,3,7,3,0,7,7,0,0,2,1,5,5,1,5,1,7,7,2,0,7,3,0,3,3,6,1,4,3,1,2,1,0,0,6,1,6,2,5,3,3,7,4,7,8,3,7,0,5,5,0,4,2,2,0,7,2,0,8,0,5,7,8,1,1,4,7,1,3,3,1,6,2,5,5,7,8,6,1,2,1,3,5,6,7,2,7,3,6,8,5,7,0,5,3,2,5,2,7,8,8,5,5,6,7,5,3,5,2,5,3,5,5,5,0,4,2,2,8,8,7,5,6,2,3,1,7,2,3,6,3,1,0,1,0,0,7,5,4,5,2,7,0,8,0,1,2,8,8,5,7,3,7,7,6,6,4,8,7,5,5,0,3,0,7,1,2,5,5,5,0,1,3,0,2,6,8,0,6,7,6,0,7,7,3,2,7,8,8,0,0,8,2,7,6,0,7,6,8,4,2,0,2,1,0,8,3,7,2,7,5,8,3,1,7,5,8,4,6,3,2,5,3,0,6,5,7,3,8,4,0,5,2,2,7,3,1,5,1,0,0,2,5,6,0,6,5,7,7,7,1,1,6,6,2,0,8,0,6,8,5,5,1,1,0,0,1,7,5,6,3,7,1,0,3,5,1,0,0,0,0,2,1,8,6,1,5,3,1,7,5,7,5,0,1,8,0,0,5,2,7,1,0,2,2,2,2,0,2,7,8,0,7,8,1,2,8,2,3,3,1,1,2,2,1,3,1,8,8,2,5,5,0,0,7,5,5,3,1,7,5,5,7,0,8,3,2,5,3,5,3,8,6,3,7,1,8,6,0,8,2,0,6,5,3,2,2,2,2,7,8,0,2,1,7,4,7,1,4,7,8,7,0,0,1,7,7,8,0,3,8,0,1,8,3,3,7,3,4,1,7,8,7,3,0,6,2,0,2,5,7,7,1,0,1,5,2,3,0,5,0,1,3,8,0,1,8,2,1,2,0,7,0,0,5,3,2,6,5,8,4,3,5,2,7,8,8,1,1,7,2,2,1,3,2,2,6,1,7,1,0,0,7,5,8,1,0,2,1,8,5,7,2,8,0,7,0,2,2,1,1,0,0,2,6,0,8,2,7,0,1,2,1,6,3,2,2,5,1,8,2,6,7,5,2,0,3,1,5,8,0,0,6,6,7,1,1,3,7,7,2,0,5,4,0,7,5,0,8,6,7,5,0,0,3,6,7,1,7,8,1,0,0,1,0,5,3,1,1,2,0,8,7,2,1,8,3,3,6,0,8,5,1,6,5,1,2,5,2,5,6,2,5,5,6,5,8,0,3,6,7,0,1,2,7,7,0,7,1,2,0,3,2,1,1,0,7,3,3,0,5,3,1,1,1,7,8,1,1,7,0,8,0,2,5,5,0,0,1,3,1,0,3,5,0,2,2,5,7,2,1,6,5,2,5,1,0,0,0,1,0,8,8,5,3,0,1,4,8,5,0,1,0,5,6,0,0,1,0,7,5,7,8,5,5,3,2,6,7,3,5,7,3,0,1,0,7,7,6,5,7,7,1,1,0,1,1,7,6,0,3,1,7,8,0,0,2,6,1,4,5,1,3,1,6,5,1,2,7,5,6,3,5,1,7,0,6,6,5,4,7,7,5,1,5,8,2,1,6,8,3,2,0,3,5,2,1,5,5,1,0,8,5,7,3,1,0,3,0,2,1,0,6,6,0,3,1,0,3,5,7,2,2,7,7,1,5,3,8,7,8,2,6,0,4,1,1,5,0,5,6,0,3,5,7,2,3,0,3,1,0,7,8,1,2,5,2,5,0,7,0,7,0,7,7,2,0,1,7,1,4,7,7,7,7,0,6,0,0,0,7,3,0,5,8,8,3,0,8,5,0,6,5,5,8,7,2,7,3,5,1,5,8,7,2,5,5,5,5,5,0,5,5,7,0,6,6,7,0,0,2,0,8,3,0,0,5,0,1,7,1,5,7,2,1,2,8,5,8,2,2,1,4,7,1,0,0,5,7,3,1,8,7,8,3,0,8,1,1,2,8,2,7,1,5,6,7,3,8,8,3,6,4,1,2,8,6,0,7,0,5,0,1,3,1,7,5,6,0,0,7,0,2,2,1,3,7,3,4,6,5,5,1,5,0,1,5,8,1,0,8,1,8,1,8,5,0,2,7,0,6,5,3,3,1,3,2,1,3,3,4,7,2,5,8,1,2,3,7,5,7,1,5,1,5,5,8,2,1,0,1,4,3,7,1,0,3,5,3,5,0,8,1,7,3,1,7,5,5,2,6,6,2,0,3,0,3,6,7,1,2,1,8,1,5,7,0,0,0,5,7,3,3,0,6,5,7,3,8,8,5,1,3,0,1,2,5,7,0,5,3,8,5,3,5,2,2,2,6,5,2,8,0,0,5,0,7,1,5,1,6,1,5,2,1,1,1,1,7,0,7,0,5,5,8,0,2,6,0,5,4,0,7,3,8,3,1,4,6,7,3,1,2,7,7,1,1,3,1,6,0,1,2,8,5,1,3,1,7,8,4,8,7,6,7,1,7,7,3,5,2,4,4,5,5,6,7,3,7,2,7,0,7,2,0,2,1,6,8,8,7,0,7,5,7,7,0,7,0,0,1,7,2,7,7,5,0,4,3,2,7,5,1,3,0,3,5,2,7,1,1,5,4,6,5,6,5,7,0,1,6,8,4,2,1,2,1,3,8,0,0,7,5,5,5,2,5,3,6,5,8,7,5,0,0,3,7,2,5,7,6,2,0,6,3,2,6,7,8,7,5,1,2,1,7,3,4,1,4,8,1,1,7,0,7,5,0,4,6,0,8,0,2,5,5,8,2,3,0,8,7,5,3,7,7,0,7,6,7,5,8,6,8,3,3,0,0,8,7,7,1,7,0,5,3,7,3,0,1,7,1,0,5,1,4,0,8,5,1,1,2,6,7,7,8,3,3,2,3,2,0,8,3,0,8,0,1,3,7,2,8,7,2,1,2,7,3,1,0,4,1,3,8,8,1,5,7,4,0,0,2,2,2,2,1,1,4,1,8,3,1,1,6,3,0,7,8,1,0,1,2,0,3,3,0,7,0,6,2,4,1,0,7,7,0,1,5,1,8,0,7,8,1,0,1,5,0,5,5,8,2,8,0,0,0,0,3,3,3,7,3,7,6,0,1,8,7,2,7,7,1,5,2,2,5,5,6,5,2,5,8,2,3,5,7,3,6,3,1,7,1,0,7,7,6,8,3,0,0,0,3,2,0,1,3,7,5,7,7,0,7,7,7,5,5,5,7,1,5,5,7,0,2,7,4,7,7,1,0,0,5,0,5,5,7,3,2,5,7,5,7,1,7,1,2,7,6,5,0,1,3,8,6,6,8,4,3,8,3,7,5,7,5,3,5,1,7,1,5,5,2,7,5,1,5,5,8,0,5,2,6,8,1,1,3,5,1,3,7,6,0,6,2,7,4,0,6,1,1,1,0,0,6,3,3,1,6,0,7,6,7,0,3,1,5,0,8,7,8,7,0,2,1,2,7,1,5,7,2,0,7,0,7,1,0,1,2,7,8,6,6,6,1,0,7,5,4,1,0,5,6,5,6,8,3,8,5,5,5,0,0,7,1,0,1,5,0,4,1,0,3,7,6,7,0,7,5,1,1,2,1,0,5,1,4,5,7,1,5,8,0,7,3,2,1,6,5,7,2,8,3,7,6,2,7,6,7,0,7,0,0,5,3,0,5,2,1,5,1,0,5,0,1,3,5,6,6,3,6,5,1,0,6,7,7,7,4,5,7,0,2,4,0,0,5,7,5,2,7,8,2,1,0,5,5,8,5,2,2,5,0,7,2,7,0,1,1,1,1,0,2,1,1,7,2,3,5,8,7,5,3,6,7,6,3,0,7,7,2,0,7,1,8,1,6,5,8,0,7,5,5,0,3,5,6,1,1,2,0,0,6,0,7,1,3,6,7,7,1,7,8,0,5,2,1,1,0,3,7,1,0,2,7,3,6,3,2,1,7,1,8,2,7,0,8,6,5,0,1,8,7,1,0,5,5,0,8,1,1,0,6,1,7,0,7,7,1,0,3,3,3,3,3,2,2,3,5,7,2,0,0,2,7,3,7,3,6,4,4,1,1,7,4,6,4,7,3,1,2,1,6,5,8,2,6,0,7,1,5,5,5,7,2,1,7,4,7

# What is your estimate of the boostedDT's accuracy?  (only your final answer)
CHALLENGE_BOOSTEDDT_ACCURACY_MEAN: 0.031




####################################################################################### 
# Answers to Implementation Exercise 1.2:  Best Classifier on Unknown Data
#
# Please list your final answers below for auto-grading.
#######################################################################################

# Copy and Paste the list of predicted labels below  (one very long line of text without spaces)
# Make sure it is all on one line
CHALLENGE_BESTCLASSIFIER_PREDICTIONS: 
5.  8.  9.  6.  6.  5.  4.  7.  9.  6.  2.  6.  1.  4.  7.  3.  2.  6.
  5.  8.  6.  2.  2.  5.  4.  6.  4.  5.  2.  5.  7.  8.  7.  8.  9.  7.
  4.  3.  1.  5.  8.  2.  7.  1.  9.  9.  6.  4.  3.  9.  2.  7.  6.  2.
  5.  7.  7.  7.  7.  4.  5.  5.  2.  2.  7.  7.  7.  4.  9.  8.  2.  6.
  5.  7.  3.  5.  1.  1.  2.  7.  2.  8.  8.  2.  1.  6.  5.  2.  7.  2.
  8.  4.  9.  9.  7.  3.  8.  5.  6.  3.  2.  4.  5.  6.  4.  3.  4.  1.
  9.  7.  3.  1.  5.  1.  5.  6.  3.  2.  7.  3.  4.  5.  4.  8.  7.  1.
  3.  5.  9.  7.  1.  6.  6.  9.  5.  2.  7.  2.  1.  2.  9.  9.  5.  4.
  4.  9.  7.  1.  5.  9.  8.  6.  2.  3.  8.  1.  2.  9.  1.  3.  8.  6.
  1.  5.  3.  5.  3.  6.  8.  5.  8.  9.  1.  7.  1.  6.  1.  9.  8.  1.
  4.  9.  7.  9.  1.  1.  6.  5.  3.  1.  3.  6.  1.  4.  3.  4.  7.  7.
  2.  7.  9.  6.  6.  1.  8.  2.  1.  2.  5.  1.  5.  2.  2.  5.  9.  3.
  9.  9.  1.  8.  3.  4.  7.  8.  9.  8.  3.  4.  1.  9.  5.  9.  9.  6.
  6.  4.  8.  6.  4.  4.  1.  1.  7.  5.  4.  7.  1.  3.  3.  7.  5.  3.
  7.  8.  5.  2.  5.  6.  3.  9.  8.  3.  3.  5.  7.  5.  2.  6.  2.  4.
  5.  8.  1.  4.  3.  4.  1.  2.  9.  5.  8.  9.  3.  7.  4.  8.  6.  3.
  3.  9.  1.  9.  8.  7.  5.  3.  7.  2.  8.  4.  9.  9.  8.  8.  6.  6.
  5.  1.  3.  4.  1.  4.  8.  5.  9.  1.  1.  7.  9.  1.  8.  1.  6.  6.
  2.  3.  5.  7.  2.  5.  8.  1.  7.  7.  3.  4.  1.  6.  9.  1.  3.  2.
  9.  4.  5.  6.  1.  9.  7.  4.  3.  2.  5.  7.  1.  8.  3.  9.  1.  6.
  5.  1.  2.  5.  6.  2.  5.  8.  3.  4.  2.  7.  8.  4.  9.  3.  1.  9.
  3.  4.  8.  7.  9.  9.  4.  2.  7.  9.  6.  5.  4.  2.  4.  5.  7.  7.
  2.  7.  4.  2.  1.  8.  5.  3.  5.  3.  2.  6.  9.  8.  7.  4.  3.  2.
  4.  2.  5.  9.  7.  7.  2.  9.  1.  8.  9.  1.  2.  2.  1.  6.  8.  9.
  3.  5.  7.  1.  2.  1.  4.  8.  9.  9.  6.  7.  9.  2.  4.  4.  2.  7.
  1.  1.  5.  5.  7.  5.  1.  1.  1.  9.  9.  6.  7.  2.  9.  5.  3.  4.
  2.  1.  2.  4.  5.  4.  3.  1.  9.  7.  4.  9.  5.  5.  5.  3.  8.  3.
  3.  4.  9.  1.  5.  3.  5.  5.  5.  3.  8.  2.  9.  2.  8.  1.  5.  6.
  8.  4.  4.  2.  9.  1.  2.  7.  1.  3.  2.  2.  2.  7.  3.  3.  1.  1.
  6.  4.  8.  1.  6.  5.  9.  6.  4.  5.  1.  3.  2.  1.  1.  9.  9.  1.
  5.  7.  2.  9.  3.  3.  7.  2.  2.  4.  9.  6.  1.  3.  5.  6.  7.  4.
  9.  1.  2.  8.  1.  3.  3.  1.  3.  7.  6.  1.  9.  1.  8.  8.  8.  2.
  1.  4.  1.  2.  2.  7.  1.  1.  7.  5.  1.  9.  1.  8.  9.  8.  7.  7.
  2.  8.  3.  7.  8.  4.  5.  6.  9.  6.  5.  5.  5.  4.  3.  4.  1.  4.
  9.  7.  6.  9.  9.  6.  8.  1.  7.  6.  5.  4.  5.  1.  5.  6.  6.  6.
  6.  3.  9.  4.  5.  4.  1.  7.  9.  4.  7.  3.  2.  3.  7.  3.  2.  7.
  8.  5.  6.  3.  3.  4.  8.  2.  4.  7.  5.  4.  5.  7.  4.  4.  6.  4.
  6.  2.  1.  2.  9.  1.  5.  6.  3.  7.  4.  7.  8.  3.  4.  5.  5.  8.
  9.  3.  9.  9.  1.  6.  4.  2.  9.  2.  2.  2.  5.  2.  9.  2.  3.  2.
  2.  9.  1.  4.  4.  8.  2.  2.  4.  1.  7.  8.  6.  9.  2.  7.  7.  7.
  6.  2.  1.  5.  1.  3.  4.  9.  8.  7.  8.  5.  4.  4.  3.  8.  4.  4.
  9.  4.  2.  5.  5.  3.  4.  7.  8.  2.  1.  2.  9.  4.  7.  2.  9.  5.
  9.  2.  4.  9.  3.  5.  1.  4.  5.  8.  6.  7.  1.  8.  5.  3.  5.  4.
  5.  6.  9.  2.  4.  4.  3.  9.  3.  3.  2.  1.  1.  2.  3.  7.  4.  2.
  5.  8.  8.  5.  6.  2.  7.  1.  6.  4.  8.  6.  3.  7.  6.  8.  7.  3.
  7.  1.  2.  7.  9.  1.  6.  3.  2.  9.  8.  3.  3.  1.  1.  1.  7.  5.
  3.  2.  3.  4.  8.  7.  6.  1.  3.  5.  8.  7.  9.  4.  3.  6.  3.  6.
  3.  1.  2.  3.  1.  9.  2.  7.  5.  1.  4.  6.  3.  6.  4.  1.  9.  3.
  9.  2.  2.  6.  1.  5.  7.  9.  5.  4.  3.  9.  5.  2.  3.  2.  9.  2.
  8.  2.  2.  9.  6.  7.  7.  3.  5.  1.  5.  2.  2.  4.  9.  2.  2.  8.
  3.  6.  7.  4.  1.  8.  5.  8.  8.  7.  6.  1.  9.  1.  5.  2.  4.  8.
  2.  4.  4.  3.  9.  5.  4.  2.  8.  8.  2.  2.  7.  2.  9.  2.  8.  2.
  5.  1.  6.  6.  6.  6.  9.  2.  9.  3.  4.  4.  8.  2.  6.  9.  3.  4.
  7.  1.  5.  4.  9.  1.  6.  4.  4.  5.  4.  7.  2.  1.  6.  6.  8.  5.
  8.  7.  7.  3.  6.  9.  4.  6.  8.  6.  2.  4.  2.  1.  9.  2.  2.  3.
  9.  2.  8.  2.  3.  3.  7.  5.  1.  2.  2.  6.  2.  8.  7.  8.  7.  5.
  5.  1.  8.  6.  9.  4.  3.  5.  3.  4.  4.  4.  2.  3.  1.  4.  4.  5.
  9.  4.  9.  7.  1.  1.  1.  8.  7.  4.  1.  6.  7.  8.  5.  3.  7.  6.
  1.  4.  6.  2.  6.  2.  5.  2.  5.  8.  8.  2.  8.  5.  2.  2.  8.  7.
  2.  6.  7.  6.  3.  6.  1.  8.  6.  1.  7.  5.  6.  3.  4.  8.  2.  8.
  4.  6.  6.  5.  8.  2.  5.  5.  3.  1.  8.  2.  4.  4.  1.  2.  7.  1.
  8.  3.  5.  9.  7.  8.  4.  3.  1.  4.  7.  7.  5.  7.  1.  1.  4.  9.
  8.  3.  2.  6.  4.  8.  7.  4.  7.  6.  7.  1.  7.  8.  4.  6.  6.  9.
  4.  4.  3.  5.  1.  8.  6.  2.  7.  5.  3.  5.  3.  2.  8.  6.  4.  7.
  4.  6.  6.  3.  2.  2.  3.  7.  9.  6.  5.  1.  1.  5.  2.  8.  2.  4.
  2.  5.  6.  8.  1.  4.  6.  9.  2.  8.  3.  2.  1.  2.  5.  3.  6.  7.
  3.  4.  4.  1.  2.  2.  1.  9.  8.  2.  2.  3.  1.  8.  9.  1.  2.  2.
  7.  8.  8.  7.  9.  7.  6.  9.  9.  4.  8.  9.  4.  3.  3.  5.  1.  2.
  2.  2.  3.  1.  6.  1.  4.  5.  8.  2.  3.  8.  7.  3.  5.  9.  5.  5.
  9.  6.  2.  4.  7.  2.  7.  3.  2.  5.  5.  3.  4.  2.  4.  2.  4.  8.
  6.  7.  2.  2.  8.  7.  6.  1.  2.  8.  4.  3.  7.  3.  1.  2.  7.  7.
  8.  1.  1.  3.  7.  5.  9.  5.  4.  1.  6.  3.  1.  1.  1.  9.  4.  8.
  1.  5.  1.  8.  5.  3.  5.  4.  8.  3.  3.  4.  8.  4.  6.  5.  6.  9.
  1.  5.  2.  4.  9.  4.  4.  4.  8.  6.  5.  7.  6.  1.  9.  5.  7.  7.
  7.  1.  1.  2.  1.  3.  9.  8.  9.  3.  2.  5.  1.  5.  6.  5.  1.  6.
  3.  1.  7.  7.  2.  1.  9.  4.  4.  1.  4.  5.  2.  8.  5.  8.  2.  4.
  2.  5.  4.  1.  8.  6.  3.  6.  4.  1.  2.  9.  3.  4.  9.  3.  4.  4.
  5.  8.  7.  8.  5.  5.  8.  6.  2.  7.  2.  2.  1.  8.  9.  9.  5.  2.
  7.  6.  3.  5.  1.  7.  9.  4.  2.  4.  2.  2.  4.  1.  4.  8.  2.  9.
  6.  6.  1.  1.  3.  3.  8.  9.  6.  3.  1.  6.  3.  5.  4.  1.  3.  8.
  1.  4.  2.  7.  2.  7.  3.  9.  2.  4.  6.  4.  4.  2.  8.  2.  2.  2.
  8.  1.  1.  1.  6.  9.  2.  9.  3.  6.  7.  7.  4.  9.  3.  3.  3.  2.
  1.  7.  6.  8.  7.  7.  1.  3.  2.  1.  8.  1.  8.  7.  5.  1.  5.  6.
  9.  5.  4.  8.  9.  3.  9.  2.  5.  3.  4.  8.  2.  3.  1.  4.  1.  8.
  7.  7.  7.  8.  6.  9.  2.  3.  7.  3.  4.  7.  5.  9.  4.  1.  3.  8.
  4.  7.  1.  2.  1.  6.  4.  5.  3.  2.  3.  9.  1.  1.  2.  7.  8.  5.
  7.  4.  7.  3.  3.  8.  3.  4.  4.  3.  9.  7.  6.  2.  9.  6.  9.  6.
  1.  7.  7.  2.  4.  5.  1.  1.  8.  3.  9.  9.  1.  1.  8.  1.  2.  5.
  5.  2.  2.  5.  5.  6.  3.  4.  1.  7.  5.  7.  2.  9.  9.  3.  8.  3.
  2.  4.  7.  2.  7.  1.  1.  8.  8.  4.  1.  4.  8.  7.  1.  6.  7.  8.
  7.  9.  2.  5.  6.  5.  4.  8.  7.  9.  5.  3.  6.  5.  1.  1.  7.  7.
  2.  7.  5.  4.  2.  7.  6.  1.  8.  9.  1.  8.  7.  2.  3.  3.  2.  3.
  8.  9.  3.  6.  6.  6.  7.  4.  9.  4.  8.  6.  7.  5.  5.  5.  5.  3.
  3.  5.  1.  4.  5.  6.  2.  5.  2.  1.  2.  5.  2.  9.  2.  7.  3.  3.
  9.  8.  8.  2.  7.  6.  8.  2.  5.  9.  1.  9.  5.  8.  5.  1.  6.  3.
  1.  1.  3.  1.  9.  4.  8.  3.  1.  4.  2.  2.  8.  7.  3.  4.  4.  1.
  2.  1.  5.  3.  8.  4.  6.  8.  8.  8.  8.  8.  6.  2.  4.  8.  1.  9.
  7.  6.  5.  6.  4.  9.  7.  1.  5.  1.  2.  8.  7.  8.  4.  6.  1.  5.
  4.  7.  9.  1.  2.  4.  6.  5.  5.  6.  2.  8.  5.  5.  3.  7.  4.  1.
  4.  3.  3.  1.  4.  6.  9.  2.  7.  8.  1.  2.  4.  4.  6.  8.  9.  9.
  9.  5.  7.  8.  7.  8.  4.  1.  5.  9.  4.  7.  5.  4.  5.  7.  5.  1.
  5.  6.  2.  8.  1.  1.  4.  7.  3.  7.  5.  9.  6.  4.  9.  6.  6.  4.
  8.  3.  6.  9.  2.  2.  4.  6.  6.  3.  8.  4.  7.  5.  2.  1.  7.  2.
  2.  1.  3.  5.  6.  3.  5.  1.  5.  9.  4.  5.  3.  1.  5.  8.  8.  1.
  1.  6.  5.  3.  5.  1.  9.  2.  6.  3.  6.  7.  8.  5.  5.  5.  2.  5.
  1.  2.  5.  5.  1.  5.  7.  1.  2.  5.  6.  6.  5.  1.  1.  9.  3.  7.
  4.  2.  2.  8.  3.  3.  6.  1.  5.  2.  1.  7.  8.  2.  9.  5.  7.  3.
  1.  1.  2.  5.  5.  3.  3.  4.  3.  9.  8.  8.  9.  8.  5.  5.  9.  4.
  7.  3.  9.  2.  4.  1.  2.  3.  5.  8.  2.  8.  3.  1.  5.  1.  9.  1.
  8.  9.  8.  5.  6.  8.  4.  1.  4.  5.  7.  6.  2.  2.  4.  8.  4.  3.
  1.  8.  1.  3.  9.  1.  1.  7.  6.  3.  1.  9.  8.  5.  8.  8.  3.  4.
  2.  9.  5.  6.  1.  1.  2.  3.  6.  8.  4.  7.  5.  3.  3.  2.  3.  4.
  8.  9.  4.  4.  2.  4.  2.  1.  6.  9.  5.  6.  3.  9.  2.  2.  3.  9.
  9.  5.  3.  3.  4.  2.  9.  9.  9.  1.  3.  8.  9.  1.  3.  5.  2.  4.
  4.  5.  1.  7.  6.  5.  8.  7.  8.  9.  1.  8.  9.  6.  3.  8.  7.  6.
  4.  2.  5.  5.  1.  5.  8.  4.  9.  7.  6.  7.  6.  3.  6.  5.  9.  2.
  9.  1.  7.  6.  3.  7.  6.  5.  8.  1.  5.  6.  8.  1.  9.  6.  8.  4.
  6.  6.  5.  2.  2.  1.  4.  2.  9.  2.  5.  7.  3.  7.  5.  5.  3.  3.
  9.  2.  9.  3.  7.  6.  3.  8.  7.  1.  4.  5.  3.  7.  4.  3.  2.  1.
  6.  3.  9.  1.  5.  5.  4.  6.  7.  8.  1.  5.  9.  5.  8.  6.  1.  4.
  7.  5.  7.  6.  4.  3.  3.  4.  3.  8.  9.  9.  1.  5.  8.  2.  7.  8.
  9.  5.  8.  5.  5.  6.  4.  5.  3.  2.  3.  3.  2.  1.  6.  4.  7.  1.
  6.  6.  2.  1.  6.  4.  2.  4.  4.  8.  1.  9.  5.  3.  1.  9.  1.  4.
  9.  5.  1.  2.  7.  5.  3.  2.  2.  7.  7.  8.  6.  8.  8.  3.  7.  1.
  6.  2.  2.  9.  1.  3.  2.  7.  1.  6.  4.  6.  4.  5.  1.  9.  6.  5.
  6.  1.  4.  1.  8.  3.  6.  4.  5.  7.  5.  6.  2.  9.  9.  6.  8.  1.
  4.  1.  6.  9.  3.  4.  7.  7.  3.  8.  3.  2.  4.  5.  1.  8.  8.  1.
  2.  3.  1.  4.  7.  9.  7.  5.  3.  9.  8.  9.  5.  4.  8.  8.  8.  1.
  2.  2.  9.  9.  3.  4.  2.  7.  5.  4.  1.  6.  9.  4.  7.  8.  8.  4.
  2.  9.  4.  8.  2.  8.  8.  3.  3.  3.  2.  6.  1.  2.  7.  2.  9.  6.
  2.  1.  2.  1.  1.  6.  7.  4.  2.  7.  5.  1.  5.  5.  6.  6.  3.  3.
  4.  4.  4.  8.  5.  4.  9.  4.  4.  9.  5.  7.  7.  4.  1.  6.  9.  9.
  3.  1.  9.  8.  5.  2.  1.  5.  6.  6.  7.  5.  7.  3.  1.  6.  5.  7.
  9.  6.  3.  4.  5.  1.  8.  7.  6.  3.  2.  7.  1.  7.  4.  1.  3.  1.
  2.  2.  8.  2.  6.  8.  2.  6.  1.  6.  5.  7.  5.  6.  4.  7.  3.  5.
  7.  8.  1.  5.  1.  9.  7.  7.  8.  1.  8.  2.  1.  7.  9.  7.  7.  6.
  8.  8.  9.  9.  5.  6.  4.  1.  7.  8.  3.  2.  3.  3.  4.  6.  7.  3.
  7.  2.  5.  2.  6.  5.  3.  7.  4.  1.  4.  5.  8.  4.  5.  5.  1.  1.
  5.  7.  8.  2.  5.  8.  3.  6.  8.  5.  5.  4.  2.  4.  7.  4.  1.  8.
  5.  1.  9.  7.  5.  9.  4.  9.  1.  1.  7.  8.  2.  9.  7.  7.  3.  8.
  8.  9.  7.  9.  3.  7.  7.  5.  3.  3.  5.  4.  4.  3.  4.  4.  3.  8.
  2.  1.  5.  4.  2.  3.  2.  1.  4.  2.  2.  5.  3.  3.  6.  3.  4.  4.
  5.  3.  4.  6.  2.  5.  8.  4.  3.  4.  2.  7.  4.  6.  3.  2.  4.  6.
  4.  4.  9.  5.  4.  3.  4.  6.  1.  5.  7.  2.  3.  1.  2.  8.  1.  2.
  2.  5.  9.  5.  8.  6.  9.  5.  6.  7.  2.  6.  9.  5.  7.  9.  2.  6.
  5.  6.  2.  5.  5.  3.  5.  8.  5.  3.  5.  4.  8.  8.  8.  2.  9.  7.
  7.  2.  6.  4.  5.  3.  3.  1.  1.  8.  8.  2.  9.  7.  8.  9.  7.  2.
  5.  1.  5.  2.  4.  2.  1.  4.  4.  4.  9.  4.  3.  5.  6.  1.  8.  3.
  1.  2.  2.  5.  8.  9.  2.  1.  7.  6.  3.  6.  9.  4.  3.  8.  8.  7.
  6.  2.  2.  6.  7.  5.  7.  9.  5.  9.  5.  2.  4.  1.  5.  2.  5.  6.
  6.  5.  4.  8.  1.  2.  9.  4.  7.  8.  7.  3.  3.  4.  8.  5.  9.  4.
  5.  8.  2.  3.  5.  3.  3.  1.  2.  8.  8.  7.  1.  2.  1.  2.  1.  4.
  1.  3.  2.  7.  3.  4.  8.  8.  8.  3.  5.  5.  8.  3.  9.  2.  7.  2.
  2.  2.  6.  6.  9.  9.  8.  7.  4.  7.  8.  4.  1.  6.  7.  9.  9.  6.
  6.  5.  4.  6.  1.  9.  7.  5.  7.  4.  2.  8.  7.  8.  6.  4.  1.  8.
  5.  8.  7.  3.  8.  4.  9.  2.  8.  4.  7.  2.  4.  3.  8.  7.  5.  1.
  2.  8.  6.  9.  3.  4.  5.  4.  1.  4.  1.  4.  6.  5.  7.  9.  7.  9.
  2.  9.  4.  7.  2.  7.  9.  6.  4.  8.  5.  5.  9.  8.  8.  5.  6.  8.
  4.  9.  9.  2.  5.  3.  2.  2.  8.  3.  3.  3.  2.  9.  2.  5.  4.  1.
  4.  5.  9.  2.  1.  7.  3.  4.  1.  5.  4.  2.  7.  3.  7.  7.  4.  2.
  8.  5.  3.  6.  3.  9.  5.  7.  7.  1.  4.  4.  4.  7.  3.  6.  1.  7.
  3.  1.  4.  3.  7.  7.  3.  7.  6.  4.  4.  1.  4.  9.  2.  5.  3.  2.
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  5.  1.  4.  9.  9.  2.  6.  8.  5.  2.  1.  5.  3.  3.  3.  1.  1.  5.
  2.  9.  6.  2.  1.  7.  4.  1.  8.  1.  2.  1.  2.  3.  2.  4.  4.  3.
  8.  1.  7.  3.  5.  2.  1.  8.  5.  2.  2.  9.  7.  9.  1.  7.  9.  2.
  1.  1.  6.  1.  6.  6.  9.  3.  9.  1.  1.  1.  2.  4.  4.  4.  5.  4.
  8.  7.  9.  2.  9.  8.  3.  7.  8.  2.  6.  3.  3.  9.  6.  7.  6.  3.
  9.  9.  3.  4.  6.  8.  4.  7.  4.  7.  8.  2.  3.  8.  8.  7.  9.  4.
  2.  1.  2.  4.  3.  2.  7.  4.  2.  6.  5.  5.  3.  9.  8.  8.  6.  4.
  6.  8.  2.  9.  6.  5.  3.  3.  8.  8.  5.  8.  2.  9.  1.  6.  1.  6.
  6.  8.  4.  3.  4.  8.  6.  8.  2.  5.  7.  3.  8.  7.  6.  1.  7.  4.
  9.  7.  7.  9.  8.  4.  9.  4.  8.  9.  5.  6.  4.  6.  2.  8.  7.  6.
  6.  3.  8.  6.  2.  4.  6.  9.  1.  6.  3.  7.  9.  2.  2.  4.  6.  1.
  4.  5.  7.  7.  2.  3.  8.  6.  2.  7.  1.  1.  7.  7.  9.  7.  4.  4.
  2.  7.  1.  8.  7.  8.  1.  4.  1.  6.  7.  9.  8.  9.  8.  9.  3.  7.
  3.  5.  2.  4.  8.  3.  1.  5.  2.  5.  2.  1.  2.  3.  5.  9.  7.  4.
  7.  1.  7.  8.  6.  5.  7.  7.  6.  7.  6.  7.  9.  4.  9.  6.  6.  4.
  2.  1.  8.  2.  1.  2.  6.  1.  5.  2.  2.  4.  8.  8.  5.  1.  8.  6.
  7.  2.  3.  7.  7.  6.  1.  5.  6.  8.  2.  9.  9.  1.  5.  4.  3.  2.
  7.  5.  8.  3.  9.  4.  5.  7.  3.  5.  7.  7.  1.  8.  9.  2.  6.  4.
  2.  6.  3.  2.  6.  7.  1.  4.  1.  2.  4.  9.  7.  7.  4.  7.  6.  1.
  1.  7.  8.  8.  2.  5.  6.  8.  5.  3.  5.  1.  1.  6.  8.  6.  5.  8.
  9.  3.  1.  5.  5.  6.  9.  9.  3.  3.  6.  2.  8.  3.  5.  9.  2.  7.
  7.  2.  1.  3.  7.  1.  8.  3.  4.  6.  9.  8.  5.  4.  7.  8.  7.  6.
  1.  8.  5.  3.  1.  8.  1.  9.  7.  7.  5.  9.  1.  5.  6.  6.  1.  4.
  6.  7.  1.  1.  3.  1.  2.  7.  1.  7.  7.  4.  7.  5.  5.  2.  8.  4.
  7.  6.  3.  2.  7.  1.  4.  8.  2.  1.  3.  8.  4.  7.  4.  3.  1.  2.
  7.  9.  9.  8.  1.  9.  7.  6.  2.  2.  9.  8.  2.  2.  6.  4.  7.  9.
  2.  1.  1.  7.  1.  8.  7.  8.  9.  7.  1.  4.  4.  4.  4.  4.  3.  3.
  4.  6.  8.  3.  1.  7.  3.  8.  4.  5.  4.  2.  6.  5.  1.  1.  8.  5.
  8.  5.  2.  4.  1.  3.  7.  7.  6.  9.  3.  7.  9.  5.  2.  6.  6.  9.
  8.  3.  2.  8.  5.  5.

# What is your estimate of your best classifier's accuracy?  (only your final answer)
CHALLENGE_BESTCLASSIFIER_ACCURACY_MEAN: 0.964825

# What ML algorithm did you use for your best classifier?  (Just a short name)
# (e.g., ID3 decision tree, SVM with Gaussian kernel, Boosted decision tree, etc.)
CHALLENGE_BESTCLASSIFIER_NAME: Random Forest

# Copy and paste your brief paragraph describing your best classifier below
CHALLENGE_BESTCLASSIFIER_DESCRIPTION:
  For this challenge, I chose to train the following ML classifier…because of the Random Forest classifier is simple, yet highly effective and accurate. It does not require pruning, and yet avoids the overfitting problem by achieving diversity amongst the various trees it generates through bootstrap sampling and splitting on a small subset of features at each node, at random. The optimal parameters include how many trees to aggregate, number of features to randomly subset at each node, the option of enabling bootstrap sampling, and calculating estimates of accuracy on out-of-sample data with out-of-bootstrap data. I enabled the model to include bootstrap sampling, set the number of features to randomly subset at each split equal to the square root of the total number of features in the data, set the number of jobs to run in parallel equal to the number of cores, ran the classifier through 100 iterations on 10, 100, 1000, and 10000 trees, computed their respective out-of-bootstrap accuracy on each iteration, and averaged the out-of-bootstrap accuracies of each of the classifiers (10, 100, 1000, and 10000). I chose the 100-tree Random Forest because (a) increasing the number of trees showed minimal gain in out-of-bootstrap accuracy and (b) after 100 trees, the run-time starts increasing, so the 100-tree Random Forest maximizes out-of-bootstrap accuracy while minimizing run-time cost.



 
 
 
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# Feedback on the Assignment (OPTIONAL)
# 
# The following information will help us improve future versions of this assignment.
# It is completely optional, but highly appreciated.  Please be honest.
#######################################################################################

# Approximately how many hours did it take you to complete this assignment?
FEEDBACK_NUM_HOURS: 72

# Please list any typos / errors you noticed in the assignment description or skeleton code
FEEDBACK_ERRORS: |
    None
 
# Please describe any problems you encountered while completing this assignment
FEEDBACK_PROBLEMS: |
    None