Statistical Machine Learning (GU4241/GR5241)
Spring 2017
https://courseworks.columbia.edu
Homework 4
Due: Tuesday 4 April 2017
Students are encouraged to work together, but homework write-ups must be done individual
...
Statistical Machine Learning (GU4241/GR5241)
Spring 2017
https://courseworks.columbia.edu
Homework 4
Due: Tuesday 4 April 2017
Students are encouraged to work together, but homework write-ups must be done individually and must
be entirely the author’s own work. Homework is due at the beginning of the class for which it is due.
Late homework will not be accepted under any circumstances. To receive full credit, students
must thoroughly explain how they arrived at their solutions and include the following information on
their homeworks: name, UNI, homework number (e.g., HW03), and class (STAT GU4241/GR5241).
All homework must be turned in online through Canvas (Courseworks) in PDF format, have a .pdf
extension (not zip or other archive!), and be less than 4MB. If programming is part of the assignment,
the code must be turned in in one or more .R files. Homeworks not adhering to these requirements will
receive no credit. For your convenience (not required), both tex and rmd templates for producing nice
PDF files can be found on Courseworks.
1. ‘
q regression (30 points)
β1
β2
^ β
x1
x2
x3
x4 x5
β1
β2
^ β
x1
x2
x3
x4 x5
The figures show the cost function components of the ‘q-regression problems with q = 0:5 (left)
and q = 4 (right).
1. (15 points) Does one/none/both of the cost functions encourage sparse estimates? If so,
which one? Explain your answer.
2. (15 points) Which of the points x1; : : : ; x5 would achieve the smallest cost under the ‘qconstrained least squares cost function? For each of the two cases, name the respective point
and give a brief explanation for your answer.
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