{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ps3-sol - CS229 Problem Set#3 Solutions 1 CS 229 Autumn...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
CS229 Problem Set #3 Solutions 1 CS 229, Autumn 2011 Problem Set #3 Solutions: Theory & Unsuper- vised learning Due in class (9:30am) on Wednesday, November 16. Notes: (1) These questions require thought, but do not require long answers. Please be as concise as possible. (2) When sending questions to [email protected] , please make sure to write the homework number and the question number in the subject line, such as Hwk 3 Q4 , and send a separate email per question. (3) If you missed the first lecture or are unfamiliar with the class’ collaboration or honor code policy, please read the policy on Handout #1 (available from the course website) before starting work. (4) For problems that require programming, please include in your submission a printout of your code (with comments) and any figures that you are asked to plot. (5) Please indicate the submission time and number of late dates clearly in your submission. SCPD students: Please email your solutions to [email protected] , and write “Prob- lem Set 3 Submission” on the Subject of the email. If you are writing your solutions out by hand, please write clearly and in a reasonably large font using a dark pen to improve legibility. 1. [23 points] Uniform convergence You are hired by CNN to help design the sampling procedure for making their electoral predictions for the next presidential election in the (fictitious) country of Elbania. The country of Elbania is organized into states, and there are only two candidates running in this election: One from the Elbanian Democratic party, and another from the Labor Party of Elbania. The plan for making our electorial predictions is as follows: We’ll sample m voters from each state, and ask whether they’re voting democrat. We’ll then publish, for each state, the estimated fraction of democrat voters. In this problem, we’ll work out how many voters we need to sample in order to ensure that we get good predictions with high probability. One reasonable goal might be to set m large enough that, with high probability, we obtain uniformly accurate estimates of the fraction of democrat voters in every state. But this might require surveying very many people, which would be prohibitively expensive. So, we’re instead going to demand only a slightly lower degree of accuracy. Specifically, we’ll say that our prediction for a state is “highly inaccurate” if the estimated fraction of democrat voters differs from the actual fraction of democrat voters within that state by more than a tolerance factor γ . CNN knows that their viewers will tolerate some small number of states’ estimates being highly inaccurate; however, their credibility would be damaged if they reported highly inaccurate estimates for too many states. So, rather than trying to ensure that all states’ estimates are within γ of the true values (which would correspond to no state’s estimate being highly inaccurate), we will instead try only to ensure that the number of states with highly inaccurate estimates is small.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern