CSCE 478/878 (Fall 2014) Homework 2

Assigned Tuesday, October 7
Due Tuesday, October 21 Thursday, October 23 at 11:59 p.m.

When you hand in your results from this homework, you should submit the following, in separate files:
  1. A single zip file called, where username is your username on cse. In this file, put:
  2. A single .pdf file with your writeup of the results for all the homework problems, including the last problem. Only pdf will be accepted, and you should only submit one pdf file, with the name username.pdf, where username is your username on cse. Include all your plots in this file, as well as a detailed summary of your experimental setup, results, and conclusions. If you have several plots, you might put a few example ones in the main text and defer the rest to an appendix. Remember that the quality of your writeup strongly affects your grade. See the web page on ``Tips on Presenting Technical Material''.

Submit everything by the due date and time using the web-based handin program.

On this homework, you must work on your own and submit your own results written in your own words.

  1. (20 pts) Design a two-input perceptron that implements the boolean function A ∧ [∼ B], where ∼ is logical negation. Design a multi-layer network of perceptrons to implement [AB] ⊕ C, where ⊕ represents exclusive OR.

  2. (15 pts) Suppose a hypothesis commits 10 errors over a sample of 65 independently drawn test examples. What is the 90% two-sided confidence interval for the true error rate? What is the 95% one-sided interval? What is the 90% one-sided interval?

  3. (85 pts) Implement an artificial neural network (ANN) with at least one hidden layer. You may hard-code the sizes of the input and hidden layers, or you may set them dynamically based on parameters passed to the program. Your ANN will be trained by the Backpropagation algorithm. If you use discrete-valued attributes or multiclass labels, explain in your report how you implemented that in your ANN.

    You are to compare your ANN's results to those from ID3 on the same UCI data sets you used for Homework 1 (if you were unsuccessful in getting your ID3 implementation working, you may utilize an existing implementation, such as Weka's or Quinlan's C4.5). Your goal is to convince the reader that, for each data set, either one of the two algorithms is superior to the other (and give a significance level as well) or that there is no statistically significant difference between them. To accomplish this task, you may use any tools from the lecture that you wish, under two conditions: (1) you must use the tools correctly and thoroughly corroborate your assertion, and (2) you must have at least one confidence interval or statistical test and at least one ROC curve in your report.

    You are to submit a detailed, well-written report, with conclusions that you can justify with your results. In particular, you should answer the following questions for both your new classifier and ID3. Did training error go to 0? Did overfitting occur? Should you have stopped training early? Was there a statistically significant difference between the performance of ID3 and that of the ANN? What algorithm would you recommend for your data sets? Of course, this is merely the minimum that is required in your report.

    Extra credit opportunities include (but are not limited to) running on extra data sets, using other activation functions, using multiclass data, and running experiments on more ANN architectures and/or with more learning rates. As always, the amount of extra credit is commensurate with the level of extra effort and the quality of your report of the results.

  4. The following problem is only for students registered for CSCE 878. CSCE 478 students who do it will receive extra credit, but the amount will be less than the number of points indicated.

  5. (20 pts) Consider a kernel K : X × X → ℝ that takes two vectors from X and returns a real number. From class we know that since K is a kernel, it computes a dot product in an induced feature space Φ. Specifically, K(xi, xj) = Φ(xi) · Φ(xj). Define the squared Euclidean distance between Φ(xi) and Φ(xj) (i.e., ‖ Φ(xi) − Φ(xj) ‖2) in terms of K.

CSCE 478/878 (Fall 2014) Home Page

Last modified 17 October 2014; please report problems to sscott AT cse.