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Unformatted text preview: Homework 4 on Gene Function Prediction CS 3824 T. M. Murali Assigned on October 28, 2011 Due on November 10, 2011 1. (20 points) In class, we proved that the Hopfield network algorithm converges in a finite number of steps when every edge in the graph has a weight of 1. The proof worked by asking how the energy changed when the algorithm changed the state of a node v by applying the update rule. We showed that the only edges that contributed to the change in energy were incident on v . We used this fact to show that the change in energy must be negative. Since all edge weights are 1, the energy must go down by a value of at least 1. We established a lower bound on the energy to conclude that the number of steps is finite. Generalise the proof when every edge in the graph has a positive edge weight. You may make some reasonable assumptions about the precision with which we represent real numbers. (Hint: Consider the case when every edge weight is a positive integer.) 2. (10 points) Consider the precision-recall curve for an algorithm such as SinkSource. During cross validation, SinkSource computes a score between 0 and 1 for every positive and every negative example. To compute the precision-recall curve, we vary a threshold t monotonically from 1 to 0. At every value of t , we compute the precision and recall. Do either or both of, we compute the precision and recall....
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