In the chapter we noted that attributes with many different possible values can cause problems with the gain measure. Such attributes tend to split the examples into numerous small classes or even singleton classes, thereby appearing to be highly relevant according to the gain measure. The gain ratio criterion selects attributes according to the ratio between their gain and their intrinsic information content—that is, the amount of information contained in the answer to the question. “What is the value of this attribute?” The gain ratio criterion therefore tries to measure how efficiently an attribute provides information on the correct classification of an example. Write a mathematical expression for the information content of an attribute, and implement the gain ratio criterion in DECISION-TREE-LEARNING.
Answer to relevant QuestionsThis exercise concerns the expressiveness of decision lists (Section 18.5).a. Show that decision lists can represent any Boolean function, if the size of the tests is not limited.b. Show that if the tests can contain at most ...Suppose one writes a logic program that carries out a resolution inference step. That is, let Resolve (c1, c2, c) succeed if c is the result of resolving cl and c2. Normally Resolve would be used as part of a theorem prover ...Consider m data points (x j, y j), where the y j s are generated from the x j s according to the linear Gaussian model in Equation (20.5). Find the values of θ1, θ2 and σ that maximize the conditional log ...Recall from that there are 22n distinct Boolean functions of n inputs. How many of these are representable by a threshold perceptron?Starting with the passive ADP agent modify it to use an approximate ADP algorithm us discussed in the text. Do this in two steps:a. Implement a priority queue for adjustments to the utility estimates. Whenever a state is ...
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