Baum–Sweet sequence: Difference between revisions

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{{lead missing|date=November 2008}}
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{{Unreferenced|date=November 2008}}


'''Information gain ratio''' is between 0 and 1, cf. ordinary [[information gain]]
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== Information Gain Calculation ==
 
Let <math>Attr</math> be the set of all attributes and <math>Ex</math> the set of all training examples,
<math>value(x,a)</math> with
<math>x\in Ex</math> defines the value of a specific example <math>x</math> for attribute <math>a\in Attr</math>, <math>H</math> specifies the [[Entropy (information theory)#Definition|entropy]].
The information gain for an attribute <math>a\in Attr</math> is defined as follows:
 
<math>IG(Ex,a)=H(Ex) -\sum_{v\in values(a)} \left(\frac{|\{x\in Ex|value(x,a)=v\}|}{|Ex|} \cdot H(\{x\in Ex|value(x,a)=v\})\right)</math>
 
The information gain is equal to the total entropy for an attribute if for each of the attribute values a unique classification can be made for the result attribute. In this case the relative entropies subtracted from the total entropy are 0.
 
== Intrinsic Value Calculation ==
The intrinsic value for a test is defined as follows:
 
<math>IV(Ex,a)= -\sum_{v\in values(a)} \frac{|\{x\in Ex|value(x,a)=v\}|}{|Ex|} * \log_2\left(\frac{|\{x\in Ex|value(x,a)=v\}|}{|Ex|}\right)</math>
 
== Information Gain Ratio Calculation ==
The information gain ratio is just the ratio between the information gain and the intrinsic value:
<math>IGR(Ex,a)=IG / IV</math>
 
==Advantages==
Information gain ratio biases the [[Decision tree learning|decision tree]] against considering attributes with a large number of distinct values. So it solves the drawback of information gain—namely, information gain applied to attributes that can take on a large number of distinct values might learn the [[training set]] too well. For example, suppose that we are building a decision tree for some data describing a business's customers. Information gain is often used to decide which of the attributes are the most relevant, so they can be tested near the root of the tree. One of the input attributes might be the customer's [[credit card number]]. This attribute has a high information gain, because it uniquely identifies each customer, but we do ''not'' want to include it in the decision tree: deciding how to treat a customer based on their credit card number is unlikely to generalize to customers we haven't seen before.
 
{{DEFAULTSORT:Information Gain Ratio}}
[[Category:Decision trees]]
[[Category:Classification algorithms]]
[[Category:Entropy and information]]
[[Category:Statistical ratios]]

Latest revision as of 12:30, 5 May 2014

Bonus: WP Twin and WP Twin Auto Backup: (link to ) While not a theme, I think this software is essential if you are maintaining your Wordpress blog or regularly create new blog sites. What I advise you do next is save the backup data file to a remote place like a CD-ROM, external disk drive if you have one or a provider such as Dropbox. This is a service where people write articles using a specific keyword you have given them. If you're using Wordpress and want to make your blog a "dofollow" blog, meaning that links from your blog pass on the benefits of Google pagerank, you can install one of the many dofollow plugins available. This particular wordpress plugin is essential for not only having the capability where you improve your position, but to enhance your organic searches for your website.

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