# decision tree lecture notes

Each leaf represents one of the n! Trivially, there is a consistent decision tree for any training set w/ one path to leaf for each example (unless f nondeterministic in x) but it probably won’t generalize to new examples Need some kind of regularization to ensure more compact decision trees CS194-10 Fall 2011 Lecture 8 7 (Figure&from&StuartRussell)& CSC 411: Lecture 06: Decision Trees Richard Zemel, Raquel Urtasun and Sanja Fidler University of Toronto Zemel, Urtasun, Fidler (UofT) CSC 411: 06-Decision Trees 1 / 39. Rooted trees can be used to model problems in which a series of decisions leads to a solution. CS7641/ISYE/CSE 6740: Machine Learning/Computational Data Analysis Decision Tree for Spam Classi cation Boosting Trevor Hastie, Stanford University 10 600/1536 280/1177 180/1065 80/861 80/652 77/423 20/238 19/236 1/2 57/185 48/113 37/101 1/12 9/72 3/229 0/209 100/204 36/123 16/94 14/89 3/5 9/29 16/81 9/112 6/109 … Please note that Youtube takes some time to process videos before they become available. leaves is at least log n!, at least log n! The biggest problem is their size. It branches out according to the answers. Example 1 illustrates an application of decision trees. possible orderings of these elements, because each of the n! From Corollary 1 of Section 11.1 it follows that the height of the decision tree is at least log3 8 = 2. They are used in non-linear decision making with simple linear decision surface. Method for solving linear homogeneous recurrence relations with constant coefficients. Note that given n elements, there are n! ), Logical Operations and Logical Connectivity, Theory of inference for the Predicate Calculas, Precedence of Logical Operators and Logic and Bit Operations, Translating from Nested Quantifiers into English, Rules of Inference for Propositional Logic, Using Rules of Inference to Build Arguments, Rules of Inference for Quantified Statements, The Abstract Definition of a Boolean Algebra, Least Upper Bounds and Latest Lower Bounds in a Lattice, Bounded, Complemented and Distributive Lattices, Digramatic Representation of Partial Order Relations and Posets. How many weighings are necessary using a balance scale to determine which of the eight coins is the counterfeit one? Refer corollary 5.5 in lecture notes 8. Binary decisions trees have some nice properties, but also some less pleasant ones. It is possible to determine the counterfeit coin using two weighings. 2 Learning Decision Trees A decision tree is a binary tree in which the internal nodes are labeled with variables and the leafs are labeled with either −1 or +1. permutations of n elements. The largest number of binary comparisons ever needed to sort a list with n elements gives the worst-case performance of the algorithm. Thus, a sorting algorithm based on binary comparisons can be represented by a binary decision tree in which each internal vertex represents a comparison of two elements. THE COMPLEXITY OF COMPARISON-BASED SORTING ALGORITHMS Many different sorting algorithms have been developed. hޤW�r�6�����XK����fl+���ib���4��HlxQHʱ���(Q��Ɲ. ?#����>"��&��5�o3%�,``�!����jƷH�lyw�����2��<8� to��A�F�-xT�0���e G��,� ��.%Q��` -q8 endstream endobj 345 0 obj <> endobj 346 0 obj <>/ProcSet[/PDF/Text]>>/Rotate 0/StructParents 0/Type/Page>> endobj 347 0 obj <>stream From Corollary 1 of Section 11.1 it follows that the height of the decision tree … Additional Lecture Notes Lecture 2: Decision Trees Overview The purposes of this lecture are (i) to introduce risk aversion; (ii) to consider the Freemark Abbey Winery case; (iii) to determine the value of information; and (iv) to introduce real options. The decision tree that illustrates how this is done is shown in Figure 3. Decision Trees EXAMPLE 1 Suppose there are seven coins, all with the same weight, and a counterfeit coin that weighs less than the others. Decision Tree as Set of RulesPetal.Length< 2.45 Petal.Width< … A binary decision tree of n variables will have 2n1 decision nodes, plus 2nlinks at the lowest level, pointing to the return values 0 and 1. qPart 6: Pros and Cons of Decision Trees qPart 7: Using R to learn Decision Trees Machine Learning Decision Tree Classification Mustafa Jarrar: Lecture Notes on Decision Trees … There are at least eight leaves in the decision tree because there are eight possible outcomes (because each of the eight coins can be the counterfeit lighter coin), and each possible outcome must be represented by at least one leaf.

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