decision tree lecture notes

decision tree lecture notes

Each leaf represents one 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. Rooted trees can be used to model problems in which a series of decisions leads to a solution. 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. Binary decisions trees have some nice properties, but also some less pleasant ones. Decision Trees Refer corollary 5.5 in lecture notes 8. ), 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. $���U �� H��� Y��@�͊����9H #i���o �X� endstream endobj startxref 0 %%EOF 364 0 obj <>stream The largest number of binary comparisons ever needed to sort a list with n elements gives the worst-case performance of the algorithm. We can use decision trees to model sorting algorithms and to determine an estimate for the worst-case complexity of these algorithms. Example 1 illustrates an application of decision trees. A rooted tree in which each internal vertex corresponds to a decision, with a subtree at these vertices for each possible outcome of the decision, is called a decision tree. ?#����>"��&��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 How many weighings are necessary using a balance scale to determine which of the eight coins is the counterfeit one? permutations of these elements can be the correct order. EXAMPLE 4 We display in Figure 4 a decision tree that orders the elements of the list a, b, c. The complexity of a sort based on binary comparisons is measured in terms of the number of such comparisons used. Lars Schmidt-Thieme, Information Systems and Machine Learning Lab (ISMLL), Institute BW/WI & Institute for Computer Science, University of Hildesheim Course on Machine Learning, winter term 2009/2010 3/68 Machine Learning / 1. What is a Decision Tree? Method for solving linear homogeneous recurrence relations with constant coefficients. Decision trees classify the examples by sorting them down the tree from the root to some leaf node, with the leaf node providing the classification to the example. Please note that Youtube takes some time to process videos before they become available. Give an algorithm for finding this counterfeit coin. interpretable/intuitive, popular in medical applications because they mimic the way a doctor thinks model discrete outcomes nicely can be very powerful, can be as complex as you need them 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. h�b```�f�� �� 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)& For instance, a binary search tree can be used to locate items based on a series of comparisons, where each comparison tells us whether we have located the item, or whether we should go right or left in a subtree. The decision tree that illustrates how this is done is shown in Figure 3. They are used in non-linear decision making with simple linear decision surface. Tuo Zhao | Lecture 6: Decision Tree, Random Forest, and Boosting 22/42. Today Decision Trees I entropy I information gain Zemel, Urtasun, Fidler (UofT) CSC 411: 06-Decision Trees 2 / 39. Using decision trees as models, a lower bound for the worst-case complexity of sorting algorithms that are based on binary comparisons can be found. 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. It is possible to determine the counterfeit coin using two weighings. Consequently, the decision tree for the sequence of weighings is a 3-ary tree. 2. 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)& permutations of n elements. EXAMPLE 1 Suppose there are seven coins, all with the same weight, and a counterfeit coin that weighs less than the others. Decision Trees a decision tree consists of Nodes: test for the value of a certain attribute Edges: correspond to the outcome of a test connect to the next node or leaf Leaves: terminal nodes that predict the outcome to classifiy an example: 1.start at the root 2.perform the test 3.follow the edge corresponding to outcome Because the height of a binary tree with n! 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. Each internal node is a question on features. The result of each such comparison narrows down the set of possible orderings. To decide whether a particular sorting algorithm is efficient, its complexity is determined. The two pans can have equal weight, the first pan can be heavier, or the second pan can be heavier. 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. The possible solutions of the problem correspond to the paths to the leaves of this rooted tree. A Decision Tree • A decision tree has 2 kinds of nodes 1. h�bbd``b`� %PDF-1.5 %���� Risk Aversion (a) Thought experiment on large coin-flip gamble The largest number of weighings needed to determine the counterfeit coin is the height of the decision tree. Lecture notes, lectures 1 - Intro to Linear Programming Lecture notes, lectures 2 - Linear Programming Examples Lecture notes, lectures 5 - Chapters 3, 6, 15 Assignment Problems Lecture notes, lectures 7 - Goal Programming Lecture notes, lectures 8 - Decision Analysis Part 1 Lecture notes, lectures 9 - Decision Analysis Part 2 �,� ��l���d``TK���s�}����V3���CX���QV��T�D`��)�2vϢ�cs3JL�4�l6\~UE��t�J� �[���-�X��ar5�3�Ql㌅�6rBYMSW��q;�ye�)h=�֒I3k궥Q,�;UW]PR9&(2gu�_Gg��QL�~NK�s��5��� �n`����%% �р�Qؕ�1-����g� Q0�Z�-� (����A&�� `Pa �a�23V� ]@, v�?

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