Decision Trees

Decision Trees. Prof. A.L. Yuille. Stat 231. Fall 2004. Duda, Hart & Stork. Chp 81-8.3 . Decision Trees. Decision Trees. Binary Classification Trees. Data can be non-metric, list of binary attributes. 2. Classification Decision Trees. Nonmetric. Data is list of binary attributes.

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Decision Diagrams

Decision Diagrams. Maciej Ciesielski Electrical & Computer Engineering University of Massachusetts, Amherst, USA ciesiel@ecs.umass.edu. Common Representations. Boolean functions ( f : B  B ) Truth table, Karnaugh map SoP, PoS, ESoP Reed-Muller expansions (PPRM, FPRM, GRM, etc.)

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Probability Tree diagrams

Black. Black. White. Black. White. White. Probability Tree diagrams. Example A bag contains 10 discs: 7 are black and 3 white. A disc is selected, and then replaced. A second disc is selected. Copy and complete the tree diagram showing all the probabilities and outcomes .

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Probability Tree diagrams

Probability Tree diagrams. Example A coin is tossed twice. Complete the probability tree diagram showing all the possible outcomes and the probability of each. What is the probability of the two tosses giving the same result?. 1 st throw. 2 nd throw. Head. Head, Head. Head. Tail.

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Influence Diagrams Basic Decision Trees

Graphic symbols . NodesSquare = decisionsCircles = chance eventsRectangles with rounded corners = valuesArrows (arcs) are used to connect nodesA node at the beginning of an arc is called a predecessorA node at the end of an arc is a called a successor . . . . . Venture Capital Decision. Value.

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Solving Influence Diagrams Plus more Decision Trees

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Decision Trees

Decision Trees. Example: Conducted survey to see what customers were interested in new model car Want to select customers for advertising campaign. training set. Basic Information Gain Computations. Result: I_Gain_Ratio: city>age>car. Result: I_Gain: age > car=city.

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Decision Trees and Decision Tables

Decision Trees and Decision Tables. Decision Trees and Decision Tables. Often our problem solutions require decisions to be made according to two or more conditions or combinations of conditions Decision trees represent such decision as a sequence of steps

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Decision Trees

Decision Trees. Highly used and successful Iteratively split the Data Set into subsets one attribute at a time, using most informative attributes first Continue until you can label each leaf node with a class Attribute Features – discrete/nominal (can extend to continuous features)

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Decision Trees

Decision Trees. Example. Example 2. Examples, which one is better?. Good when. Samples are attribute-value pairs Target function has discrete output values Disjunctions required Missing, noisy training data. Construction. Top down construction

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Probability: Tree Diagrams

Probability: Tree Diagrams. Today you will learn to: calculate the probability of an event using tree diagrams. M07.D-S. 3.1.1: Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible.

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Decision Trees

Decision Trees. Shalev Ben-David. Definition. Given a function and oracle access to , determine f(x) with minimum number of queries E.g. f is OR on the bits of x – Grover search D(f) is the deterministic query complexity R(f) is the randomized query complexity

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Solving Influence Diagrams

Solving Influence Diagrams. Influence Diagrams are usually solved using software Freeware and Commercial software exists For the exam, follow procedure used in today’s lecture. Simple tricks for Solving Influence Diagrams.

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Decision Trees

Decision Trees. Prof. A.L. Yuille. Stat 231. Fall 2004. Duda, Hart & Stork. Chp 81-8.3. Decision Trees. Decision Trees. Binary Classification Trees. Data can be non-metric, list of binary attributes. 2. Classification Decision Trees. Nonmetric. Data is list of binary attributes.

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Chapter 6 Decision Trees and Influence Diagrams

Chapter 6 Decision Trees and Influence Diagrams. Introduction. Decision problems are multi-stage in character when the choice of a given option may result in circumstances which will require yet another decision to be made.

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PROBABILITY RULES AND TREES

PROBABILITY RULES AND TREES. Rule of complement Addition rule Multiplication rule Probability tree. RULE OF COMPLEMENT. The simplest probability rule involves the complement of an event. If the probability of A is P( A ), then the probability of its complement, P( A c ), is

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Decision Trees

Decision Trees. The “No Free Lunch” Theorem. Is there any representation that is compact (ie, sub-exponential in n) for all functions? Function = truth table n attributes  2^n rows in table Classification/target column is 2^n long

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Constructing influence diagrams

Constructing influence diagrams. Decision-maker: EPA Decision: Permit use of potentially carcinogenic chemical? Alternative courses of action Permit Restrict Ban Uncertainty: hazards Imperfect information: test and survey. Consequences. Value. Decision. Usage decision. Economic

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Decision Trees

Decision Trees. Jianping Fan Dept of Computer Science UNC-Charlotte. The problem of Classification. Given a set of training samples and their attribute values (x) and labels (y), try to determine the labels y of new examples. Classifier Training y = f(x) Prediction y given x.

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Influence Diagrams, Decision Trees and Probability

Influence Diagrams, Decision Trees and Probability. Reference: Clemen & Reilly. Making Hard Decisions , 2nd ed. Chapter 3. Duxbury, 2001. NOTE: Some materials for this presentation courtesy of Dr. Dan Maxwell. Influence Diagrams. Another way to structure decision problems

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