BAYESIAN  LEARNING

Machine learning : Tom Mitchell 저, McGRAW-HILL, 1997, Page 154~199

1. INTRODUCTION

2. BAYES THEOREM

  (1) An Example

3. BAYES THEOREM AND CONCEPT LEARNING

  (1) Brute-Force Bayes Concept Learning

  (2) MAP Hypotheses and Consistent Learners

4. MAXIMUM LIKELIHOOD AND LEAST-SQUARED ERROR HYPOTHESES

5. MAXIMUM LIKELIHOOD HYPOTHESES FOR PREDICTING PROBABILITIES

  (1) Gradient Search to Maximize Likelihood in a Neural Net

6. MINIMUM DESCRIPTION LENGTH PRINCIPLE

7. BAYES OPTIMAL CLASSIFIER

8. GIBBS ALGORITHM

9. NAIVE BAYES CLASSIFIER

  (1) An Illustrative Example

    (1.1) ESTIMATING PROBABILITIES

10. AN EXAMPLE : LEARNING TO CLASSIFY TEXT

  (1) Experimental Results

11. BAYESIAN BELIEF NETWORKS

  (1) Conditional Independence

  (2) Representation

  (3) Inference

  (4) Learning Bayesian Belief Networks

  (5) Gradient Ascent Training of Bayesian Networks

  (6) Learning the Structure of Bayesian Networks

12. THE EM ALGORITHM

  (1) Estimating Means of Gaussians

  (2) General Statement of EM Algorithm

  (3) Derivation of the Means Algorithm

13. SUMMARY AND FURTHER READING

EXERCISES

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1. INTRODUCTION

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2. BAYES THEOREM

Bayes theorem :

                                           (1)

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                               (2)

                                       (3)

(1) An Example

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3. BAYES THEOREM AND CONCEPT LEARNING

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표 1

(1) Brute-Force Bayes Concept Learning

                           (i.e., )            

BRUTE-FORCE MAP LEARNING algorithm

1.    

2.

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1.    

2.    

3.

for all in

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if  is inconsistent with

                       (5)

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(2) MAP Hypotheses and Consistent Learners

그림 1

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4. MAXIMUM LIKELIHOOD AND LEAST-SQUARED ERROR HYPOTHESES

그림 2

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Probability density function:

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                                 (6)

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5. MAXIMUM LIKELIHOOD HYPOTHESES FOR PREDICTING PROBABILITIES

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                           (7)

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               (8)

                               (9)

                               (10)

                           (11)

                       (12)

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               (13)

(1) Gradient Search to Maximize Likelihood in a Neural Net

                   (14)

   th        th        

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                               (15)

                 (16)

6. MINIMUM DESCRIPTION LENGTH PRINCIPLE

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                   (16)

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                       (17)

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7. BAYES OPTIMAL CLASSIFIER

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                               (18)

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8. GIBBS ALGORITHM

1.    

2.    

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9. NAIVE BAYES CLASSIFIER

                     (19)

                       (20)

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(1) An Illustrative Example

               (21)

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(1.1) ESTIMATING PROBABILITIES

                                           (22)

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                   -estimate                                        

10. AN EXAMPLE : LEARNING TO CLASSIFY TEXT

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               th            

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(1) Experimental Results

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1.

2.    

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11. BAYESIAN BELIEF NETWORKS

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(1) Conditional Independence

                                         (23)

                                                           (24)

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그림 3

(2) Representation

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(3) Inference

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(4) Learning Bayesian Belief Networks

(5) Gradient Ascent Training of Bayesian Networks

                               (25)

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                               (26)

(6) Learning the Structure of Bayesian Networks

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12. THE EM ALGORITHM

(1) Estimating Means of Gaussians

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그림 4

                           (27)

                                           (28)

                           th                        

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Step 1 :        

Step 2 :                    

               th

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(2) General Statement of EM Algorithm

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Step 1 :             

Step 2 :            

(3) Derivation of the Means Algorithm

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                                               (29)

                   (30)

                                                                   (31)

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13. SUMMARY AND FURTHER READING

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EXERCISES

1. ￢cancer

2.        

3. (a)        

(b)        

(c)        

5.                        

(c)