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Introduction to Data Mining: Probability and Random Variables

This lecture covers the basics of probability theory and its interpretation, along with the concept of random variables and their relationships. Topics include probability interpretation, probability calculus, frequentist and subjective views, conditional density and dependency, sampling, estimation techniques, and probabilistic model-based clustering.

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Introduction to Data Mining: Probability and Random Variables

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  1. DATA MINING van data naar informatie Ronald Westra Dep. Mathematics Maastricht University

  2. DATA ANALYSIS AND UNCERTAINTY Data Mining Lecture V [Chapter 4, Hand, Manilla, Smyth ]

  3. 4.1 Introduction 4.2 Probability and its interpretation4.3 (multiple) random variables4.4 samples, models, and patterns

  4. 4.2 Probability and its interpretation Probability,Possibility,Chance,Randomness,luck,hazard,fate,…

  5. 4.2 Probability and its interpretation Probability Theory: interpretationProbability Calculus: mathematical manipulation and computing

  6. 4.2 Probability and its interpretation Frequentist view: probability is objective: Prob = # times/# total EXAMPLE: traditional Prob.Theor.Subjective probability: subjective probabilities EXAMPLE: Bayesian statistics.

  7. 4.3 Random Variables and their Relationships Random Variables [4.3]random variable X:multivariate random variablesmarginal density

  8. 4.3 Random Variables and their Relationships conditional density & dependency: * example: supermarket purchases

  9. 4.3 Random Variables

  10. 4.3 Random Variables

  11. RANDOM VARIABLES Example: supermarket purchasesX = n customers x p products; X(i,j) = Boolean variable: “Has customer #i bought a product of type j ?” nA= sum(X(:,A)) is number of customers that bought product AnB= sum(X(:,B)) is number of customers that bought product BnAB= sum(X(:,A).*X(:,B)) is number of customers that bought both products A and B

  12. RANDOM VARIABLES Example: supermarket purchasescustomer# A B1 1 02 0 13 1 14 1 1pA = 3/4pB = 3/4pAB = 2/4pA.pB≠ pAB

  13. RANDOM VARIABLES (conditionally) independent:p(x,y) = p(x)*p(y) i.e. : p(x|y) = p(x)

  14. Markov Models

  15. RANDOM VARIABLES

  16. RANDOM VARIABLES

  17. RANDOM VARIABLES

  18. SAMPLING

  19. SAMPLING

  20. ESTIMATION

  21. Maximum Likelihood Estimation

  22. Maximum Likelihood Estimation

  23. Maximum Likelihood Estimation

  24. BAYESIAN ESTIMATION

  25. BAYESIAN ESTIMATION

  26. BAYESIAN ESTIMATION

  27. BAYESIAN ESTIMATION

  28. BAYESIAN ESTIMATION

  29. PROBABILISTIC MODEL-BASED CLUSTERING USING MIXTURE MODELS Data Mining Lecture VI [4.5, 8.4, 9.2, 9.6, Hand, Manilla, Smyth ]

  30. [*Jensen’s inequality]

  31. for a concave-down function, the expected value of the function is less than the function of the expected value. The gray rectangle along the horizontal axis represents the probability distribution of x, which is uniform for simplicity, but the general idea applies for any distribution

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