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VSSML16 L2. Ensembles and Logistic Regression


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VSSML16 L2. Ensembles and Logistic Regression
Valencian Summer School in Machine Learning 2016
Day 1 VSSML16
Lecture 2
Ensembles and Logistic Regression
Poul Petersen (BigML)

Published in: Data & Analytics
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VSSML16 L2. Ensembles and Logistic Regression

  1. 1. September 8-9, 2016
  2. 2. BigML, Inc 2 Ensembles Poul Petersen CIO, BigML, Inc Making trees unstoppable
  3. 3. BigML, Inc 3Supervised Learning • Rather than build a single model… • Combine the output of several “weaker” models into a powerful ensemble… • Q1: Why would this work? • Q2: How do we build “weaker” models? • Q3: How do we “combine” models? Ensemble Idea
  4. 4. BigML, Inc 4Supervised Learning 1. Every “model” is an approximation of the “real” function and there may be several good approximations. 2. ML Algorithms use random processes to solve NP-hard problems and may arrive at different “models” depending on the starting conditions, local optima, etc. 3. A given ML algorithm may not be able to exactly “model” the real characteristics of a particular dataset. 4. Anomalies in the data may cause over-fitting, that is trying to model behavior that should be ignored. By using several models, the outliers may be averaged out. Why Ensembles In any case, if we find several accurate “models”, the combination may be closer to the real “model”
  5. 5. BigML, Inc 5Supervised Learning Ensemble Demo #1
  6. 6. BigML, Inc 6Supervised Learning Weaker Models 1. Bootstrap Aggregating - aka “Bagging” If there are “n” instances, each tree is trained with “n” instances, but they are sampled with replacement. 2. Random Decision Forest - In addition to sampling with replacement, the tree randomly selects a subset of features to consider when making each split. This introduces a new parameter, the random candidates which is the number of features to randomly select before making the split.
  7. 7. BigML, Inc 7Supervised Learning Over-fitting Example Diameter Color Shape Fruit 4 red round plum 5 red round apple 5 red round apple 6 red round plum 7 red round apple Bagging! Random Decision Forest! All Data: “plum” Sample 2: “apple” Sample 3: “apple” Sample 1: “plum” }“apple” What is a round, red 6cm fruit?
  8. 8. BigML, Inc 8Supervised Learning 1. Plurality - majority wins. 2. Confidence Weighted - majority wins but each vote is weighted by the confidence. 3. Probability Weighted - each tree votes the distribution at it’s leaf node. 4. K Threshold - only votes if the specified class and required number of trees is met. For example, allowing a “True” vote if and only if at least 9 out of 10 trees vote “True”. 5. Confidence Threshold - only votes the specified class if the minimum confidence is met. Voting Methods Linear and non-linear combinations of votes using stacking
  9. 9. BigML, Inc 9Supervised Learning Ensemble Demo #2
  10. 10. BigML, Inc 10Supervised Learning Model vs Bagging vs RF Model Bagging Random Forest Increasing Performance Decreasing Interpretability Increasing Stochasticity Increasing Complexity
  11. 11. BigML, Inc 11Supervised Learning Ensemble Demo #3
  12. 12. BigML, Inc 12Supervised Learning • How many trees? • How many nodes? • Missing splits? • Random candidates? • Too many parameters? SMACdown
  13. 13. BigML, Inc 2 Logistic Regression Poul Petersen CIO, BigML, Inc Modeling probabilities
  14. 14. BigML, Inc 3Supervised Learning • Classification implies a discrete objective. How can this be a regression? • Why do we need another classification algorithm? • more questions…. Logistic Regression Logistic Regression is a classification algorithm
  15. 15. BigML, Inc 4Supervised Learning Linear Regression
  16. 16. BigML, Inc 5Supervised Learning Linear Regression
  17. 17. BigML, Inc 6Supervised Learning Polynomial Regression
  18. 18. BigML, Inc 7Supervised Learning • What function can we fit to discrete data? Regression Key Take-Away: Fitting a function to the data
  19. 19. BigML, Inc 8Supervised Learning Discrete Data Function?
  20. 20. BigML, Inc 9Supervised Learning Discrete Data Function? ????
  21. 21. BigML, Inc 10Supervised Learning Logistic Function •x→-∞ : f(x)→0 •x→∞ : f(x)→1 •Looks promising, but still not 
  22. 22. BigML, Inc 11Supervised Learning Probabilities P≈0 P≈10<P<1
  23. 23. BigML, Inc 12Supervised Learning • Assumes that output is linearly related to "predictors"
 … but we can "fix" this with feature engineering • How do we "fit" the logistic function to real data? Logistic Regression LR is a classification algorithm … that models the probability of the output class.
  24. 24. BigML, Inc 13Supervised Learning Logistic Regression β₀ is the "intercept" β₁ is the "coefficient" The inverse of the logistic function is called the "logit": In which case solving is now a linear regression
  25. 25. BigML, Inc 14Supervised Learning Logistic Regression If we have multiple dimensions, add more coefficients:
  26. 26. BigML, Inc 15Supervised Learning Logistic Regression Demo #1
  27. 27. BigML, Inc 16Supervised Learning LR Parameters 1. Bias: Allows an intercept term. Important if P(x=0) != 0 2. Regularization: • L1: prefers zeroing individual coefficients • L2: prefers pushing all coefficients towards zero 3. EPS: The minimum error between steps to stop. 4. Auto-scaling: Ensures that all features contribute equally. • Unless there is a specific need to not auto-scale, it is recommended.
  28. 28. BigML, Inc 17Supervised Learning Logistic Regression • How do we handle multiple classes? • What about non-numeric inputs?
  29. 29. BigML, Inc 18Supervised Learning LR - Multi-Class • Instead of a binary class ex: [ true, false ], we have multi- class ex: [ red, green, blue, … ] • k classes • solve one-vs-rest LR • coefficients βᵢ for 
 each class
  30. 30. BigML, Inc 19Supervised Learning LR - Field Codings • LR is expecting numeric values to perform regression. • How do we handle categorical values, or text? Class color=red color=blue color=green color=NULL red 1 0 0 0 blue 0 1 0 0 green 0 0 1 0 NULL 0 0 0 1 One-hot encoding Only one feature is "hot" for each class
  31. 31. BigML, Inc 20Supervised Learning LR - Field Codings Dummy Encoding Chooses a *reference class* requires one less degree of freedom Class color_1 color_2 color_3 *red* 0 0 0 blue 1 0 0 green 0 1 0 NULL 0 0 1
  32. 32. BigML, Inc 21Supervised Learning LR - Field Codings Contrast Encoding Field values must sum to zero Allows comparison between classes …. so which one? Class field "influence" red 0.5 positive blue -0.25 negative green -0.25 negative NULL 0 excluded
  33. 33. BigML, Inc 22Supervised Learning LR - Field Codings • The "text" type gives us new features that have counts of the number of times each token occurs in the text field. "Items" can be treated the same way. token "hippo" "safari" "zebra" instance_1 3 0 1 instance_2 0 11 4 instance_3 0 0 0 instance_4 1 0 3 Text / Items ?
  34. 34. BigML, Inc 23Supervised Learning Logistic Regression Demo #2
  35. 35. BigML, Inc 24Supervised Learning Curvilinear LR Instead of We could add a feature Where ???? Possible to add any higher order terms or other functions to match shape of data
  36. 36. BigML, Inc 25Supervised Learning Logistic Regression Demo #3
  37. 37. BigML, Inc 26Supervised Learning LR versus DT • Expects a "smooth" linear relationship with predictors. • LR is concerned with probability of a discrete outcome. • Lots of parameters to get wrong: 
 regularization, scaling, codings • Slightly less prone to over-fitting
 • Because fits a shape, might work better when less data available.
 • Adapts well to ragged non-linear relationships • No concern: classification, regression, multi-class all fine. • Virtually parameter free
 • Slightly more prone to over-fitting
 • Prefers surfaces parallel to parameter axes, but given enough data will discover any shape. Logistic Regression Decision Tree
  38. 38. BigML, Inc 27Supervised Learning Logistic Regression Demo #4