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) https://bigml.com/events/valencian-summer-school-in-machine-learning-2016

1. September 8-9, 2016

2. BigML, Inc 2
Ensembles
Poul Petersen
CIO, BigML, Inc
Making trees unstoppable

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. 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. BigML, Inc 5Supervised Learning
Ensemble Demo #1

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. 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. 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. BigML, Inc 9Supervised Learning
Ensemble Demo #2

10. BigML, Inc 10Supervised Learning
Model vs Bagging vs RF
Model Bagging Random Forest
Increasing Performance
Decreasing Interpretability
Increasing Stochasticity
Increasing Complexity

11. BigML, Inc 11Supervised Learning
Ensemble Demo #3

12. BigML, Inc 12Supervised Learning
• How many trees?
• How many nodes?
• Missing splits?
• Random candidates?
• Too many parameters?
SMACdown

13. BigML, Inc 2
Logistic Regression
Poul Petersen
CIO, BigML, Inc
Modeling probabilities

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. BigML, Inc 4Supervised Learning
Linear Regression

16. BigML, Inc 5Supervised Learning
Linear Regression

17. BigML, Inc 6Supervised Learning
Polynomial Regression

18. BigML, Inc 7Supervised Learning
• What function can we fit to discrete data?
Regression
Key Take-Away: Fitting a function to the data

19. BigML, Inc 8Supervised Learning
Discrete Data Function?

20. BigML, Inc 9Supervised Learning
Discrete Data Function?
????

21. BigML, Inc 10Supervised Learning
Logistic Function
•x→-∞ : f(x)→0
•x→∞ : f(x)→1
•Looks promising, but still not
"discrete"

22. BigML, Inc 11Supervised Learning
Probabilities
P≈0 P≈10<P<1

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. 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. BigML, Inc 14Supervised Learning
Logistic Regression
If we have multiple dimensions, add more coefficients:

26. BigML, Inc 15Supervised Learning
Logistic Regression Demo #1

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. BigML, Inc 17Supervised Learning
Logistic Regression
• How do we handle multiple classes?
• What about non-numeric inputs?

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. 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. 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. 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. 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. BigML, Inc 23Supervised Learning
Logistic Regression Demo #2

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. BigML, Inc 25Supervised Learning
Logistic Regression Demo #3

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. BigML, Inc 27Supervised Learning
Logistic Regression Demo #4