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A Gentle Introduction to Machine Learning
#VSSML17
September 2017
#VSSML17 A Gentle Introduction to Machine Learning Septe...
Outline
1 A Machine Learning Fable
2 Machine Learning: Some Intuition
3 School Overview
4 The Basic Idea: Create a Program...
Outline
1 A Machine Learning Fable
2 Machine Learning: Some Intuition
3 School Overview
4 The Basic Idea: Create a Program...
A Churn Problem
• You’re the CEO of a mobile
phone service
(congratulations!)
• Some percent of your
customers leave every...
Begin with the End In Mind
• Currently, you use a simple targeting strategy designed by hand,
which identifies the 10,000 (...
You Have The Data!
Luckily, you’ve been tracking customer outcomes for months, along
with a number of relevant customer at...
Now . . . magic!
• Can we use the data to create
a better targeting strategy, with
virtually no other work?
(Spoiler: YES)...
Outline
1 A Machine Learning Fable
2 Machine Learning: Some Intuition
3 School Overview
4 The Basic Idea: Create a Program...
In a Nutshell
• Collect row-column data about
past data from your prediction
problem (e.g., previous
months of customer da...
Traditional Expert System: Expert and Programmer
• Machine learning breaks the
traditional paradigm of expert
systems
• Ex...
Using Machine Learning: Data and Algorithm
• With machine learning, data replaces the expert
Is often more accurate than “...
Outline
1 A Machine Learning Fable
2 Machine Learning: Some Intuition
3 School Overview
4 The Basic Idea: Create a Program...
Today
• Morning
Introduction, Models, and Evaluations
Ensembles and Logistic Regressions
• Afternoon
Clusters and Anomaly ...
Tomorrow
• Morning
Basic Transformations, Feature Engineering
Time Series, Deepnets
• Afternoon
REST API, Bindings, and Ba...
Outline
1 A Machine Learning Fable
2 Machine Learning: Some Intuition
3 School Overview
4 The Basic Idea: Create a Program...
First: The Data
In the simplest and most numerous cases, machine learning begins
with row-column data.
Minutes Used Last M...
Rows: What is the Prediction About?
• Each row (or instance) in the
data represents the thing
about which you are making a...
Columns: What information Will Help Us Predict?
• Each column (or field, or feature) represents a piece of
information abou...
Objective: What are we Trying to Predict?
• One of the columns is special:
The “objective” is the column
in the data that ...
The Goal: Creating a Prediction Machine
• Feed this data to a machine learning algorithm
• The algorithm constructs a prog...
When is this a Good Idea?
• Remember: Machine learning
replaces expert and
programmer with data and
algorithm
• Is it hard...
People Can’t Tell You How They Do It
• Optical character recognition
(label a written character given
its image)
• Object ...
Human Experts are Rare or Expensive
• Medical diagnosis, MRI
reading, etc. (predict
bio-abnormalities from tests)
• Autono...
Everyone Needs Their Own Algorithm
• Spam detection (predict
spam/not spam from e-mail
text)
• Activity recognition (predi...
Every Little Bit Counts
• Market activity modeling
(buy/sell at a given time)
• Recognition tasks that are
“easy” (handwri...
When is this a Bad idea?
• Human experts are relatively cheap and easy to come by
Natural language processing for stock tr...
Outline
1 A Machine Learning Fable
2 Machine Learning: Some Intuition
3 School Overview
4 The Basic Idea: Create a Program...
Searching in Hypothesis Space
• Machine learning algorithms don’t exactly create a program
• More accurately, they search ...
Some Hypothesis Spaces
• Logistic regression: Sets of all
possible feature coefficients
and a bias term
• Neural network: W...
A Simple Hypothesis Space
Consider thresholds on a single variable, and predict “majority class” of
the resulting subsets
...
A Simple Hypothesis Space
Visits to Website > 0
#VSSML17 A Gentle Introduction to Machine Learning September 2017 31 / 55
A Simple Hypothesis Space
Minutes > 200
#VSSML17 A Gentle Introduction to Machine Learning September 2017 32 / 55
A Simple Hypothesis Space
Last Bill > $180
#VSSML17 A Gentle Introduction to Machine Learning September 2017 33 / 55
Good Question
• Subset purity
• Large difference between the
prior and posterior objective
distributions
• How to find the ...
Expanding the Space
There’s no reason to stop at just one question:
Last Bill > $180
#VSSML17 A Gentle Introduction to Mac...
Expanding the Space
There’s no reason to stop at just one question:
Last Bill > $180 AND Support Calls > 0
#VSSML17 A Gent...
The Decision Tree
• Why stop at two?
• Suggests a recursive
algorithm:
Choose a threshold
Partition the data into
subsets
...
Visualizing a Decision Tree
• Each node in the tree
represents a threshold; a
question asked of the data
• Branches leadin...
When to Stop?
• How do we know when to stop splitting the data?
• Several possible criteria:
When the subset is totally pu...
Predicting Using a Decision Tree
• The process of building the tree from the training data is called
learning, induction, ...
Outline
1 A Machine Learning Fable
2 Machine Learning: Some Intuition
3 School Overview
4 The Basic Idea: Create a Program...
Prediction Confidence - Intuition
• Each terminal node return a prediction . . .
• . . . but are some terminal nodes “bette...
Prediction Confidence - Calculation
• Compute a 95% confidence
bound about the probability
implied by the terminal node
subs...
Field Importance - Intuition
• Which fields drive the model predictions the most?
• Why might we want to know?
Improve data...
Field Importance - Calculation
• For each node in the tree:
Compute the error of the
prediction in the subset at
that node...
Outline
1 A Machine Learning Fable
2 Machine Learning: Some Intuition
3 School Overview
4 The Basic Idea: Create a Program...
Evaluating Your Model
• You want to know if your
model is good before putting it
in production
• In your data, you know th...
Don’t Evaluate on the Training Data!
• Never train and test on the same data
• Many non-parametric models are able to memo...
Watch out For Luck!
• Even splitting your data is
sometimes not enough
• You may draw an “easy”
subset (especially possibl...
Accuracy Can Be Misleading
• The top-line evaluation number is accuracy; the number of correct
predictions divided by the ...
The Confusion Matrix
• What to do if accuracy isn’t what you want?
• Look at the specific types of mistakes the algorithm m...
What If You Don’t Like it?
• You see your confusion matrix
and it’s making “the wrong
mistakes”
• Use “probability thresho...
The Right Thing is Always The Right Thing
• To guide threshold setting, it’s sometimes helpful to formulate a
loss functio...
Regression Evaluation: Generally Less Fraught
• To evaluate regression models, we first measure how much error
we would hav...
Fin!
Questions?
#VSSML17 A Gentle Introduction to Machine Learning September 2017 55 / 55
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VSSML17 L1. Introduction, Models, and Evaluations

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Valencian Summer School in Machine Learning 2017 - Day 1
Lecture 1: Introduction, Models, and Evaluations. By Charles Parker (BigML).
https://bigml.com/events/valencian-summer-school-in-machine-learning-2017

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VSSML17 L1. Introduction, Models, and Evaluations

  1. 1. A Gentle Introduction to Machine Learning #VSSML17 September 2017 #VSSML17 A Gentle Introduction to Machine Learning September 2017 1 / 55
  2. 2. Outline 1 A Machine Learning Fable 2 Machine Learning: Some Intuition 3 School Overview 4 The Basic Idea: Create a Program From Data 5 Modeling 6 Do More With Your Model 7 Evaluation #VSSML17 A Gentle Introduction to Machine Learning September 2017 2 / 55
  3. 3. Outline 1 A Machine Learning Fable 2 Machine Learning: Some Intuition 3 School Overview 4 The Basic Idea: Create a Program From Data 5 Modeling 6 Do More With Your Model 7 Evaluation #VSSML17 A Gentle Introduction to Machine Learning September 2017 3 / 55
  4. 4. A Churn Problem • You’re the CEO of a mobile phone service (congratulations!) • Some percent of your customers leave every month (churn) • You want to reach out to the ones you think are going to leave next month (but you can’t call everyone) • And who might they be? #VSSML17 A Gentle Introduction to Machine Learning September 2017 4 / 55
  5. 5. Begin with the End In Mind • Currently, you use a simple targeting strategy designed by hand, which identifies the 10,000 (5%) of customers most likely to churn • For every five people you call, two are considering leaving (4,000, precision of 40%) • On these customers, your operators can convince half (2,000) to stay • Each customer saved is worth $500 (Total revenue = $500 * 2000 = $1m) • What if you could increase that precision to 60%? (Hint: More Money!) #VSSML17 A Gentle Introduction to Machine Learning September 2017 5 / 55
  6. 6. You Have The Data! Luckily, you’ve been tracking customer outcomes for months, along with a number of relevant customer attributes. Minutes Used Last Month Bill Support Calls Website Visits Churn? 104 $103.60 0 0 No 124 $56.33 1 0 No 56 $214.60 2 0 Yes 2410 $305.60 0 5 No 536 $145.70 0 0 No 234 $122.09 0 1 No 201 $185.76 1 7 Yes 111 $83.60 3 2 No #VSSML17 A Gentle Introduction to Machine Learning September 2017 6 / 55
  7. 7. Now . . . magic! • Can we use the data to create a better targeting strategy, with virtually no other work? (Spoiler: YES) • Can we use the data to evaluate that strategy, confirming a better false positive rate? (Spoiler: YES) • How? (Spoiler: MACHINE LEARNING) #VSSML17 A Gentle Introduction to Machine Learning September 2017 7 / 55
  8. 8. Outline 1 A Machine Learning Fable 2 Machine Learning: Some Intuition 3 School Overview 4 The Basic Idea: Create a Program From Data 5 Modeling 6 Do More With Your Model 7 Evaluation #VSSML17 A Gentle Introduction to Machine Learning September 2017 8 / 55
  9. 9. In a Nutshell • Collect row-column data about past data from your prediction problem (e.g., previous months of customer data) • Feed this data to a machine learning algorithm • The algorithm creates a program (alternately, “predictive model” or “classifier”) that makes predictions on future data #VSSML17 A Gentle Introduction to Machine Learning September 2017 9 / 55
  10. 10. Traditional Expert System: Expert and Programmer • Machine learning breaks the traditional paradigm of expert systems • Experts know how the prediction is made • Programmers know how to translate the expert’s knowledge into a computer program that makes the prediction • Constructing a system requires both (though they may be the same person) #VSSML17 A Gentle Introduction to Machine Learning September 2017 10 / 55
  11. 11. Using Machine Learning: Data and Algorithm • With machine learning, data replaces the expert Is often more accurate than “expertise” Article: “Specialist Knowledge is Useless and Unhelpful”1 Requires no human expertise except how to collect the data The data may already be there • Algorithms replace programmers Algorithms are faster than programmers, enabling iteration Algorithms are more modular than programmers Data offers the opportunity for performance measurement (which you would be doing in any case, right?) 1 https://www.newscientist.com/article/ mg21628930-400-specialist-knowledge-is-useless-and-unhelpful/ #VSSML17 A Gentle Introduction to Machine Learning September 2017 11 / 55
  12. 12. Outline 1 A Machine Learning Fable 2 Machine Learning: Some Intuition 3 School Overview 4 The Basic Idea: Create a Program From Data 5 Modeling 6 Do More With Your Model 7 Evaluation #VSSML17 A Gentle Introduction to Machine Learning September 2017 12 / 55
  13. 13. Today • Morning Introduction, Models, and Evaluations Ensembles and Logistic Regressions • Afternoon Clusters and Anomaly Detection Association Discovery and Latent Dirichlet Allocation #VSSML17 A Gentle Introduction to Machine Learning September 2017 13 / 55
  14. 14. Tomorrow • Morning Basic Transformations, Feature Engineering Time Series, Deepnets • Afternoon REST API, Bindings, and Basic Workflows Advanced Workflows: Algorithms as Workflows #VSSML17 A Gentle Introduction to Machine Learning September 2017 14 / 55
  15. 15. Outline 1 A Machine Learning Fable 2 Machine Learning: Some Intuition 3 School Overview 4 The Basic Idea: Create a Program From Data 5 Modeling 6 Do More With Your Model 7 Evaluation #VSSML17 A Gentle Introduction to Machine Learning September 2017 15 / 55
  16. 16. First: The Data In the simplest and most numerous cases, machine learning begins with row-column data. Minutes Used Last Month Bill Support Calls Website Visits Churn? 104 $103.60 0 0 No 124 $56.33 1 0 No 56 $214.60 2 0 Yes 2410 $305.60 0 5 No 536 $145.70 0 0 No 234 $122.09 0 1 No 201 $185.76 1 7 Yes 111 $83.60 3 2 No #VSSML17 A Gentle Introduction to Machine Learning September 2017 16 / 55
  17. 17. Rows: What is the Prediction About? • Each row (or instance) in the data represents the thing about which you are making a prediction • Churn prediction: Each row is a customer • Medical diagnosis: Each row is a patient • Credit card fraud detection: Each row is a transaction • Market closing price forecast: Each row is a day #VSSML17 A Gentle Introduction to Machine Learning September 2017 17 / 55
  18. 18. Columns: What information Will Help Us Predict? • Each column (or field, or feature) represents a piece of information about the thing in each row Churn prediction: minutes used, calls to support Medical diagnosis: BMI, temperature, test results Credit card fraud detection: Amount, transaction type, Geographical information (maybe difference from previous transactions) Market closing price forecast: Opening price, previous day’s open/close, five day trend • How much and what type of information should you collect? There’s no general answer here; it’s “domain-specific” Question one: How much does it matter (as a function of model accuracy)? Question two: How much does it cost to collect? #VSSML17 A Gentle Introduction to Machine Learning September 2017 18 / 55
  19. 19. Objective: What are we Trying to Predict? • One of the columns is special: The “objective” is the column in the data that contains the information we want to predict • Churn prediction: Customer did or did not churn • Medical diagnosis: Positive or negative for some disease • Credit card fraud detection: Transaction is or is not fraudulent • Market closing price forecast: The closing price on the given day #VSSML17 A Gentle Introduction to Machine Learning September 2017 19 / 55
  20. 20. The Goal: Creating a Prediction Machine • Feed this data to a machine learning algorithm • The algorithm constructs a program (or model or classifier): Inputs: A single row of data, excluding the objective Outputs: A prediction of the objective for that row • Most importantly, the input row need not come from the training data #VSSML17 A Gentle Introduction to Machine Learning September 2017 20 / 55
  21. 21. When is this a Good Idea? • Remember: Machine learning replaces expert and programmer with data and algorithm • Is it hard to find an expert? • Can the programmer encode the knowledge (quickly enough, accurately enough)? #VSSML17 A Gentle Introduction to Machine Learning September 2017 21 / 55
  22. 22. People Can’t Tell You How They Do It • Optical character recognition (label a written character given its image) • Object detection (image does or does not contain an object) • Speech recognition (label a sentence given spoken sound file) #VSSML17 A Gentle Introduction to Machine Learning September 2017 22 / 55
  23. 23. Human Experts are Rare or Expensive • Medical diagnosis, MRI reading, etc. (predict bio-abnormalities from tests) • Autonomous helicopter operation • Game playing (at extremely high levels) #VSSML17 A Gentle Introduction to Machine Learning September 2017 23 / 55
  24. 24. Everyone Needs Their Own Algorithm • Spam detection (predict spam/not spam from e-mail text) • Activity recognition (predict user activity from mobile sensors) • Location prediction (predict future user location given current state) • Anything that’s “personalized”, and generates enough data (mobiles!) • Aside: IoT has the potential to be huge for machine learning #VSSML17 A Gentle Introduction to Machine Learning September 2017 24 / 55
  25. 25. Every Little Bit Counts • Market activity modeling (buy/sell at a given time) • Recognition tasks that are “easy” (handwriting detection) • Churn prediction? • Any time there’s a performance critical hand-built system #VSSML17 A Gentle Introduction to Machine Learning September 2017 25 / 55
  26. 26. When is this a Bad idea? • Human experts are relatively cheap and easy to come by Natural language processing for stock traders Automatic defect detection in printer operation • A program is easily written by hand Some simple if-then rules often perform well The best program is the one that’s already there • The data is difficult or expensive to acquire Medical domains Automatic processing of images #VSSML17 A Gentle Introduction to Machine Learning September 2017 26 / 55
  27. 27. Outline 1 A Machine Learning Fable 2 Machine Learning: Some Intuition 3 School Overview 4 The Basic Idea: Create a Program From Data 5 Modeling 6 Do More With Your Model 7 Evaluation #VSSML17 A Gentle Introduction to Machine Learning September 2017 27 / 55
  28. 28. Searching in Hypothesis Space • Machine learning algorithms don’t exactly create a program • More accurately, they search for a program consistent with the training data Search must be very clever Usually there is some sort of “Occam’s razor” involved • The space of possible solutions in which the algorithm search is called its hypothesis space • The algorithm is trying to do “reverse science”! #VSSML17 A Gentle Introduction to Machine Learning September 2017 28 / 55
  29. 29. Some Hypothesis Spaces • Logistic regression: Sets of all possible feature coefficients and a bias term • Neural network: Weights for all nodes in the network • Support vector machines: Coefficients on each training point • Note: Parametric vs. Non-parametric #VSSML17 A Gentle Introduction to Machine Learning September 2017 29 / 55
  30. 30. A Simple Hypothesis Space Consider thresholds on a single variable, and predict “majority class” of the resulting subsets #VSSML17 A Gentle Introduction to Machine Learning September 2017 30 / 55
  31. 31. A Simple Hypothesis Space Visits to Website > 0 #VSSML17 A Gentle Introduction to Machine Learning September 2017 31 / 55
  32. 32. A Simple Hypothesis Space Minutes > 200 #VSSML17 A Gentle Introduction to Machine Learning September 2017 32 / 55
  33. 33. A Simple Hypothesis Space Last Bill > $180 #VSSML17 A Gentle Introduction to Machine Learning September 2017 33 / 55
  34. 34. Good Question • Subset purity • Large difference between the prior and posterior objective distributions • How to find the best question? Try them all! #VSSML17 A Gentle Introduction to Machine Learning September 2017 34 / 55
  35. 35. Expanding the Space There’s no reason to stop at just one question: Last Bill > $180 #VSSML17 A Gentle Introduction to Machine Learning September 2017 35 / 55
  36. 36. Expanding the Space There’s no reason to stop at just one question: Last Bill > $180 AND Support Calls > 0 #VSSML17 A Gentle Introduction to Machine Learning September 2017 36 / 55
  37. 37. The Decision Tree • Why stop at two? • Suggests a recursive algorithm: Choose a threshold Partition the data into subsets Choose a threshold for the subsets, and so on • This is a decision tree #VSSML17 A Gentle Introduction to Machine Learning September 2017 37 / 55
  38. 38. Visualizing a Decision Tree • Each node in the tree represents a threshold; a question asked of the data • Branches leading from the node indicate the two or more paths data could take • Thickness of the branches indicates the amount of training data that took that path • At the leaf or terminal node, we decide on a prediction; usually the majority class for the subset at that leaf. #VSSML17 A Gentle Introduction to Machine Learning September 2017 38 / 55
  39. 39. When to Stop? • How do we know when to stop splitting the data? • Several possible criteria: When the subset is totally pure (Note: Subsets of size 1 are trivially pure) When the size reaches a predetermined minimum When the number of nodes or tree depth is too large When you can’t get any statistically significant improvement • Nodes that don’t meet the latter criteria can be removed after tree construction via pruning #VSSML17 A Gentle Introduction to Machine Learning September 2017 39 / 55
  40. 40. Predicting Using a Decision Tree • The process of building the tree from the training data is called learning, induction, or training. • The payoff of using the tree for prediction is inference, prediction, or scoring. • To do prediction with a tree, given an instance: Start at the root node, subjecting the instance to the threshold “Send” the instance down the appropriate path, to the next threshold Continue until you reach a terminal node, then make a prediction #VSSML17 A Gentle Introduction to Machine Learning September 2017 40 / 55
  41. 41. Outline 1 A Machine Learning Fable 2 Machine Learning: Some Intuition 3 School Overview 4 The Basic Idea: Create a Program From Data 5 Modeling 6 Do More With Your Model 7 Evaluation #VSSML17 A Gentle Introduction to Machine Learning September 2017 41 / 55
  42. 42. Prediction Confidence - Intuition • Each terminal node return a prediction . . . • . . . but are some terminal nodes “better” than others? • Given a terminal node, how “confident” are we (perhaps for ranking)? • Depends on two things: The number of instances that reach that terminal node The purity of that subset • Think of each terminal node as a “mixture of experts” #VSSML17 A Gentle Introduction to Machine Learning September 2017 42 / 55
  43. 43. Prediction Confidence - Calculation • Compute a 95% confidence bound about the probability implied by the terminal node subset • The Wilson score interval: ˆp + 1 2n z2 ± z ˆp(1−ˆp) n + z2 4n2 1 + 1 nz2 • Use the lower bound as the confidence • Similarish for regression models #VSSML17 A Gentle Introduction to Machine Learning September 2017 43 / 55
  44. 44. Field Importance - Intuition • Which fields drive the model predictions the most? • Why might we want to know? Improve data collection practices Reduce the number of features in your model Model validation (Watch out for data leakage: objective in the training data) • Depends on two things: Number of times the node uses that feature for the threshold How much it “matters” when it’s used #VSSML17 A Gentle Introduction to Machine Learning September 2017 44 / 55
  45. 45. Field Importance - Calculation • For each node in the tree: Compute the error of the prediction in the subset at that node (before) Compute the error of the two child subsets (after) Compute the improvement (the difference between the two) • Sum up the improvements for all nodes corresponding to a given feature #VSSML17 A Gentle Introduction to Machine Learning September 2017 45 / 55
  46. 46. Outline 1 A Machine Learning Fable 2 Machine Learning: Some Intuition 3 School Overview 4 The Basic Idea: Create a Program From Data 5 Modeling 6 Do More With Your Model 7 Evaluation #VSSML17 A Gentle Introduction to Machine Learning September 2017 46 / 55
  47. 47. Evaluating Your Model • You want to know if your model is good before putting it in production • In your data, you know the right answer! • So use the data to test how often your model is right #VSSML17 A Gentle Introduction to Machine Learning September 2017 47 / 55
  48. 48. Don’t Evaluate on the Training Data! • Never train and test on the same data • Many non-parametric models are able to memorize the training data • This results in evaluations that are sometimes wildly optimistic (which is the worst) • Solution: Split your data into training and testing subsets (80% and 20% is customary) #VSSML17 A Gentle Introduction to Machine Learning September 2017 48 / 55
  49. 49. Watch out For Luck! • Even splitting your data is sometimes not enough • You may draw an “easy” subset (especially possible with small data) • Can be disastrous if the “edge” you’re expecting is small • Solution: Do multiple runs and average (or cross-validate) #VSSML17 A Gentle Introduction to Machine Learning September 2017 49 / 55
  50. 50. Accuracy Can Be Misleading • The top-line evaluation number is accuracy; the number of correct predictions divided by the number of total predictions • Accuracy can be misleading! Suppose only 5% of my customers churn every month Suppose I just predict “no churn” for everybody Ta-da! 95% accuracy! But I get the same 95% accuracy if predict all “churn” instances correct with a 50% false positive rate! • Lesson: Accuracy is broken when classes are unbalanced #VSSML17 A Gentle Introduction to Machine Learning September 2017 50 / 55
  51. 51. The Confusion Matrix • What to do if accuracy isn’t what you want? • Look at the specific types of mistakes the algorithm makes • This is the confusion matrix #VSSML17 A Gentle Introduction to Machine Learning September 2017 51 / 55
  52. 52. What If You Don’t Like it? • You see your confusion matrix and it’s making “the wrong mistakes” • Use “probability threshold” to set the model’s aggressiveness • Can be used to set implicit mistake penalties • Can be used to conform to external constraints (e.g., a “budget” for positives) #VSSML17 A Gentle Introduction to Machine Learning September 2017 52 / 55
  53. 53. The Right Thing is Always The Right Thing • To guide threshold setting, it’s sometimes helpful to formulate a loss function • A common form is the cost matrix: How much does a mistake of each type cost? Total cost = cFPnFP + cFNnFN where cx is the cost of a mistake of type x (false positive or false negative), and nx is the number of mistakes of that type. • This is an important part of what you, the domain expert, bring to the table! Don’t ignore it! #VSSML17 A Gentle Introduction to Machine Learning September 2017 53 / 55
  54. 54. Regression Evaluation: Generally Less Fraught • To evaluate regression models, we first measure how much error we would have if we just predicted the mean objective for the whole dataset • This functions as a baseline • How much (as a fraction) of the baseline error does the model eliminate? 1.0 is best 0.0 is not good at all And of course, we can go negative • This is R2 • What is “good?” Again, this is domain-specific, but at least improvement with R2 is usually fairly monotonic #VSSML17 A Gentle Introduction to Machine Learning September 2017 54 / 55
  55. 55. Fin! Questions? #VSSML17 A Gentle Introduction to Machine Learning September 2017 55 / 55

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