d

1. Learning From Data
Lecture 1
The Learning Problem
Introduction
Motivation
Credit Default - A Running Example
Summary of the Learning Problem
M. Magdon-Ismail
CSCI 4100/6100

2. Resources
1. Web Page: www.cs.rpi.edu/∼magdon/courses/learn.php
– course info: www.cs.rpi.edu/∼magdon/courses/learn/info.pdf
– slides: www.cs.rpi.edu/∼magdon/courses/learn/slides.html
– assignments: www.cs.rpi.edu/∼magdon/courses/learn/assign.html
2. Text Book:
Learning From Data
Abu-Mostafa, Magdon-Ismail, Lin
3. Book Forum: book.caltech.edu/bookforum
– discussion about any material in book including problems and exercises.
– additional material
4. TA.
5. Professor.
6. Prerequisites? assignment #0
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 2 /16 The storyline −→

3. The Storyline
1. What is Learning?
2. Can We do it?
3. How to do it?
4. How to do it well?
5. General principles?
6. Advanced techniques.
7. Other Learning Paradigms.
concepts
theory
practice
our language will be mathematics . . .
. . . our sword will be computer algorithms
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 3 /16 The applications −→

4. c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 4 /16 Define a tree −→

5. Let’s Define a Tree?
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 5 /16 A definition −→

6. Let’s Define a Tree?
A brown trunk moving upwards and branching with leaves . . .
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 6 /16 Does it work? −→

7. Are These Trees?
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 7 /16 Learning a Tree −→

8. Learning “What are Trees” is ‘Easy’
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 8 /16 Recognizing is easy −→

9. Defining is Hard; Recognizing is Easy
Hard to give a complete mathematical definition of a tree.
Even a 3 year old can tell a tree from a non-tree.
The 3 year old has learned from data. (Other tasks like graphics or GAN?)
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 9 /16 Rating movies −→

10. Learning to Rate Movies
• Can we predict how a viewer would rate a movie?
• Why? So that Netflix can make better movie recommendations, and get more rentals.
• $1 million prize for a mere 10% improvement in their recommendation system.
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 10 /16 There’s a pattern, we have data −→

11. Previous Ratings Reflect Future Ratings
movie:
viewer:
likes
Tom
Cruise?
likes
com
edy?
likes
action?
c
o
m
e
d
y
c
o
n
t
e
n
t
T
o
m
C
r
u
i
s
e
i
n
i
t
?
a
c
t
i
o
n
c
o
n
t
e
n
t
b
l
o
c
k
b
u
s
t
e
r
?
predicted
rating
Match corresponding factors
then add their contributions
prefers
blockbusters?
• Viewer taste & movie content imply viewer rating.
• No magical formula to predict viewer rating.
• Netflix has data. We can learn to identify movie
“categories” as well as viewer “preferences”
Class Motto:
A pattern exists. We don’t know it. We have data to learn it.
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 11 /16 Credit approval −→

12. Credit Approval
Let’s use a conceptual example to crystallize the issues.
age 32 years
gender male
salary 40,000
debt 26,000
years in job 1 year
years at home 3 years
. . . . . .
Approve for credit?
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 12 /16 There’s a pattern, we have data −→

13. Credit Approval
Let’s use a conceptual example to crystallize the issues.
• Using salary, debt, years in residence, etc., approve for credit or not.
• No magic credit approval formula.
• Banks have lots of data.
– customer information: salary, debt, etc.
– whether or not they defaulted on their credit.
age 32 years
gender male
salary 40,000
debt 26,000
years in job 1 year
years at home 3 years
. . . . . .
Approve for credit?
A pattern exists. We don’t know it. We have data to learn it.
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 13 /16 Key players −→

14. The Key Players
• Salary, debt, years in residence, . . . input x ∈ Rd
= X.
• Approve credit or not output y ∈ {−1, +1} = Y.
• True relationship between x and y target function f : X 7→ Y.
(The target f is unknown.)
• Data on customers data set D = (x1, y1), . . . , (xN, yN).
(yn = f(xn).)
X Y and D are given by the learning problem;
The target f is fixed but unknown.
We learn the function f from the data D.
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 14 /16 Learning −→

15. Learning
• Start with a set of candidate hypotheses H which you think are likely to represent f.
H = {h1, h2, . . . , }
is called the hypothesis set or model.
• Select a hypothesis g from H. The way we do this is called a learning algorithm.
• Use g for new customers. We hope g ≈ f.
X Y and D are given by the learning problem;
The target f is fixed but unknown.
We choose H and the learning algorithm
This is a very general setup (eg. choose H to be all possible hypotheses)
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 15 /16 Summary of learning setup −→

16. Summary of the Learning Setup
(ideal credit approval formula)
(historical records of credit customers)
(set of candidate formulas)
(learned credit approval formula)
UNKNOWN TARGET FUNCTION
f : X 7→ Y
TRAINING EXAMPLES
(x1, y1), (x2, y2), . . . , (xN , yN )
HYPOTHESIS SET
H
FINAL
HYPOTHESIS
g ≈ f
LEARNING
ALGORITHM
A
yn = f(xn)
c AM
L Creator: Malik Magdon-Ismail The Learning Problem: 16 /16