1. What is machine learning
Introduction
What is machine learning
Machine Learning

2. Machine Learning definition
Arthur Samuel (1959). Machine Learning: Field of study that gives computers the ability to learn without being explicitly programmed.
Tom Mitchell (1998) Well-posed Learning Problem: A computer program is said to learn from experience E with respect to some task T and some performance measure P, if its performance on T, as measured by P, improves with experience E.

3. Machine learning algorithms:
Supervised learning
Unsupervised learning
Others: Reinforcement learning, recommender systems.
Also talk about: Practical advice for applying learning algorithms.

4. Introduction
Supervised Learning
Machine Learning

5. Housing price prediction.
in 1000’s
Size in feet2
Supervised Learning
“right answers” given
Regression: Predict continuous valued output (price)

6. Breast cancer (malignant, benign)
Harmful
Not Harmful
Breast cancer (malignant, benign)
Classification
Discrete valued output (0 or 1)
1(Y)
Malignant?
0(N)
Tumor Size
[Feature 1]
Another way of representing above graph
Tumor Size
We have given training data set (past medical records) which tells whether a particular tumor size lead to a breast cancer or not. We want to know , the given tumor size falls in which category

7. Uniformity of Cell Size Uniformity of Cell Shape …
Clump Thickness
Uniformity of Cell Size
Uniformity of Cell Shape …
Age
[Feature 2]
Tumor Size
[Feature 1]

8. You’re running a company, and you want to develop learning algorithms to address each of two problems.
Problem 1: You have a large inventory of identical items. You want to predict how many of these items will sell over the next 3 months.
Problem 2: You’d like software to examine individual customer accounts, and for each account decide if it has been hacked/compromised.
Should you treat these as classification or as regression problems?
Treat both as classification problems.
Treat problem 1 as a classification problem, problem 2 as a regression problem.
Treat problem 1 as a regression problem, problem 2 as a classification problem.
Treat both as regression problems.

9. Unsupervised Learning
Introduction
Unsupervised Learning
Machine Learning

10. Supervised Learning x2 x1

11. Unsupervised Learningx2 x1

12. Organize computing clusters Social network analysis
Image credit: NASA/JPL-Caltech/E. Churchwell (Univ. of Wisconsin, Madison)
Astronomical data analysis image obtained from NASA website.
RCW 79 is seen in the southern Milky Way, 17,200 light-years from Earth in the constellation Centaurus. The bubble is 70-light years in diameter, and probably took about one million years to form from the radiation and winds of hot young stars. The balloon of gas and dust is an example of stimulated star formation. Such stars are born when the hot bubble expands into the interstellar gas and dust around it. RCW 79 has spawned at least two groups of new stars along the edge of the large bubble. Some are visible inside the small bubble in the lower left corner. Another group of baby stars appears near the opening at the top. NASA's Spitzer Space Telescope easily detects infrared light from the dust particles in RCW 79. The young stars within RCW79 radiate ultraviolet light that excites molecules of dust within the bubble. This causes the dust grains to emit infrared light that is detected by Spitzer and seen here as the extended red features. Image credit: NASA/JPL-Caltech/E. Churchwell (Univ. of Wisconsin, Madison)
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Market segmentation
Astronomical data analysis

13. Cocktail party problem
Speaker #1
Microphone #1
Speaker #2
Microphone #2

14. Microphone #1: Microphone #2: Output #1: Output #2: Microphone #1:
[Audio clips courtesy of Te-Won Lee.]

15. Cocktail party problem algorithm
[W,s,v] = svd((repmat(sum(x.*x,1),size(x,1),1).*x)*x');
[Source: Sam Roweis, Yair Weiss & Eero Simoncelli]

16. Of the following examples, which would you address using an unsupervised learning algorithm? (Check all that apply.)
Given labeled as spam/not spam, learn a spam filter.
Given a set of news articles found on the web, group them into set of articles about the same story.
Given a database of customer data, automatically discover market segments and group customers into different market segments.
Given a dataset of patients diagnosed as either having diabetes or not, learn to classify new patients as having diabetes or not.

17. Model representation Linear regression with one variable
Machine Learning

18. Housing Prices (Portland, OR)
(in 1000s of dollars)
Size (feet2)
Supervised Learning
Given the “right answer” for each example in the data.
Regression Problem
Predict real-valued output

19. Training set of housing prices (Portland, OR)
Size in feet2 (x)
Price ($) in 1000's (y)
2104
460
1416
232
1534
315
852
178 …
Notation:
m = Number of training examples
x’s = “input” variable / features
y’s = “output” variable / “target” variable

20. Training Set How do we represent h ? Learning Algorithm Size of house
Estimated price
Linear regression with one variable.
Univariate linear regression.

21. Linear regression with one variable
Cost function
Machine Learning

22. Training Set Hypothesis: ‘s: Parameters How to choose ‘s ?
Size in feet2 (x)
Price ($) in 1000's (y)
2104
460
1416
232
1534
315
852
178 …
Hypothesis:
‘s: Parameters
How to choose ‘s ?

24. Idea: Choose so that is close to for our training examplesy x
Idea: Choose so that is close to for our training examples

25. Cost function intuition I
Linear regression with one variable
Cost function intuition I
Machine Learning

26. Simplified
Hypothesis:
Parameters:
Cost Function:
Goal:

27. (for fixed , this is a function of x)
(function of the parameter ) y x

28. (function of the parameter )
(for fixed , this is a function of x) y x

29. (function of the parameter )
(for fixed , this is a function of x) y x

30. Cost function intuition II
Linear regression with one variable
Cost function intuition II
Machine Learning

31. Hypothesis:
Parameters:
Cost Function:
Goal:

32. (for fixed , this is a function of x)
(function of the parameters )
Price ($)
in 1000’s
Size in feet2 (x)

34. (for fixed , this is a function of x)
(function of the parameters )

35. (for fixed , this is a function of x)
(function of the parameters )

36. (for fixed , this is a function of x)
(function of the parameters )

37. (for fixed , this is a function of x)
(function of the parameters )

38. Linear regression with one variable
Gradient descent
Machine Learning

39. Have some function
Want
Outline:
Start with some
Keep changing to reduce until we hopefully end up at a minimum

40. J(0,1) 1 0

41. J(0,1) 1 0

42. Gradient descent algorithm
Correct: Simultaneous update
Incorrect:

43. Gradient descent intuition
Linear regression with one variable
Gradient descent intuition
Machine Learning

44. Gradient descent algorithm

46. If α is too small, gradient descent can be slow.
If α is too large, gradient descent can overshoot the minimum. It may fail to converge, or even diverge.

47. at local optima
Current value of

48. Gradient descent can converge to a local minimum, even with the learning rate α fixed.
As we approach a local minimum, gradient descent will automatically take smaller steps. So, no need to decrease α over time.

49. Gradient descent for linear regression
Linear regression with one variable
Gradient descent for linear regression
Machine Learning

50. Gradient descent algorithm
Linear Regression Model

52. Gradient descent algorithm
update
and
simultaneously

53. J(0,1) 1 0

55. (for fixed , this is a function of x)
(function of the parameters )

56. (for fixed , this is a function of x)
(function of the parameters )

57. (for fixed , this is a function of x)
(function of the parameters )

58. (for fixed , this is a function of x)
(function of the parameters )

59. (for fixed , this is a function of x)
(function of the parameters )

60. (for fixed , this is a function of x)
(function of the parameters )

61. (for fixed , this is a function of x)
(function of the parameters )

62. (for fixed , this is a function of x)
(function of the parameters )

63. (for fixed , this is a function of x)
(function of the parameters )

64. “Batch”: Each step of gradient descent uses all the training examples.
“Batch” Gradient Descent
“Batch”: Each step of gradient descent uses all the training examples.

65. Linear Algebra review (optional)
Matrices and vectors
Machine Learning

66. Matrix: Rectangular array of numbers:
Dimension of matrix: number of rows x number of columns

67. Matrix Elements (entries of matrix)
“ , entry” in the row, column.

68. Vector: An n x 1 matrix.
1-indexed vs 0-indexed:
element
n-dimensional vector

69. Addition and scalar multiplication
Linear Algebra review (optional)
Addition and scalar multiplication
Machine Learning

70. Matrix Addition

71. Scalar Multiplication

72. Combination of Operands

73. Matrix-vector multiplication
Linear Algebra review (optional)
Matrix-vector multiplication
Machine Learning

74. Example

75. To get , multiply ’s row with elements of vector , and add them up.
Details:
m x n matrix
(m rows,
n columns)
n x 1 matrix
(n-dimensional
vector)
m-dimensional vector
To get , multiply ’s row with elements of vector , and add them up.

76. Example

77. House sizes:

78. Matrix-matrix multiplication
Linear Algebra review (optional)
Matrix-matrix multiplication
Machine Learning

79. Example

80. Details: The column of the matrix is obtained by multiplying
m x n matrix
(m rows,
n columns)
n x o matrix
(n rows,
o columns)
m x o
matrix
The column of the matrix is obtained by multiplying
with the column of (for = 1,2,…,o)

81. Example 7 2 7

82. House sizes:
Have 3 competing hypotheses: 1. 2. 3.
Matrix
Matrix

83. Matrix multiplication properties
Linear Algebra review (optional)
Matrix multiplication properties
Machine Learning

84. Let and be matrices. Then in general,
(not commutative.)
E.g.

85. Let
Compute
Let
Compute

86. Examples of identity matrices:
Identity Matrix
Denoted (or ).
Examples of identity matrices:
2 x 2
3 x 3
4 x 4
For any matrix ,

87. Inverse and transpose Linear Algebra review (optional)
Machine Learning

88. Not all numbers have an inverse.
Matrix inverse:
If A is an m x m matrix, and if it has an inverse,
Matrices that don’t have an inverse are “singular” or “degenerate”

89. Matrix Transpose
Example:
Let be an m x n matrix, and let
Then is an n x m matrix, and