1.3 Six Elements of ML
A defining framework for understanding concepts in the course
Recap: Machine Learning
What we saw in the previous chapter?
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A jargon cloud
How do you make sense of all the jargon?
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From jargons to jars
What are the six jars of Machine Lerarning
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Data data everywhere
What is the fuel of Machine Learning?
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Data data everywhere
How do you feed data to machines ?
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We encode all data into numbers - typically high dimension
For instance, in this course you will learn to embed image and text data as large vectors
Data entries are related - eg. given a MRI scan whether there is a tumour or not
Include a table that shows two/three MRI scans in first col, shows large vectors in second column, 1/0 for last column of whether there is tumour or not
Include a table that shows two/three reviews in first col, shows large vectors in second column, 1/0 for last column for whether review is positive or negative
Title the columns as x and y
All data encoded as numbers
Typically high dimensional
\mathbb{R}^n
x
y
| scans | ||
|---|---|---|
| 2.3 | 5.9 | ... | 11.0 | -0.3 | 8.9 | 0 |
|---|
| -8.5 | -1.7 | ... | -1.3 | 9.0 | 7.2 | 1 |
|---|
| -0.4 | 6.7 | ... | -2.4 | 4.7 | -7.3 | 0 |
|---|
| 1.6 | -0.4 | ... | -4.6 | 6.4 | 1.9 | 1 |
|---|
| 3.9 | -4.1 | ... | 6.7 | -3.1 | 2.1 | 1 |
|---|
| 5.1 | 3.7 | ... | 1.8 | -4.2 | 9.3 | 1 |
|---|
Data data everywhere
How do you feed data to machines ?
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We encode all data into numbers - typically high dimension
For instance, in this course you will learn to embed image and text data as large vectors
Data entries are related - eg. given a MRI scan whether there is a tumour or not
Include a table that shows two/three MRI scans in first col, shows large vectors in second column, 1/0 for last column of whether there is tumour or not
Include a table that shows two/three reviews in first col, shows large vectors in second column, 1/0 for last column for whether review is positive or negative
Title the columns as x and y
All data encoded as numbers
Typically high dimensional
\mathbb{R}^n
x
y
| Document | ||
|---|---|---|
| 1.9 | 3.2 | ... | -9.8 | -6.7 | 1.2 |
|---|
| 1.3 | 3.6 | ... | -5.4 | 9.1 | 2.3 |
|---|
| 0.4 | 7.6 | ... | -0.1 | -1.4 | 8.7 |
|---|
| 1.5 | -0.8 | ... | 7.8 | 8.4 | 0.3 |
|---|
Don't buy this MI 6 Pro, Speaker volume is very bad
Delivered as shown. Good price and fits perfect
What a phone.. A handy epic phone. MI at its best ...
Its look stunning in pictures , but not in real.
negative
negative
positive
positive
Amazing camera and battery. Good deal!
| 2.5 | -5.7 | ... | 0.9 | 5.3 | -8.1 |
|---|
positive
Data data everywhere
How do you feed data to machines ?
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| 1.3 | -4.3 | 2.1 | -6.7 | ... | 1.5 | 8.9 | 10.1 | -4.5 |
| 2.6 | 7.9 | -0.3 | 8.1 | ... | -4.2 | 0.3 | 1.2 | 9.4 |
| -5.2 | -3.2 | 4.2 | 0.3 | ... | 3.5 | 8.3 | -1.4 | -8.7 |
| 8.5 | 2.1 | -6.3 | 5.3 | ... | 7.2 | -1.3 | -4.5 | 11.8 |
| 2.3 | -5.6 | -1.2 | 7.8 | ... | 9.9 | 10.1 | -1.1 | 3.5 |
All data encoded as numbers
Typically high dimensional
\mathbb{R}^n
In this course
text
image
Data curation
Where do I get the data from?
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I am lucky
I am rich
I am smart
+ मुंबई
= मुंबई
In this course
Data data everywhere
What is the fuel of Machine Learning?
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Data
Tasks
What do you do with this data?
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Input
Output
Hello John,
Hello John,
From product description to structured specifications
From specifications + revies to writing FAQs
From specifications + reviews + FAQs to Question Answering
From specifications + reviews + personal data to recommendations
+
+
+
Hello John,
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Tasks
What do you do with this data?
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From images identify people
Shahrukh Khan
Aamir Khan
From images identify activities
Eating
From images identify places
Gym
From posts recommend posts
Output
Input
Tasks
What do you do with this data?
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Supervised
Classification
x
y
| 3.2 | 5.9 | ... | 11.0 | 8.9 | 1 |
|---|
| -8.5 | -1.7 | ... | 9.0 | 7.2 | 1 |
|---|
| -0.4 | 6.7 | ... | 4.7 | -7.2 | 0 |
|---|
| 2.7 | 3.1 | ... | -2.1 | 9.7 | 0 |
|---|
| 3.9 | 7.8 | ... | -5.1 | 3.7 | 0 |
|---|
| 7.1 | 0.9 | ... | 1.5 | -4.2 | 1 |
|---|
Tasks
What do you do with this data?
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Supervised
Regression
x
| -8.5 | -1.7 | ... | 9.0 | 7.2 | 2.3 | 1.2 | 9.2 | 10.1 |
|---|
x
y
left\_x
left\_y
width
height
| 0.9 | -2.1 | ... | -8.1 | 1.9 | 4.3 | 4.2 | 7.1 | 5.1 |
|---|
| 2.9 | -4.5 | ... | -3.7 | 8.9 | 2.3 | 7.2 | 6.9 | 7.3 |
|---|
width
height
left\_x
left\_y
Tasks
What do you do with this data?
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Clustering
Unupervised
x
| 3.2 | 5.9 | ... | 11.0 | 8.9 |
|---|
| -8.5 | -1.7 | ... | 9.0 | 7.2 |
|---|
| -0.4 | 6.7 | ... | 4.7 | -4.1 |
|---|
| 2.7 | 3.1 | ... | -2.1 | 9.7 |
|---|
| 3.9 | 7.8 | ... | -5.1 | 3.7 |
|---|
| 7.1 | 0.9 | ... | 1.5 | -4.2 | 1 |
|---|
Tasks
What do you do with this data?
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Generation
Unupervised
x
| 3.2 | 5.9 | ... | 11.0 | 8.9 |
|---|
| -8.5 | -1.7 | ... | 9.0 | 7.2 |
|---|
| -0.4 | 6.7 | ... | 4.7 | -4.1 |
|---|
| 2.7 | 3.1 | ... | -2.1 | 9.7 |
|---|
| 3.9 | 7.8 | ... | -5.1 | 3.7 |
|---|
| 7.1 | 0.9 | ... | 1.5 | -4.2 | 1 |
|---|
Tasks
What do you do with this data?
Generation
Unupervised
x
| Tweets | |
|---|---|
| 2.3 | 5.9 | ... | 11.0 | -0.3 | 8.9 |
|---|
| -8.5 | -1.7 | ... | -1.3 | 9.0 | 7.2 |
|---|
| -0.4 | 6.7 | ... | -2.4 | 4.7 | -6.2 |
|---|
| 1.6 | -0.4 | ... | -4.6 | 6.4 | 1.9 |
|---|
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Tasks
What do you do with this data?
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\( `` \)
Supervised Learning has created 99% of economic value in AI
In this course
Classification
Regression
x
y
width
height
left\_x
left\_y
Tasks
What do you do with this data?
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Data
Task
What is the mathematical formulation of a task?
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\( x \)
\( y \)
bat
car
dog
cat
Models
\( \left[\begin{array}{lcr} 2.1, 1.2, \dots, 5.6, 7.2 \end{array} \right]\)
\( \left[\begin{array}{lcr} 0, 0, 1,0, 0 \end{array} \right]\)
\( y = f(x) \) [true relation, unknown]
\( \hat{y} = \hat{f}(x) \) [our approximation]
ship
\( \left[\begin{array}{lcr} 0, 1, 0, 0, 0 \end{array} \right]\)
\( \left[\begin{array}{lcr} 0, 0, 0, 0, 1 \end{array} \right]\)
\( \left[\begin{array}{lcr} 1, 0, 0, 0, 0 \end{array} \right]\)
\( \left[\begin{array}{lcr} 0, 0, 1, 0, 0 \end{array} \right]\)
\( \left[\begin{array}{lcr} 0.1, 3.1, \dots, 1.7, 3.4\end{array} \right]\)
\( \left[\begin{array}{lcr} 0.5, 9.1,\dots, 5.1, 0.8 \end{array} \right]\)
\( \left[\begin{array}{lcr} 1.2, 4.1, \dots, 6.3, 7.4 \end{array} \right]\)
\( \left[\begin{array}{lcr} 3.2, 2.1, \dots, 3.1, 0.9 \end{array} \right]\)
Models
What are the choices for \( \hat{f} \) ?
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\( \hat{y} = mx + c \)
\(\hat{ y} = ax^2 + bx + c \)
\( y = \sigma(wx + b) \)
\( y = Deep\_NN(x) \)
\( \hat{y} = \hat{f}(x) \) [our approximation]
\( \left [\begin{array}{lcr} 0.5\\ 0.2\\ 0.6\\ \dots\\0.3\ \end{array} \right]\)
\( \left [\begin{array}{lcr} 14.8\\ 13.3\\ 11.6\\ \dots\\6.16 \end{array} \right]\)
\( x \)
\( y \)
\(\hat{ y} = ax^3 + bx^2 + cx + d \)
\(\hat{ y} = ax^4 + bx^3 + cx + d \)
Data
In this course
\( y = Deep\_CNN(x) \) ...
\( y = RNN(x) \) ...
Data is drawn from the following function
\vdots
\(\hat{ y} = ax^{25} + bx^{24} + \dots + cx + d \)
Models
Why not just use a complex model always ?
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\( \left [\begin{array}{lcr} 0.1\\ 0.2\\ 0.4\\ ....\\0.8 \end{array} \right]\)
\( \left [\begin{array}{lcr} 2.6\\ 2.4\\ 3.1\\ ....\\4.1 \end{array} \right]\)
\( x \)
\( y \)
\( y = mx + c \) [true function, simple]
\(\hat{y} = ax^{100} + bx^{99} + ... + c \)
[our approximation, very complex]
Later in this course
Bias-Variance Tradeoff
Overfitting
Regularization
Models
What are the choices for \( \hat{f} \) ?
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Model
Data
Task
Loss Function
How do we know which model is better ?
\( \left [\begin{array}{lcr} 0.00\\ 0.10\\ 0.20\\ ....\\6.40 \end{array} \right]\)
\( \left [\begin{array}{lcr} 0.24\\ 0.08\\ 0.12\\ ....\\0.36 \end{array} \right]\)
\( x \)
\( y \)
?
\( \hat{f_1}(x) \)
\( \left [\begin{array}{lcr} 0.25\\ 0.09\\ 0.11\\ ....\\0.36 \end{array} \right]\)
\( \left [\begin{array}{lcr} 0.32\\ 0.30\\ 0.31\\ ....\\0.22 \end{array} \right]\)
\( \left [\begin{array}{lcr} 0.08\\ 0.20\\ 0.14\\ ....\\0.15 \end{array} \right]\)
\( \hat{f_1}(x) = 1.79x^{25} - 4.54 x^{24} + ... - 1.48x + 2.48 \)
\( \hat{f_2}(x) = 2.27x^{25} + 9.89x^{24} + ... + 2.79x + 3.22 \)
\( \hat{f_3}(x) = 3.78x^{25} + 1.57x^{24} + ... + 1.01x + 8.68 \)
\( \begin{array}{lcr} 1\\ 2\\ 3\\ ....\\n \end{array} \)
\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \)
\( \hat{f_2}(x) \)
\( \hat{f_3}(x) \)
\( \mathscr{L}_2 = \sum_{i=1}^{n} (y_i - \hat{f}_2(x_i))^2 \)
\( \mathscr{L}_3 = \sum_{i=1}^{n} (y_i - \hat{f}_3(x_i))^2 \)
True Function
\( \hat{f_1}(x) \)
\( \hat{f_2}(x) \)
\( \hat{f_3}(x) \)
why not use numbers ?
whose function is better?
?
Loss Function
How do we know which model is better ?
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\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 = ? \)
\( \mathscr{L}_2 = \sum_{i=1}^{n} (y_i - \hat{f}_2(x_i))^2 = 2.02\)
\( \mathscr{L}_3 = \sum_{i=1}^{n} (y_i - \hat{f}_3(x_i))^2 = 2.34 \)
In this course
Square Error Loss
Cross Entropy Loss
KL divergence
\( \left [\begin{array}{lcr} 0.00\\ 0.10\\ 0.20\\ ....\\6.40 \end{array} \right]\)
\( \left [\begin{array}{lcr} 0.24\\ 0.08\\ 0.12\\ ....\\0.36 \end{array} \right]\)
\( x \)
\( y \)
\( \hat{f_1}(x) \)
\( \left [\begin{array}{lcr} 0.25\\ 0.09\\ 0.11\\ ....\\0.36 \end{array} \right]\)
\( \left [\begin{array}{lcr} 0.32\\ 0.30\\ 0.31\\ ....\\0.22 \end{array} \right]\)
\( \left [\begin{array}{lcr} 0.08\\ 0.20\\ 0.14\\ ....\\0.15 \end{array} \right]\)
\( \begin{array}{lcr} 1\\ 2\\ 3\\ ....\\n \end{array} \)
\( \hat{f_2}(x) \)
\( \hat{f_3}(x) \)
\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \)
\( = (0.24-0.25)^2 + (0.08-0.09)^2 + \newline (0.12-0.11)^2 + ... + (0.36-0.36)^2 \)
\( = 1.38 \)
\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 = 1.38\)
\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 = ? \)
Loss Function
What does a loss function look like ?
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Loss
Model
Data
Task
Learning Algorithm
How do we identify parameters of the model?
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\( \hat{f_1}(x) = 3.5x_1^2 + 2.5x_2^{3} + 1.2x_3^{2} \)
\( \hat{f_1}(x) = ax_1^2 + bx_2^{3} + cx_3^{2} \)
\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \)
| Budget in (100crs) |
Box Office Collection in (100 crs) | Action Scene in times (100 mins) | IMDB Rating |
|---|---|---|---|
| 0.55 | 0.66 | 0.22 | 4.8 |
| 0.68 | 0.91 | 0.77 | 7.2 |
| 0.66 | 0.88 | 0.67 | 6.7 |
| 0.72 | 0.94 | 0.97 | 8.1 |
| 0.58 | 0.74 | 0.35 | 5.3 |
\vdots
\vdots
\vdots
\vdots
Learning Algorithm
How do you formulate this mathematically ?
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\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \)
In practice, brute force search is infeasible
Find \(a, b, c \) such that
is minimized
\( \hat{f_1}(x) = ax_1^2 + bx_2^{3} + cx_3^{2} \)
| Budget (100crore) |
Box Office Collection(100 crore) | Action Scene times (100 mins) | IMDB Rating |
|---|---|---|---|
| 0.55 | 0.66 | 0.22 | 4.8 |
| 0.68 | 0.91 | 0.77 | 7,2 |
| 0.66 | 0.88 | 0.67 | 6.7 |
| 0.72 | 0.94 | 0.97 | 8.1 |
| 0.58 | 0.74 | 0.35 | 5.3 |
\vdots
\vdots
\vdots
\vdots
Learning Algorithm
How do you formulate this mathematically ?
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\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \)
Many optimization solvers are available
\(min_{a,b,c}\)
\( \hat{f_1}(x) = ax_1^2 + bx_2^{3} + cx_3^{2} \)
\vdots
\vdots
\vdots
\vdots
| Budget (100crore) |
Box Office Collection(100 crore) | Action Scene times (100 mins) | IMDB Rating |
|---|---|---|---|
| 0.55 | 0.66 | 0.22 | 4.8 |
| 0.68 | 0.91 | 0.77 | 7,2 |
| 0.66 | 0.88 | 0.67 | 6.7 |
| 0.72 | 0.94 | 0.97 | 8.1 |
| 0.58 | 0.74 | 0.35 | 5.3 |
Learning Algorithm
How do you formulate this mathematically ?
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\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \)
Many optimization solvers are available
\(min_{a,b,c}\)
\( \hat{f_1}(x) = ax_1^2 + bx_2^{3} + cx_3^{2} \)
In this course
Gradient Descent ++
Adagrad
RMSProp
Adam
| Budget (100crore) |
Box Office Collection(100 crore) | Action Scene times (100 mins) | IMDB Rating |
|---|---|---|---|
| 0.55 | 0.66 | 0.22 | 4.8 |
| 0.68 | 0.91 | 0.77 | 7,2 |
| 0.66 | 0.88 | 0.67 | 6.7 |
| 0.72 | 0.94 | 0.97 | 8.1 |
| 0.58 | 0.74 | 0.35 | 5.3 |
\vdots
\vdots
\vdots
\vdots
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Learning Algorithm
How do you formulate this mathematically ?
Learning
Loss
Model
Data
Task
Evaluation
How do we compute a score for our ML model?
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\( \left[\begin{array}{lcr} 2.1, 1.2, \dots, 5.6, 7.8 \end{array} \right]\)
\( \left[\begin{array}{lcr} 3.5, 6.6, \dots, 2.5, 6.3 \end{array} \right]\)
\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)
\( \left[\begin{array}{lcr} 2.8, 3.6, \dots, 7.5, 2.1 \end{array} \right]\)
\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)
True Labels
Predicted Labels
1
2
3
4
5
5
4
1
3
1
\tiny{Accuracy=\frac{\text{Number of correct predictions}}{\text{Total number of predictions}}}
| Class Labels | |
|---|---|
| Lion | 1 |
| Tiger | 2 |
| Cat | 3 |
| Giraffe | 4 |
| Dog | 5 |
\tiny{=\frac{\textrm{4}}{\textrm{7}}}=\textrm{0.55}
\( \left[\begin{array}{lcr} 1.9, 3.3, \dots, 4.2, 1.1 \end{array} \right]\)
\( \left[\begin{array}{lcr} 2.2, 1.7, \dots, 2.5, 1.8 \end{array} \right]\)
3
5
2
5
Top - 1
Evaluation
How do we compute a score for our ML model?
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\( \left[\begin{array}{lcr} 2.1, 1.2, \dots, 5.6, 7.8 \end{array} \right]\)
\( \left[\begin{array}{lcr} 3.5, 6.6, \dots, 2.5, 6.3 \end{array} \right]\)
\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)
\( \left[\begin{array}{lcr} 2.8, 3.6, \dots, 7.5, 2.1 \end{array} \right]\)
\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)
True Labels
Predicted Labels
1
2
3
4
5
| Class Labels | |
|---|---|
| Lion | 1 |
| Tiger | 2 |
| Cat | 3 |
| Giraffe | 4 |
| Dog | 5 |
\( \left[\begin{array}{lcr} 1.9, 3.3, \dots, 4.2, 1.1 \end{array} \right]\)
\( \left[\begin{array}{lcr} 2.2, 1.7, \dots, 2.5, 1.8 \end{array} \right]\)
3
5
Top - 3
\( \left[\begin{array}{lcr} 1, 2, 3\end{array} \right]\)
\( \left[\begin{array}{lcr} 1, 2, 3\end{array} \right]\)
\( \left[\begin{array}{lcr} 1, 2, 3\end{array} \right]\)
\( \left[\begin{array}{lcr} 4, 5, 3\end{array} \right]\)
\( \left[\begin{array}{lcr} 5, 2, 1\end{array} \right]\)
\( \left[\begin{array}{lcr} 2, 1, 4\end{array} \right]\)
\( \left[\begin{array}{lcr} 5, 4, 1\end{array} \right]\)
\tiny{=\frac{\textrm{6}}{\textrm{7}}}=\textrm{0.86}
\tiny{Accuracy=\frac{\text{Number of correct predictions in top-3}}{\text{Total number of predictions}}}
Evaluation
How is this different from loss function ?
(c) One Fourth Labs
Evaluation
Brake
/Go
Loss function
\( maximize \)
#( ) +
____________________
#( )
#( )
#( ) +
____________________
#( )
#( )
Evaluation
Should we learn and test on the same data?
(c) One Fourth Labs
\( \left[\begin{array}{lcr} 2.1, 1.2, \dots, 5.6, 7.8 \end{array} \right]\)
\( \left[\begin{array}{lcr} 3.5, 6.6, \dots, 2.5, 6.3 \end{array} \right]\)
\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)
\( \left[\begin{array}{lcr} 2.8, 3.6, \dots, 7.5, 2.1 \end{array} \right]\)
\( \left[\begin{array}{lcr} 2.2, 1.7, \dots, 2.5, 1.8 \end{array} \right]\)
1
2
3
4
2
\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)
\( \left[\begin{array}{lcr} 2.8, 3.6, \dots, 7.5, 2.1 \end{array} \right]\)
\( \left[\begin{array}{lcr} 2.2, 1.7, \dots, 2.5, 1.8 \end{array} \right]\)
1
3
4
x
y
x
y
Training Data
Test Data
\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \)
\( \hat{f_1}(x) = ax_1^2 + bx_2^{3} + cx_3^{2} \)
\(min_{a,b,c}\)
\tiny{Accuracy=\frac{\text{Number of correct predictions}}{\text{Total number of predictions}}}
Evaluation
How is this different from loss function ?
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Learning
Loss
Model
Data
Task
Evaluation
Putting it all together
How does all the jargon fit into these jars?
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Linear Algebra
Probability
Calculus
Data
Model
Loss
Learning
Task
Evaluation
Data, democratisation, devices
Why ML is very successful?
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Data
Model
Loss
Learning
Task
Evaluation
Improvised
Democratised
Abundance
Typical ML effort
How to distribute your work through the six jars?
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Your Job
Model
Loss
Learning
Evaluation
Data
Task
Mix and Match
Connecting to the Capstone
How to distribute your work through the six jars?
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Mumbai
/
/
मुंबई \( \rightarrow \) Mumbai
\( \sum_{i=1}^{n} (y_i - \hat{f}(x_i))^2 \)
\( -\sum_{i=1}^{n} \log \hat{f}(x_i) \)
Accuracy
Precision/Recall
Top-k accuracy
Data
Model
Loss
Learning
Task
Evaluation
Assignment
How do you apply the six jars to a problem that you have encountered?
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Explain the problem
Give link to the quiz
1. Formulate 3 problems from data.gov.in
2. In the dataturks labelled data, define tasks that you can perform and collect 10 data points for each
// Binary classification of whether there is text
// Detect text with bounding box - is accuracy easy to define here?
Copy of Copy of Final_1.3_Six_Elements_of_ML
By Shubham Patel
