Machine Learning

Question 1

List ML algorithm categories.

Answer 1

• Supervised learning
• Unsupervised learning
• Reinforcement learning
• Recommender systems

Question 2

Examples of supervised learning

Answer 2

• Regression: Predicting continuous value output
• Classification (Logistic regression): Predicting discrete value output

Question 3

Examples of unsupervised learning

Answer 3

• Clustering: Google news, computer cluster analysis, market segmentation, cocktail party problem, SN analysis

Question 4

Hypothesis (model) and cost function for linear regression with a single variable

Answer 4

h_θ(x) = θ₀ + θ₁*x

J(θ) = 1/(2m) * Σ{i=1~m} (h_θ(x(i)) - y(i))²

• m: number of the training data.

Question 5

How to find the parameter set for a linear regression problem?

Answer 5

Find a parameter set that minimizes the cost function, i.e.,
min_θJ(θ)

One way of solving this optimization problem is the gradient descent algorithm.

Question 6

Describe the gradient descent algorithm.

Answer 6

repeat until convergence {
for all j’s (simultaneously)
for i=1 to m {
θ_j := θ_j - a* (d/dθ_j J(θ))
}
}
}

a: learning parameter - Note that all ‘theta_j’ are updated simultaneously.

Question 7

Discuss the learning rate of the gradient descent algorithm.

Answer 7

a: too small –> converges too slow a: too big –> might fail to converge or even diverge

Question 8

Gradient descent algorithm for a linear regression with a single variable.

Answer 8

repeat until convergence {
for i=1 to m {
θ₀ := θ₀ - a* (h(x(i)-y(i))
θ₁ := θ₁ - a* (h(x(i)-y(i))*x(i)
}
}

* Note: This is a batch gradient descent.

Question 9

What is “batch” gradient descent?

Answer 9

Each step of the gradient descent uses all the training samples.

Question 10

Hypothesis and cost function of a linear regression with multi-variables.

Answer 10

h_θ(X) = θ^T•X

• θ^T = [θ₀, … , θ_n]
• X^T = [1, x₁, …, x_n]

J(θ) = 1/(2m) * Σ{_i=1~m} (h_θ(X(i)) - y(i))²

• m: number of the training data.

Question 11

Gradient descent of a linear regression with multi-variables.

Answer 11

repeat until convergence {
for all j in {0, 1, …, n}
for i=1 to m
θ_j := θ - a* (h_θ(X(i))-y(i))
}

Question 12

Feature scaling and GD

Answer 12

For GD to work well, features must have a similar scale. Mean normalization can be used. X := (X - mu)/S - mu: mean vector - S: std or (max-min)

Question 13

How do you make sure GD is working?

Answer 13

Plot the J(θ) as the number of iteration and see if it decreases at each iteration.

Question 14

How to extend a linear regression to Polynomial regression for non-linear function?

Answer 14

Create new features from the existing ones.
For example,
x₁ = x₁
x₂ = x₁²
x₃ = x₁³
Then, solve the new feature sets using the linear regression technique.

Question 15

Normal equation for linear regression.

Answer 15

θ=(X^T•X)^-1•X^T•y

Question 16

Explain Logistic Regression

Answer 16

In solving a {0, 1} classification problem, we want the hypothesis (model) function value to be in [0 1] range.

• For linear regression, h_θ(X) =θ^T•X
• For logistic regression, h_θ(X) = g(θ^T•X) = 1/(1+exp(-θ^T•X))
  
  • g(t) = 1/(1+exp(-t)): Sigmoid (logistic) function
• Interpretation: h_θ(X) = p(y=1 | x ; θ) –> Probability y = 1, given X, parameterized by θ

Question 17

Decision boundary for logistic regression

Answer 17

Suppose

• Predict “y=1” if h_θ(X) >= 0.5
• Predict “y=0” if h_θ(X) < 0.5

Then the decision boundary is θ^T•X=0.

Question 18

Cost function for Logistic Regression

Answer 18

J(θ)=1/m*Σ_{i=1~m} cost(h_θ(X(i)), y(i))

where cost(h_θ(X(i)), y(i)) is

• -log(h_θ(X(i))) if y = 1
• -log(1-h_θ(X(i))) if y = 0

If you combine the above two terms, then

cost(•) = -y*log(h_θ(X(i))) -(1-y)*log(1-h_θ(X(i)))

Question 19

After training, your found your ML algorithm produce high prediction error with test data. What can you do?

Answer 19

• Get more examples –> helps to fix high variance
  
  • Not good if you have high bias (underfitting)
• Smaller set of features –> fixes high variance (overfitting)
  
  • Not good if you have high bias
• Try adding additional features –> fixes high bias (because hypothesis is too simple, make hypothesis more specific)
• Add polynomial terms –> fixes high bias problem
• Decreasing λ –> fixes high bias
• Increases λ –> fixes high variance