Maths

Question 1

What is the cost function for Linear Regression (Mean Squared Error)?

Answer 1

J(θ) = (1/2n) Σ (yᵢ - (θ₀ + θ₁xᵢ))²

Question 2

What is the hypothesis function for Linear Regression?

Answer 2

h(x) = θ₀ + θ₁x

Question 3

What is the logistic (sigmoid) function formula?

Answer 3

σ(z) = 1 / (1 + exp(-z))

Question 4

What is the cost function for Logistic Regression?

Answer 4

J(θ) = -(1/n) Σ [yᵢ log(h(xᵢ)) + (1 - yᵢ) log(1 - h(xᵢ))]

Question 5

What is the Ridge Regression cost function?

Answer 5

J(θ) = (1/2n) Σ (yᵢ - h(xᵢ))² + λ Σ θⱼ²

Question 6

What is the Lasso Regression cost function?

Answer 6

J(θ) = (1/2n) Σ (yᵢ - h(xᵢ))² + λ Σ |θⱼ|

Question 7

What is the formula for the Bayes’ theorem?

Answer 7

P(A|B) = [P(B|A) × P(A)] / P(B)

Question 8

What is the equation for a simple decision boundary in LDA?

Answer 8

δₖ(x) = xᵀΣ⁻¹μₖ - (1/2)μₖᵀΣ⁻¹μₖ + log(πₖ)

Question 9

What is the PCA objective function?

Answer 9

Maximize variance = maximize (1/n) Σ (zᵢ)² where zᵢ are projections onto components.

Question 10

What is the update rule for Gradient Descent?

Answer 10

θ := θ - α ∇J(θ)