Machine Learning

Week 1 - Intro

What is Machine Learning

• Checkers playing computer (Arthur Samuel)

Supervised Learning

Right answer is provided. Types of problems

• Regression
• Classification

Unsupervised Learning

The data has no "correct answer"

Cocktail party algorithm

Week 1 - Linear Regression with One variable

Model Representation

Working with housing prices in Portland as our dataset.

Symbols used

• m - number of training examples
• x - input variables
• y - output variable
• h - hypothesis (function h(x) = y)

Univariate linear regression

Cost Function

h_Θ(x) = Θ₀ + Θ₁x

sum of square error as our cost function. He's using 1/2m rather than 1/m, I'm not sure why.

Cost Function - Intuition : 1

Demo of technique.

Cost Function - Intuition : 2

Contour plots.

Gradient Descent

Θ_j = Θ_j - α (d/dΘ_j) * J(Θ₀, Θ₁)

Gradient Descent Intuition

Explaining gradient descent.

Gradient Descent for Linear Regression

• Θ₀ = Θ₀ - α(1/m) Σ^m (h_Θ(x_i) - y_i)
• Θ₁ = Θ₁ - α(1/m) Σ^m (h_Θ(x_i) - y_i) * x_i

Linear Regression with Multiple Variables - Week 2

Gradient Descent for Multiple Variables

• Parameters: Θ₀,Θ₁,...,Θ_n
• Cost Function: J( Θ₀,Θ₁,...,Θ_n ) or simply J(Θ)

Much like before, gradient descent is calculated for all Θs before being applied. To make the formula more uniform we set x_0,i = 1 for all i then the formula becomes

 Θj = Θj - (α/m) * Σi=1m (h(Θ, xi) - yi) * xi,j

Note: I may have my notation for rows and columns mixed up in the formula - double check before using.

Gradient Descent in Practice 1 - Feature Scaling

Try to make features on a similar scale. In the house example, if our features are size 0-2000ft² and bedrooms (1-5), it will take a long time to converge, because the first feature is three orders of magnitude larger. Either scale bedrooms up or the ft² down. A simple way to do this is scale all features filling the range (-1, 1). If future data lies outside this range, it is not a problem. If future data falls way outside this range, you'll have bigger problems.

Try and set the mean to 0. This is "mean normalization".

Of course, none of this applies to x₀ = 1.

Gradient Descent in Practice 2 - Learning Rate

The correct α should cause J to decrease continuously. There is not a good automatic way to choose α at this time, but by looking at the iterations graph you can see that the slope is decreasing quickly enough, but not increasing.