Machine Learning - Introduction

TL;DR

• Teaching a machine to learn its task without being explicitly programmed
  • The machine is practicing/learning on its own to improve its performance.

Supervised Learning

1. right answers are given for a data set

   • so do your best to produce a right answer for another input

2. Types of supervised learning:

   • Regression: Predict continuous valued output

     • something like house prices.

   • Classification: Discrete answers

     • either 0 or 1 : true or false

       • could be also 0, 1, 2, 3

     • what is the probability that the input turns out to be true or false?

     • if you need to consider more than one parameter, the graph may look different

Unsupervised Learning

1. No right answers given

   • no labeling for a data.
   • don’t know if it’s true or false
   • but there are some sorts of clusters: you could organize them

2. something like organizing news.

   • not given how each article is related, but Google somehow organizes them by headline
   • you have to find the relationship between/among the given data set

Model Representation

1. Notation

   • training set: a dataset given to train a model
   • m : # of training examples
   • x: input variables/features
   • y: output variable/ target variable
   • (xⁱ, yⁱ) = ith training example (ith row from the training set table)

2. Training set -> Fed into learning algorithm -> hypothesis(h)

   • hypothesis takes an input and produce an output
   • h maps from x’s to y’s
   • how to represent h ?
   • h_θ(x) = h(x) = θ₀ + θ₁x (for a linear function, think of it like a f(x))

Cost Function

1. Measures the performance of a machine learning model: the goal is to find thetas that minimize the cost function

   • θ₀ and θ₁ are parameters
   • x₁ and x₂ are features
   • choose the best θ₀ and θ₁ to make it close to y as much as possible
   • so minimize (1/2m) * SIGMA ((h_θ(x)-y)²)(sum of these is the cost function I think)

2. Finding θ₁ which minimizes J(θ) when θ₀ = 0

   • this is where differential equation comes in.
   • minimum when differential = 0

3. Contour plots are used to indicate cost functions

Gradient Descent

1. A way to minimize the cost function J

2. Start at some random θ₀ and θ₁ and keep changing them simultaneously in order to reduce J(θ₀, θ₁)

   • θ_j := θ_j -α * derivative_with_respect_to*θ_j(J(θ₀, θ₁))
   • α is called learning rate
   • temp0 := θ₀ equation
   • temp1 := θ₁ equation
   • θ₀ := temp0
   • θ₁ := temp1
   • same theta’s have to be used in order to calculate a temp value

3. Intuition

   • repeat until convergence: until you reach the global minimum
   • think about the equation: θ_j := θ_j -α * derivative_with_respect_to*θ_j(J(θ₀, θ₁))
   • if the derative is positive, you know that your entire term is getting smaller, and if negative, its getting bigger
   • if the learning rate is too small, gradient descent can be slow. because you would need more iteration
   • if the learning rate is too large, gradient descent can overshoot the minimum -> could even diverge
   • you don’t need to decrease the learning rate over time because the derivate term will decrease as you approach the minimum

4. Batch

   • Each step of gradient descent uses all the training examples
   • you are computing all the sums to take the next step in gradient descent