ML class overview

• ML class
• INTRODUCTION
  • Examples of machine learning
    • Database mining (Large datasets from growth of automation/web)
      • clickstream data
      • medical records
      • biology
      • engineering
    • Applications that can't be programmed by hand
      • autonomous helicopter
      • handwriting recognition
      • most of Natural Language Processing (NLP)
      • Computer Vision
    • Self-customising programs
      • Amazon
      • Netfilx product recommendations
    • Understanding human learning (brain, real AI)
  • What is Machine Learning?
    • Definitions of Machine Learning
      • Arthur Samuel (1959). Machine Learning: Field of study that gives computers the ability to learn without being explicitly programmed.
      • Tom Mitchell (1998). Well-posed Learning Problem: A computer program is said to learn from experience E with respect to some task T and some performance measure P, if its performance on on T, as measured by P, improves with experience E.
    • There are several different types of ML algorithms. The two main types are:
      • Supervised learning
        • teach computer how to do something
      • Unsupervised learning
        • computer learns by itself
    • Other types of algorithms are:
      • Reinforcement learning
      • Recommender systems
  • Supervised Learning
    • Supervised Learning in which the "right answers" are given
      • Regression: predict continuous valued output (e.g. price)
      • Classification: discrete valued output (e.g. 0 or 1)
  • Unsupervised Learning
    • Unsupervised Learning in which the categories are unknown
      • Clustering: cluster patterns (categories) are found in the data
      • Cocktail party problem: overlapping audio tracks are separated out
        • [W,s,v] = svd((repmat(sum(x.*x,1),size(x,1),1).*x)*x');
• LINEAR REGRESSION WITH ONE VARIABLE
  • Model Representation
    • e.g. housing prices, price per square-foot
      • Supervised Learning
      • Regression
    • Dataset called training set
    • Notation:

m	number of training examples
x's	"input" variable / features
y's	"output" variable / "target" variable
(x,y)	one training example
(x(i),y(i))	ith training example

• • • Training Set -> Learning Algorithm -> h (hypothesis)
    • Size of house (x) -> h -> Estimated price (y)
      • h maps from x's to y's
    • How do we represent h?
      • h_Θ(x) = h(x) = Θ₀ + Θ₁x
    • Linear regression with one variable (x)
      • Univariate linear regression
  • Cost Function
    • Helps us figure out how to fit the best possible straight line to our data
    • h_Θ(x) = Θ₀ + Θ₁x
    • Θ_i's: Parameters
    • How to choose parameters (Θ_i's)?
      • Choose Θ₀, Θ₁ so that h_Θ(x) is close to y for our training examples (x,y)
      • Minimise ${\frac {1}{2m}}\sum _{i=1}^{m}(h_{\theta }(x^{(i)})-y^{(i)})^{2}$ for Θ₀, Θ₁
        • h_Θ(x⁽ⁱ⁾) = Θ₀ + Θ₁x⁽ⁱ⁾
      • J(Θ₀,Θ₁) = ${\frac {1}{2m}}\sum _{i=1}^{m}(h_{\theta }(x^{(i)})-y^{(i)})^{2}$
      • J(Θ₀,Θ₁) is the Cost Function, also known in this case as the Squared Error Function
  • Cost Function - Intuition I
    • Summary:
      • Hypothesis: h_Θ(x) = Θ₀ + Θ₁x
      • Parameters: Θ₀, Θ₁
      • Cost Function: J(Θ₀,Θ₁) = ${\frac {1}{2m}}\sum _{i=1}^{m}(h_{\theta }(x^{(i)})-y^{(i)})^{2}$
      • Goal: minimise Θ₀, Θ₁ J(Θ₀, Θ₁)
    • Simplified:
      • h_Θ(x) = Θ₁x
      • minimise Θ₁ J(Θ₁)
    • Can plot simplified model in 2D
  • Cost Function - Intuition II
    • Can plot J(Θ₀,Θ₁) in 3D
    • Can plot with Contour Map (Contour Plot)
  • Gradient Descent
    • repeat until convergence { $\theta _{j}\colon =\theta _{j}-\alpha {\frac {\partial }{\partial \theta _{j}}}J(\theta _{0},\theta _{1})$ }
    • α = learning rate
  • Gradient Descent Intuition

    • min Θ1

      J(Θ1)

      • For Θ₁ > local minimum: ${\frac {d}{d\theta _{1}}}J(\theta _{1})$ positive, moves toward local minimum
      • For Θ₁ < local minimum: ${\frac {d}{d\theta _{1}}}J(\theta _{1})$ negative, moves toward local minimum
    • If learning rate α is too small algorithm takes a long time to run
    • If learning rate α is too large algorithm may not converge or may diverge
    • When partial derivative is zero Θ₁ converges
    • As we approach a local minimum, gradient descent automatically takes smaller steps
      • So no need to decrease α over time
  • Gradient Descent for Linear Regression
    • Gradient descent algorithm:
      • repeat until convergence { $\theta _{j}\colon =\theta _{j}-\alpha {\frac {\partial }{\partial \theta _{j}}}J(\theta _{0},\theta _{1})$; for j=1 and j=0 }
    • Linear Regression Model:
      • h_Θ(x) = Θ₀ + Θ₁x
      • J(Θ₀,Θ₁) = ${\frac {1}{2m}}\sum _{i=1}^{m}(h_{\theta }(x^{(i)})-y^{(i)})^{2}$

      • min Θ0,Θ1

        J(Θ0,Θ1)

    • j=0: ${\frac {\partial }{\partial \theta _{0}}}J(\theta _{0},\theta _{1})={\frac {1}{m}}\sum _{i=1}^{m}(h_{\theta }(x^{(i)})-y^{(i)})$
    • j=1: ${\frac {\partial }{\partial \theta _{1}}}J(\theta _{0},\theta _{1})={\frac {1}{m}}\sum _{i=1}^{m}(h_{\theta }(x^{(i)})-y^{(i)}).x^{(i)}$