Source

1 Classes of Problems in Machine Learning

• Evolved from AI, new capability for computers
• Database mining (web click data, medical records, biology, engineering)
• Robotics, handwriting recognition, self-customizing programs

Formal Definition: program learns from experience E with respect to class of tasks T and performance measure P, if performance (P) at tasks in T improve with experience (E)

Supervised Learning

• Given data set, with intended output, produce right answer
• Regression problem, output of continuous values
• Linear approximation and taylor polynomial
• Classification problem, determine probability of a discrete valued output (0,1)

Unsupervised Learning

• Given data set, not necessarily with knowledge of the data, find some structure to data (clustering of data)
• Algorithm will discover conclusive information and structure from data
• Ex: Cocktail party algorithm, takes audio inputs of two speakers, separate to independent files
• Ex: group people with similar genetics together in clusters
• Octave is a language tailored well to Machine Learning.

Linear Regression One Var

In regression problems, given input variables, try to find a continuous expected result function

• univariate linear regression is used to predict a single output value y from single input x
• supervised learning, we have an idea of what input/output should be
• Hypothesis function is of the form of linear approximation: ŷ = h.theta(x) = theta0 + theta1•x
  • based on random guesses and iterations, the hypothesis function fits itself to the training data
• Cost Function measures the accuracy of our hypothesis function
  • use squared error function, or mean squared error function J(theta0, theta1) = (1/2)•x̄, where x̄ is the mean squared error
  • we define error as ŷi-yi, square each difference and take the mean of these
  • since we're calculating the distance from hypothesis to actual values, we want euclidean distance
  • sum of squares has the nice property of punishing overestimation and underestimation equally
  • squaring function can be differentiated, yielding linear forms which can be used for optimization
  • sum of squares is a convex cost function, guaranteeing a global min for convergence
  • absolute value functions are non differentiable, so sum of squares is superior

Gradient Descent

Recall that the gradient vector ∇f = (fx, fy) is like a derrivative for a field (fx = ∂f/∂x)

• if we graph the hypothesis function based on its fields theta0 and theta1 (graphing the cost function as a function of the parameter estimates)
  • that is, if we tested all possible inputs for theta0 and theta1 in a constrained x-y region, plotting the resulting cost function on the z-axis, we get 3D curve that we can find the local min of using constrained optimization
• gradient descent is recursively finding the derivative at some point, following the tangent line's slope down closer to the min
  • reminds me of applying Newton's method for approximating the absolute minimum
  • the size of each step is determined by the learning rate, related to the parameter α
  • repeat until convergence: θ_j := θ_j - α•∂/∂θ_j • J(theta0,theta1)
• α is the learning rate, too low is slow and too high results in divergence