Outline is subject to change

Intro

• What is machine learning?
• Course logistics
• An example: curve fitting

Calculus review

• Motivation: optimization
• Derivatives: intuition and rules
• Convex, concave functions
• Find minimum of convex function by setting derivative to zero

Linear regression in one variable

• Paradigm: supervised learning
• Linear regression
  • Setup
  • Cost function
  • Minimize cost function (one parameter—slope only) by setting derivative to zero
• Gradient descent
• Geometry of functions in higher dimensions
  • Contour plots
• GD for linear regression with two parameters (slope, intercept)
  • Intuition of partial derivatives
  • Partial derivatives of the linear regression cost function

Intro to MATLAB

• Interactive session to show basic / important MATLAB features
• From Brown tutorial:
  1. Basics
     • Comments
     • Suppressing output
     • Statements separated by commas, semicolons, or newlines
     • help / doc
  2. Types, assignments, literals
     • Entering vectors and matrices
     • Accessing entries and submatrices
  3. Operations on vectors and matrices
     • Elementwise operators and funcitons
     • Other vector and matrix functions
  4. Control flow (briefly)
  5. Functions
     • Multiple inputs / output
     • Assigment of multiple outputs
• Did not cover
  1. Debugging
  2. Plotting
  3. Load and save
  4. Formatting strings: disp / sprintf / fprintf
• Advanced topics (to cover in future classes)
  • logical indexing
  • cell arrays
  • structs

Homework 1

• Exercises
  • Partial derivatives
  • Intuition and geometry
• Problems
  • 1D linear regression derivations
  • Implement 1D linear regression by gradient descent
  • Convergence of gradient descent
  • Run 1D linear regression on own data
• Follow-up notes
  • Feature normalization
  • Gradient descent: simultaneous updates of all parameters

Linear algebra review

• Motivation: want to move to more complicated ML setups
  • Many inputs \(x_1, \ldots, x_n\)
  • More complex functions, e.g. polynomials
• Linear algebra
  • Succinct language for linear expressions of many variables
  • Saves coding
  • Inspires new ML methods
• Matrices
• Vectors
• Matrix-Matrix multiplication (and special cases)
• Tranpose
• Inverse

Multivariate linear regression

• MATLAB pointers
  • Concatenation of vectors / matrices
  • Subscripted assignment
• First multivariate prediction models
• Geometry of linear functions in high dimensions
  • “Tilted” planes through the origin
    • (Affine function = linear function translated away from origin)
  • Contours are parallel lines
  • Gradient is vector orthogonal to contours
  • Length of gradient = “slope” of plane
• Multivariate linear regression
  • Motivation
  • Model
  • Cost function
  • Normal equations
  • Gradient descent
• Features
  • Normalization
  • Feature design
  • Non-linearity by feature expansion
  • Polynomial regression

Homework 2

• Linear algebra exercises
• Normal equations
• Features
  • Feature engineering
  • Feature normalization
• Stochastic gradient descent?
• Polynomial regression

Logistic regression

• First classifier
• Widely used “workhorse” of predictive stats and ML
• Examples
  • MNIST: 4 vs. 9
  • Breast cancer
• Outline
  • Classification
  • Model
  • Cost function
  • Gradient descent
  • Decision boundaries

Nonlinearity, overfitting, regularization

• Fit a non-linear function using linear models
• What is Overfitting?
• How to Diagnose Overfitting
• Regularization

Homework 3

• Logistic regression
• Feature normalization
• Log loss

Multiclass classifcation

• One-vs-all
• One-vs-many

Evaluation methodology

• Different evaluation goals
  • Estimate performance of deployed system
  • Model selection
  • Compare algorithms
• Data splits
  • Train / validation / test
  • Cross-validation
• Classification performance measures
  • Accuracy
  • Confusion matrix
  • Precision
  • Recall
  • F1
  • Precision-recall curve
• Tools
  • Grid search
  • Training curve
  • Precision-recall curve

Instance-based classification

• First inherently non-linear methods
• Different learning paradigm: no training phase
• Example: time-series classification
• Nearest neighbor
• k-NN
• Kernel regression

Decision trees

Support vector machines

• Linear separators
• Idea of margin
• Formulate max-margin optimization problem

Weka tutorial

• Guest lecture by Kevin Winner, UMass Ph.D. student
• Learn about Weka
  • Comprehensive ML toolkit
  • Easy to use
  • Java based: both interactive GUI and programmatic API

Soft-margin SVMs

• What if data is not linearly separable?
• Penalty in optimization problem
• “Hinge-loss”
• Comparison with logistic regression

Kernel SVMs

• SVM dual training and prediction
• Dot-products
• Kernel trick: redefine dot-product
• Feature expansions
• Example kernels
• SVM with RBF kernel visualization

Designing and debugging ML systems

• See Andrew Ng’s slides

Clustering: K-means

• TBD

Dimensionality reduction: principal component analysis

*

Probability review

• Fourth Hour
• Probability spaces and events
• Conditional probability
• Random variables
• Expected value

Bayes / Naive Bayes

• Bayes rule
• Generative model
• Naive Bayes
• Text classification

Hidden Markov models

Bayes nets

K-means

*

Gaussian mixture models

• This may be too hard… there is no way to get thre

EM algorithm

Odds and ends

• Stochastic gradient descent