Fall 24 Midterm Review

 

Shen Shen

October 18, 2024

Intro to Machine Learning

Outline

  • Rundown
  • Past Exams
  • Q&A

Week 1 - IntroML

  • Terminologies
    • Training, validation, testing
    • Identifying overfitting and underfitting
  • Concrete processes
    • Learning algorithm
    • Validation and Cross-validation
    • Concept of hyperparameter

Week 2 - Regression

  • Problem Setup
  • Analytical solution formula \(\theta^*=\left(\tilde{X}^{\top} \tilde{X}\right)^{-1} \tilde{X}^{\top} \tilde{Y}\) (and what's \(\tilde{X}\))
  • When \(\tilde{X}^{\top} \tilde{X}\) not invertible (optimal solutions still exist; just not via the "formula")
    • Practically (two scenarios)
    • Visually (obj fun no longer of "bowl" shape, instead has "half-pipe" shape)
    • Mathematically (loss of solution uniqueness)
  • Regularization
    • Motivation, how to, when to

Week 3 - Gradient Descent

  • The gradient vector (both analytically and conceptually)
  • The gradient-descent algorithm and the key update formula
  • (Convex + small-enough step-size + gradient descent + global min exists + run long enough) guarantee convergence to a global min
    • What happens when any of these conditions is violated
  • How does the stochastic variant differ (Set up, run-time behavior, and conclusion)

Week 4 - Classification  

  • (Binary) linear classifier (sign based)
  • (Binary) Logistic classifiers (sigmoid, NLL loss)
  • Linear separator (the equation form, visual form with normal vector)​
  • Linear separability (interplay with features)
  • How to handle multiple classes
    • Softmax generalization (Softmax, cross-entropy)
    • Multiple sigmoids
    • One-vs-one, one-vs-all

Week 5 - Features

  • Feature transformations
    • Apply a fixed feature transformation
    • Hand-design feature transformation (e.g. towards getting linear separability)
    • Interplay between the number of features, the quality of features, and the quality of learning algorithms
  • Feature encoding
    • One-hot, thermometer, factored, numerical, standardization
    • When and why to use any of those

Week 6 - Neural Networks

  • Forward-pass (for evaluation)
  • Backward-pass (via backpropogation, for optimization)
  • Source of expressiveness
  • Output layer design
    • dimension, activation, loss
  • Hand-designing weights
    • to match some given function form
    • achieve some goal (e.g. separate a given data set)
import random
terms= ["spring2024",
        "fall2023",
        "spring2023",
        "fall2022",
        "spring2022",
        "fall2021",
        "fall2019",
        "spring2019",
        "fall2018"]
qunums = range(1,10)
base_URL = "https://introml.mit.edu/_static/fall24/midterm/review/midterm-"

term = random.choice(terms)
num = random.choice(qunums)
print("term:", term)
print("question number:", num)
print(f"Link: {base_URL+term}.pdf")
  • Past exams

General problem-solving tips

More detailed CliffsNotes

General exam tips

  • Arrive 5min early to get settled in.
  • Bring a pencil (and eraser), a watch, and some water.
  • Look over whole exam and strategize for the order you do problems.

Good luck!