Welcome to CSCI 0451: Machine Learning!

Spring 2026

Prof. Phil Chodrow
Department of Computer Science
Middlebury College

Hi everyone!

I’m Prof. Phil Chodrow. Please call me “Phil” or “Prof. Phil.” “Prof. Chodrow” is ok if that’s what makes you comfortable.

I think about….

Math, social networks, dynamical systems, data science, applied statistics, information theory, effective teaching

I like…

♟️ Chess (let’s play!), 🎿 nordic skiing, 🍵 tea, 🍵 hiking, 🥘 cooking, 📖 reading, 🖖🏻 Star Trek Deep: Space Nine.

Two fun facts

I have two cats who also love math




I practice aikido (and had short hair)

Today



  • What is machine learning and why should we study it?
  • What are we going to learn in this course?
  • How will we learn and demonstrate our learning?
  • Introducing Data = Signal + Noise

But first!!

Your Affinity Vegetable



1. Split into teams

2. Go around and share your name and:

If you were a vegetable, which vegetable would you be and why?

Hello! My name is Phil and if I were a vegetable, I would be garlic. Garlic can be either a quiet helper or a charismatic center of a dish, and that reflects my personality as part introvert and part performer.

Culinary vegetables like tomatoes, zucchini, and eggplant are ok!

Your Affinity Vegetable



3. As a group identify a delicious dish that incorporates all of your vegetables.

Be ready to share!

Today



  • What is machine learning and why should we study it?
  • What are we going to learn in this course?
  • How will we learn and demonstrate our learning?
  • Introducing Data = Signal + Noise




Machine learning is…

…the theory and practice…
…of designing automated systems for prediction and decision-making…
…which adapt their behavior based on data.

Machine learning powers our modern information landscape

Machine learning is the theory and practice of designing automated systems for prediction and decision-making which adapt their behavior based on data.

  • Amazon makes recommendations for things you might want to buy based on your browsing and purchase history.
  • TikTok curates your feed based on your previous interactions and searches.
  • GPT/Copilot/Gemini/Claude generate text, code, images, and music in response to your prompts after training on huge internet corpora.

How many times have you interacted with an automatic recommendation, a personalized ad, a curated feed, or a generative AI model since you woke up today?

Example: Learning to Classify












As technical specialists, we’ll be especially interested in understanding what is happening in the training process and how to measure how well it worked.

Today



  • What is machine learning and why should we study it?
  • What are we going to learn in this course?
  • How will we learn and demonstrate our learning?
  • Introducing Data = Signal + Noise

Learning objectives


Theory: math of models and training.

Experimentation: evaluating the performance of models on real and synthetic data

Social Responsibility: thinking critically about the social impacts of the models we build.

Implementation: creating models in structured code.

Navigation: working with the Python ecosystem, especially pytorch.

Why so much theory?

The future of machine learning belongs to those who understand why models work, how to evaluate them, and when to use them.

This includes:

\[ \begin{aligned} f(\mathbf{x}; \mathbf{w}) &= \sigma(\mathbf{w}^\top \mathbf{x}) &\text{(model)} \\ \ell(y_i, s) &= - \left[ y_i \log(s) + (1 - y_i) \log(1 - s) \right] &\text{(loss function)}\\ L(\mathbf{w}) &= \sum_{i=1}^n \ell(y_i, f(\mathbf{x}_i; \mathbf{w})) \\ \nabla_{\mathbf{w}} L(\mathbf{w}) &= \sum_{i=1}^n (f(\mathbf{x}_i; \mathbf{w}) - y_i) \mathbf{x}_i &\text{(gradient)} \\ \mathbf{w}' &\leftarrow \mathbf{w} - \eta \nabla_{\mathbf{w}} L(\mathbf{w}) &\text{(training loop)} \\ \end{aligned} \]

You don’t need to understand this right now but you will by the end of the course.

Today



  • What is machine learning and why should we study it?
  • What are we going to learn in this course?
  • How will we learn and demonstrate our learning?
  • Introducing Data = Signal + Noise

A Typical Class Day



Before
Complete the warmup problem ahead of class and submit on Gradescope
During
Present the warmup problem to your group (~15 mins).
Lecture: theory (~25 mins) + implementation and experiments (~25 mins).
After
Work on the week’s homework assignment or miniproject.
Study lecture notes to prep for quizzes and exam.

Formative (Learning) Assessments

Formative assessments are for you to deepen your understanding outside of class.

Homework assignments (roughly 5)
  • Problems for practicing concepts from lecture.
  • Will often involve math (differential calculus, linear algebra)
  • Prepare for quizzes and exams
  • Opportunity for revision if submitted by first due date.
  • Warmup problem is graded on effort and counts towards homework grade.
Mini-projects (roughly 4)
  • Open-ended implementation and experimentation projects.
  • Mostly coding and writing in Jupyter notebooks
  • (Optional): post your miniprojects on an online portfolio.

Summative Assessments

Summative assessments are to hold you accountable to good learning practices and evaluate your growth in the material.

Timed Assessments
  • Quizzes (in class, roughly 3)
  • Midterm exam
  • Oral exam

Closed book, timed, proctored assessments that draw on a similar problem bank as the homework.

Project

A ~4 week long project in which you apply methods from class to a project of your choice, completed as a group.









Questions??

Onward: First Steps Towards Modeling

Suppose we have the following data set which we’d like to model:

Interpolation

Perfectly fitting the data is called interpolation:

Interpolation fails to generalize

This approach will perform poorly on similar new data:

This is also called “failure to generalize” or “overfitting.”

Data = Signal + Noise

A theoretical, schematic view of the data:

\[ \begin{aligned} y_i = f(x_i) + \epsilon_i \end{aligned} \]

Successful machine learning modeling learns the signal \(f(x_i)\) while ignoring the noise \(\epsilon_i\).

Data = Signal + Noise

Learning the true signal allows us to generalize better to new data:

\[ \begin{aligned} MSE = \frac{1}{n} \sum_{i=1}^n (y_{i,\mathrm{actual}} - \hat{y}_{i,\mathrm{prediction}})^2 \end{aligned} \]

Lower MSE on test set \(\implies\) better predictive performance.

Coming up…

Modeling signal and noise with linear trends and Gaussian probability distributions.

\[ \begin{aligned} p(\epsilon;\mu, \sigma^2) &= \frac{1}{\sigma \sqrt{2 \pi}} \exp\left( -\frac{(\epsilon - \mu)^2}{2 \sigma^2} \right) \end{aligned} \]

Before Wednesday

Read the syllabus and post questions on Campuswire.

Complete the warmup problem (go/cs-451) and submit on Gradescope.

Email me LOAs

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