Lecture Notes from Lecture 1

Course Overview and Intro to Machine Learning

Course Overview

About the Course

STAT 453 introduces the fundamental concepts, methods, and tools used in machine learning, deep learning, and generative modeling. The course focuses on understanding both the ideas behind machine learning methods and how to apply them in practice.

Find details on course logistics, schedule, lecture notes, and assignments on the course website at https://adaptinfer.org/dgm-fall-2026.

Instructors

Professor Ben Lengerich

Email: lengerich@wisc.edu

Office Hours: Thursdays from 11:00 am to 12:00 pm in Morgridge 5530

Professor Lengerich’s research blends data science with medicine using context-adaptive models to understand diseases and improve precision medicine.

TA Baiheng Chen

Email: bchen342@wisc.edu

Office Hours: Wednesdays/Fridays from 2:00-3:00 PM on Zoom

Grading

• Homework: 20%
• Midterm Exam: 20%
  • Tentatively on 10/15
  • In-Class, Open-note, No calculator/phone
• Final Exam: 30%
  • Scheduled 12/12
  • Location TBA, Open-note, No calculator/phone
• Final Project: 30%
• Lecture Notes: Up to 5% of extra credit
  • 2% of extra credit for signing up to write notes for a lecture
    • Sign up here: https://docs.google.com/spreadsheets/d/1sRF3iMyxBJqUcGnHgSN8OMbAY7Los42bnqg_hYgCMlI/edit?usp=sharing
    • Template here: https://adaptinfer.org/dgm-fall-2026/notes/lecture-notes-template/
  • 3 x 1% of extra credit for editing a peer’s notes

Grades will not be curved

• A: 93-100
• AB: 88-92
• B: 83-87
• BC: 78-82
• C: 70-77
• D: 60-69
• F: Below 60

Homeworks/Project

Late homework submissions via Canvas will incur a penalty of 10% per day for up to three days, then they will not be accepted.

The project is broken down into parts. The proposal (5%), midway report (5%), presentation (5%), and report (15%). Teams of up to four students are allowed.

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What is Machine Learning?

Machine learning (ML) is a way of creating programs that improve their performance at a task through experience. More formally, a program is considered to learn from experience $E$ with respect to a task $T$ and performance measure $P$ if its performance at task $T$, as measured by $P$, improves with experience $E$.

This definition can be broken down into three important components:

• Task ($T$): What the machine learning system is trying to accomplish.
• Experience ($E$): The data or interactions that the system learns from.
• Performance measure ($P$): How we determine whether the system is performing well.

Traditional programming and machine learning differ in how the program is created. In traditional programming, the programmer provides a program that takes inputs and produces outputs. In machine learning, the computer uses inputs and outputs to learn a program.

Figure 1: Comparison of traditional programming and machine learning.

Three Fundamental Questions in Machine Learning

When building a machine learning system, there are three fundamental questions to consider:

1. Representation: How should we represent the problem and the information contained in the data?

   In probabilistic form, suppose we have variables $X_1, X_2, \ldots, X_8$. To represent the joint distribution of all eight variables, if each variable is Boolean, there are $2^8 = 256$ possible configurations of the variables. By using the conditional independence relationships between variables, a graphical model can represent the same joint distribution using far fewer parameters.

2. Inference: Given the representation, what can we conclude or predict about unknown information?

   In probabilistic form, suppose we want to determine the probability of one variable given another:

   \[P(X_8 \mid X_1)\]

   Using the definition of conditional probability:

   \[P(X_8 \mid X_1) = \frac{P(X_8, X_1)}{P(X_1)}\]

   If the other variables are unobserved, we can marginalize over them:

   \[P(X_8 \mid X_1) = \frac{\sum_{X_2,\ldots,X_7} P(X_1,\ldots,X_8)} {P(X_1)}\]

   For Boolean variables, this requires summing over $2^6$ configurations of the six unobserved variables. Independence assumptions can simplify this calculation. Graphical models can be useful because they provide an intermediate representation between explicitly representing every possibility and assuming complete independence.

3. Learning: How can we use available data or experience to learn the appropriate model? What model is “right” for the data?

   In probabilistic form,

   \[M = \underset{M \in \mathcal{H}}{\operatorname{argmax}} \; F(D; M)\]

   where:

   • $M$ is the selected model.
   • $\mathcal{H}$ is the hypothesis space, or set of possible models.
   • $D$ is the available data.
   • $F(D; M)$ is a function that evaluates how well model $M$ fits or performs on the data.

   An important question in learning is how to constrain the hypothesis space $\mathcal{H}$ so that we can efficiently search for a useful model rather than considering every possible model.

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The Broad Categories of ML

1. Supervised Learning

• Labeled data
• Direct feedback
• Trying to predict some outcome

Regression

• Function that predicts Y from X

Classification

• Observe examples from different classes
• Learn a boundary/rule that separates them

Definition

Task (T):

• Learn a function (h) that maps X → Y

Experience (E):

• Labeled samples containing both X and Y

Performance (P):

• A measure of how accurate (h) is

2. Unsupervised Learning

• There are no Y/labels, only inputs (X)
• Goal: Find hidden structure or patterns in the data
• Examples: PCA, clustering, autoencoders

Definition

Task (T):

• Discover structure in the data

Experience (E):

• A set of X values with no Y labels

Performance (P):

• Measure of fit

3. Reinforcement Learning

• Instead of every X being mapped to a Y, the goal is to learn which actions lead to the best expected reward

Example: LLM Feedback

• A model generates outputs/conversations
• Humans provide feedback such as a thumbs-up/down or preference
• That feedback provides a reward signal

Definition

Task (T):

• Learn a policy (π) mapping states to actions

Experience (E):

• Interaction with the environment

Performance (P):

• Expected reward

The Supervised Learning Workflow

Training vs. Testing Data

In supervised learning:

Training Data

• Contains observed inputs and outputs
• Used to learn the model’s parameters

Testing Data

• Kept separate from training
• Used to evaluate how well the learned parameters model real phenomena

Structured vs. Unstructured Data

Structured Data

Usually organized into:

• Tables
• Matrices

Unstructured Data

• Images

• Natural language

Necessary ML Notation and Jargon

• Training model = fitting a model = parameterizing a model = learning from data
• Training example = training record = training instance = training sample
• Feature = observation = predictor = variable = independent variable = input = attribute = covariate
  • A feature is an individual measurable input that is used by a model to make a prediction.
• Target = outcome = ground truth = output = response variable = dependent variable
  • The target is the correct value that the model is trying to predict.
• Output/Prediction = the valye produced by the model for a given inupt
  • The Target is the correct answer, while the prediction is the model’s estimated answer

For a given training example:

Input/features -> model -> prediction

The prediction is compared with the target to evaluate how well the model performed.

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About the Practical Aspects and Tools

The primary tules used throughout this course will be:

• PyTorch
• Python
• Jupyter Notebooks
• Matplotlib

We will also use additional machine learning libraries and tools including

• MLxtend
• scikit-learn
• Hugging Face

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