artificial-intelligence

Artificial Intelligence (AI) aims to build systems that can learn, adapt, and make decisions.
One powerful tool is the neural network, inspired by the brain.

From Statistics to AI

• Regression predicts Y from X
• Logistic regression predicts probability (0–1)
• Neural networks generalize this idea: many inputs, many layers, nonlinear patterns

The Structure of a Neural Network

1. Input layer — variables (X₁, X₂, …)
2. Hidden layers — units that transform the input
3. Output layer — prediction or classification

Each connection has a weight (like a slope in regression).

Formula for a Neuron

A single unit in the network:

$$z = \sum w_i X_i + b$$

$$y = f(z)$$

Where:

• $$w_i$$ = weights
• $$X_i$$ = inputs
• $$b$$ = bias (like an intercept)
• $$f(z)$$ = activation function (e.g., logistic, ReLU)

Learning in a Network

The network predicts outputs and compares them with the true answers.
The error is sent backward through the network to adjust weights.
This is called backpropagation.

Example

Predicting if a student will pass or fail based on:

• Study hours
• Attendance
• Practice problems completed

Inputs → combined with weights → logistic activation → output: probability of passing.

Visuals

Figure 18.1 — Simple Neural Network (Inputs → Hidden → Output)

Figure 18.2 — Activation Functions

Why This Matters

• Neural networks extend regression and logistic regression.
• They allow learning from large, complex datasets (images, speech, language).
• Modern AI (translation, recognition, chatbots) is powered by these models.

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Machine learning is where statistics meets computers.
Instead of only writing formulas, we teach a computer to learn patterns from data.

What is Machine Learning?

Machine learning uses algorithms to improve automatically with experience.

• Supervised learning: the computer is given examples with correct answers.
• Unsupervised learning: the computer finds patterns without answers.

Supervised Learning

Goal: predict Y from X.

Examples:

• Predict exam scores from study hours
• Predict house price from size, location, and age

Steps:

1. Split data into training set and test set
2. Train the model on training data
3. Test accuracy on new (unseen) data

Formula (simple linear regression as machine learning):
$$\hat{Y} = a + bX$$

Here, the computer “learns” $$a$$ and $$b$$ from the data.

Unsupervised Learning

Goal: find hidden structure in the data.

Examples:

• Group students by study habits
• Cluster shoppers by buying patterns

Algorithms:

• k-means clustering
• Hierarchical clustering

No “correct answer” is given — the computer organizes the data.

Overfitting vs. Generalization

• Overfitting: the model memorizes the training data but fails on new data.
• Generalization: the model captures the underlying pattern and works on new data.

Example:
If a student memorizes past exam answers (overfit), they may fail a new test.
If they learn the concepts (generalize), they succeed.

Key Concepts

• Training set: data used to build the model
• Test set: data used to evaluate performance
• Accuracy: how well the model predicts new data

Visuals

Figure 16.1 — Supervised learning example: regression line predicting Y from X.

Figure 16.2 — Unsupervised learning example: scatterplot with clusters (k-means).

Figure 16.3 — Overfitting vs. generalization: wiggly curve vs. smooth line.

Why This Matters

Machine learning grows directly out of statistics:

• Regression → prediction
• ANOVA → group classification
• Clustering → organizing data

By learning the basics of ML, students see how statistics powers AI.

Practice self-test quiz

In the space below, please find practice problems and self-test quizzes. For full access, please signup free.