Gradient Descent

February 21, 2026

Gradient Descent for Linear Regression #

Revision:
Gradient descent is the step-by-step method for reducing the cost function when a direct closed-form solution is not convenient.

Where Gradient Descent Fits in ML ☆ #

Gradient descent is used when we want the model to learn parameters by repeatedly improving them.

For linear regression, it adjusts the slope and intercept until the prediction error becomes small.

flowchart LR
    A["Initial Parameters"] --> B["Make Predictions"]
    B --> C["Compute Cost"]
    C --> D["Compute Gradient"]
    D --> E["Update Parameters"]
    E --> B

    style A fill:#E1F5FE,stroke:#5b7db1,color:#000
    style B fill:#C8E6C9,stroke:#5f8f6a,color:#000
    style C fill:#FFF9C4,stroke:#b59b3b,color:#000
    style D fill:#EDE7F6,stroke:#8a6fb3,color:#000
    style E fill:#C8E6C9,stroke:#5f8f6a,color:#000

Core Idea ☆ #

The gradient tells us the direction in which the cost increases fastest.

Classification (Linear)

Linear models for Classification #

• categorises data by finding a linear boundary (hyperplane) that separates classes
• calculating a weighted sum of input features plus bias

flowchart TD
T["Linear<br/>classification<br/>models"] --> P["Perceptron"]
T --> LR["Logistic<br/>regression"]
T --> SVM["Linear<br/>SVM"]

P -->|uses| STEP["Step<br/>activation"]
LR -->|uses| SIG["Sigmoid<br/>+ log loss"]
SVM -->|uses| HNG["Hinge<br/>loss"]

style T fill:#90CAF9,stroke:#1E88E5,color:#000

style P fill:#C8E6C9,stroke:#2E7D32,color:#000
style LR fill:#C8E6C9,stroke:#2E7D32,color:#000
style SVM fill:#C8E6C9,stroke:#2E7D32,color:#000

style STEP fill:#CE93D8,stroke:#8E24AA,color:#000
style SIG fill:#CE93D8,stroke:#8E24AA,color:#000
style HNG fill:#CE93D8,stroke:#8E24AA,color:#000

• Discriminant Functions
• Decision Theory
• Probabilistic Discriminative Classifiers
• Logistic Regression

Logistic Regression #

• Supervised machine learning algorithm
• Binary classification algorithm
• requires data to be linearly separable
• predicts the probability that an input belongs to a specific class
• uses Sigmoid function to convert inputs into a probability value between 0 and 1

Key takeaway: Logistic regression predicts $P(y=1\mid x)$ using a sigmoid of a linear score $z=w\cdot x+b$, then learns $w,b$ by maximising likelihood (equivalently minimising log-loss).

Hypothesis Testing

Hypothesis Testing #

Hypothesis testing is a statistical decision-making method used to decide whether sample evidence is strong enough to reject an initial assumption about a population.

It connects probability, sampling distributions, confidence intervals, significance levels, and decision rules.

Key takeaway:
Hypothesis testing is not about proving something with certainty.

It is about asking:

If the null hypothesis were true, how surprising would this sample result be?

Rewards, Returns, Policies and Value Functions

Rewards, Returns, Policies and Value Functions #

An MDP describes how states, actions, rewards and transitions fit together. The next task is to evaluate behaviour: what should the agent try to achieve, how should future rewards be counted, and how good is a state or action over the long term?

Rewards define the objective, returns combine rewards across time, a policy describes behaviour, and value functions predict the long-term quality of that behaviour.

Foundation Models

December 14, 2025

Foundation Model #

AI models trained on massive datasets to perform a wide range of tasks with minimal fine-tuning.

• are large deep learning neural networks

• are large AI models trained on massive and diverse datasets (text, images, audio, or multiple modalities).

• Contain millions or billions of parameters.

• designed to perform a broad range of general tasks

• designed for general-purpose intelligence, not a single task.

• acts as base models for building specialised AI applications

LLM - Model

LLM – Large Language Model #

Large Language Models (LLMs) are advanced AI systems designed to process, understand, and generate human-like text.

They learn language by analysing massive amounts of text data, discovering patterns in:

• grammar

• meaning

• context

• relationships between words and sentences

• Built on Deep Learning

• Implemented using Neural Networks

• Based on Transformers

• Often combined with tools like:

  • Retrieval (RAG)
  • Agents
  • External APIs
  • Memory systems

What makes an LLM special? #

• Built using deep neural networks
• Trained on very large datasets (books, articles, code, web text)
• Can perform many tasks without task-specific training
• General-purpose language understanding, not single-task models

Foundation: Transformer Architecture #

LLMs are based on the Transformer Architecture, which allows models to understand context and long-range dependencies in text.

AI Agents

December 15, 2025

AI Agents #

Also referred to as Agentic AI.

AI agents are intelligent systems that can plan, make decisions, and take actions to achieve goals with minimal human intervention.

• A common use case is task automation

• for example booking travel based on a user’s request.

• AI agents typically build on Generative AI and use Large Language Models (LLMs) as the reasoning core.

• Agents often interact with tools (APIs, databases, calendars) to complete multi-step workflows.

Retrieval-Augmented Generation (RAG)

Retrieval-Augmented Generation (RAG) #

Retrieval-Augmented Generation (RAG) is a system design pattern that improves an LLM’s answers by:

1. Retrieving relevant information from an external knowledge source, and then
2. Augmenting the LLM prompt with that retrieved context before generating the final response.

RAG helps an LLM look things up first, then answer using evidence.

Why RAG is Useful #

RAG is commonly used when:

• Your knowledge is in private documents (PDFs, policies, internal wiki)
• You need up-to-date information (things not in the model’s training data)
• You want fewer hallucinations by grounding answers in retrieved sources
• You want traceability (show “where the answer came from”)

RAG does not change the model weights.
It changes what the model sees at inference time by adding retrieved context.

Decision Tree

Decision Tree #

A decision tree classifies an example by asking a sequence of questions about its attributes until it reaches a leaf (final decision).

Key takeaway: A decision tree grows by repeatedly splitting the training data into purer subsets using an impurity measure (Entropy / Gini / Classification Error).

• Information Theory
• Entropy Based Decision Tree Construction
• Avoiding Overfitting
• Minimum Description Length
• Handling Continuous valued attributes, missing attributes

Information Theory #

Decision trees need a way to measure: “How mixed are the class labels at a node?”

Prediction & Forecasting

Prediction & Forecasting #

Prediction and forecasting use statistical models to estimate unknown or future values.

In this module, the focus is on correlation, regression, and time series forecasting.

Key takeaway:
Prediction estimates a value using a model.

Forecasting is prediction where the order of time matters.

• Correlation
• Regression
• Time series analysis
• Components of time series data
• Moving average and weighted moving average
• AR model
• ARMA model
• ARIMA model
• SARIMA and SARIMAX
• VAR and VARMAX
• Simple exponential smoothing

Prediction vs Forecasting ☆ #

Overall Workflow #

flowchart LR
    A[Data] --> B[Explore Pattern]
    B --> C[Choose Model]
    C --> D[Train or Fit]
    D --> E[Validate]
    E --> F[Predict or Forecast]
    F --> G[Interpret Error]

    style A fill:#E1F5FE
    style B fill:#C8E6C9
    style C fill:#FFF9C4
    style D fill:#EDE7F6
    style E fill:#C8E6C9
    style F fill:#E1F5FE
    style G fill:#FFF9C4

Correlation ☆ #

Correlation measures the direction and strength of linear relationship between two variables.