AI

flowchart TD
    A[Dataset] --> B[Central Tendency]
    A --> C[Variability]
    B --> B1[Mean]
    B --> B2[Median]
    B --> B3[Mode]
    C --> C1[Range]
    C --> C2[Variance]
    C --> C3[Standard Deviation]
    C --> C4[IQR]

Measures of Central Tendency #

Central tendency tells you where the “middle” of the data is. Describes a set of scores with a single number that describes the PERFORMANCE of the group.

Basic Probability

AI, Statistics

Basic Probability #

Probability models uncertainty: what you don’t know yet, but want to reason about.

Key takeaway: Probability is a number between 0 and 1 that measures how likely an event is. The whole topic is about defining events clearly and applying a few core rules consistently.

Probability quantifies uncertainty: a number between 0 and 1.

0 means: impossible
1 means: certain

Terminology #

Random experiment #

A random experiment is an action whose outcome is not known in advance.

Neural Networks

AI, ML

AI, ML, Neural Networks

Neural Networks #

A network of artificial neurons inspired by how neurons function in the human brain.
At its core - a mathematical model designed to process and learn from data.
Neural networks form the foundation of Deep Learning (involves training large and complex networks on vast amounts of data).

flowchart LR
 subgraph subGraph0["Input Layer"]
        I1(("Input 1"))
        I2(("Input 2"))
        I3(("Input 3"))
  end
 subgraph subGraph1["Hidden Layer"]
        H1(("Hidden 1"))
        H2(("Hidden 2"))
        H3(("Hidden 3"))
  end
 subgraph subGraph2["Output Layer"]
        O(("Output"))
  end
    I1 --> H1 & H2 & H3
    I2 --> H1 & H2 & H3
    I3 --> H1 & H2 & H3
    H1 --> O
    H2 --> O
    H3 --> O

    style I1 fill:#C8E6C9
    style I2 fill:#C8E6C9
    style I3 fill:#C8E6C9
    style H1 stroke:#2962FF,fill:#BBDEFB
    style H2 fill:#BBDEFB
    style H3 fill:#BBDEFB
    style O fill:#FFCDD2
    style subGraph0 stroke:none,fill:transparent
    style subGraph1 stroke:none,fill:transparent
    style subGraph2 stroke:none,fill:transparent

Structure of a Neural Network #

A typical neural network has three main layers:

Conditional Probability & Bayes’ Theorem

March 12, 2026

AI, Statistics

AI, Statistics, Probability

Conditional Probability & Bayes’ Theorem #

Probability often changes when we learn new information.

Conditional probability and Bayes’ theorem give a structured way to update beliefs using evidence.

Conditional probability updates probabilities after observing an event.
Bayes’ theorem lets you estimate a hidden cause from observed evidence.
Naïve Bayes turns Bayes’ theorem into a practical classifier by assuming conditional independence of features given the class.

flowchart TD

A[Conditional<br/>probability] -->|foundation| B[Bayes<br/>theorem]
D[Independent<br/>events] -->|implies| C[Independence]
C -->|simplifies| A

E[Prior] -->|with likelihood| B
F[Likelihood] -->|updates| H[Posterior]
G[Evidence] -->|normalises| B
B -->|yields| H

I[Naïve<br/>Bayes] -->|uses| B
J[Naïve<br/>assumption] -->|assumes| C
K[Features] -->|given class| J
L[Class] -->|conditions| J
I -->|predicts| M[Classification]
M -->|selects| L

style A fill:#90CAF9,stroke:#1E88E5,color:#000
style B fill:#90CAF9,stroke:#1E88E5,color:#000
style C fill:#90CAF9,stroke:#1E88E5,color:#000

style D fill:#CE93D8,stroke:#8E24AA,color:#000
style E fill:#CE93D8,stroke:#8E24AA,color:#000
style F fill:#CE93D8,stroke:#8E24AA,color:#000
style G fill:#CE93D8,stroke:#8E24AA,color:#000
style J fill:#CE93D8,stroke:#8E24AA,color:#000
style K fill:#CE93D8,stroke:#8E24AA,color:#000
style L fill:#CE93D8,stroke:#8E24AA,color:#000

style H fill:#C8E6C9,stroke:#2E7D32,color:#000
style I fill:#C8E6C9,stroke:#2E7D32,color:#000
style M fill:#C8E6C9,stroke:#2E7D32,color:#000

Quick summary #

Conditional probability: updates probability after an event is known.
Multiplication rule: computes joint probability from conditional parts.
Independence: tested using \( P(A\cap B)=P(A)P(B) \) .
Total probability: breaks a probability into weighted cases.
Bayes’ theorem: reverses conditioning to infer causes from evidence.

What’s next #

Probability Distributions
Move from events to random variables and distributions.

Machine Learning

August 6, 2024

AI, ML

Machine Learning #

stateDiagram-v2

    %% ===== CLASS DEFINITIONS (Math-based colours) =====
    classDef algebra fill:#cfe8ff,stroke:#1e3a8a,stroke-width:1px
    classDef probability fill:#d1fae5,stroke:#065f46,stroke-width:1px
    classDef geometry fill:#ffedd5,stroke:#9a3412,stroke-width:1px
    classDef logic fill:#ede9fe,stroke:#5b21b6,stroke-width:1px
    classDef category font-style:italic,font-weight:bold,fill:#aaaaaa,stroke:#374151,stroke-width:3px

    %% ===== ROOT =====
    ML: Machine Learning

    %% ===== SUPERVISED =====
    ML --> SL:::category
    SL: Supervised Learning

    SL --> Regression
    Regression --> LR:::algebra
    LR: Linear Regression

    LR --> NN:::algebra
    NN: Neural Network

    NN --> DT:::logic
    DT: Decision Tree

    SL --> Classification
    Classification --> NB:::probability
    NB: Naive Bayes

    NB --> KNN:::geometry
    KNN: k-Nearest Neighbours

    KNN --> SVM:::algebra
    SVM: Support Vector Machine
    
    %% ===== UNSUPERVISED =====
    ML --> USL:::category
    USL: Unsupervised Learning

    USL --> Clustering
    Clustering --> KM:::geometry
    KM: K-Means

    KM --> GMM:::probability
    GMM: Gaussian Mixture Model

    GMM --> HMM:::probability
    HMM: Hidden Markov Model

    %% ===== REINFORCEMENT =====
    ML --> RL:::category
    RL: Reinforcement Learning

    RL --> DM:::logic
    DM: Decision Making

Mathematical Legend

Algebra / Linear Algebra (Blue) #

Used heavily when models rely on:

AI Stack

AI Stack #

The AI Stack describes the layers required to build an end-to-end AI system, from infrastructure at the bottom to user-facing applications at the top.

Different organisations represent the AI stack differently; this is a simplified conceptual view for learning.

Each layer depends on the one below it.

graph TB

    subgraph APP["Applications"]
        A[User Interfaces & Integrations]
    end

    subgraph ORCH["Orchestration"]
        O[Workflows • Agents • Control Logic]
    end

    subgraph DATA["Data"]
        D[Data Sources • Pipelines • Vector DBs]
    end

    subgraph MODEL["Models"]
        M[ML • DL • Foundation Models • LLMs]
    end

    subgraph INFRA["Infrastructure"]
        I[Cloud • On-prem • GPUs • Storage]
    end

    %% Styling
    style APP fill:#FFCCBC
    style ORCH fill:#90CAF9
    style DATA fill:#BBDEFB
    style MODEL fill:#C8E6C9
    style INFRA fill:#E1F5FE

    style A fill:#FFE0B2
    style O fill:#B3E5FC
    style D fill:#E3F2FD
    style M fill:#DCEDC8
    style I fill:#E1F5FE

1. Infrastructure #

The foundation that provides compute and storage.

Artificial Neuron and Perceptron

AI, ML

AI, ML, Neural Networks

Artificial Neuron and Perceptron #

knowledge in neural networks is stored in connection weights, and learning means modifying those weights.

Biological Neuron #

A biological neuron is a specialised cell that processes and transmits information through electrical and chemical signals.

Core components:

Dendrites: receive signals from other neurons
Cell body (soma): processes incoming signals
Axon: transmits the output signal
Synapses: connection points between neurons

Biological intuition:

many inputs arrive to one neuron
one neuron can connect out to many neurons
massive parallelism enables fast perception and recognition

Artificial Neuron #

An artificial neuron is a simplified computational model inspired by biological neurons.

ML Workflow

AI, ML

Machine learning Workflow #

Data is the foundation of any machine learning system. Quality of data matters more than model complexity.

Role of Data #

Data determines:

What patterns the model can learn
How well it generalises
Whether bias or noise is introduced

Bad data → bad model (even with perfect algorithms).

Data Preprocessing, wrangling #

Raw data is never ready for training.

Data Issues

Noise
- For objects, noise is an extraneous object
- For attributes, noise refers to modification of original values
- Use Log or Z Transfer to convert to mean
Outliers
- Data objects with characteristics that are considerably different than most of the other data objects in the data set
- Handle: Use IQR method
- Find Lower and Upper Bound and replace Outlier with Lower or Upper Bound
Missing Values
- Eliminate data objects or variables
- Handle: Estimate missing values
  - Mean, Median or Mode
  - Prefer Median if there are missing outliers
- Ignore the missing value during analysis
Duplicate Data
- Major issue when merging data from heterogeneous sources
Inconsistent Codes
- Find all Unique and transfer all inconsistent to

Data Preprocessing techniques