March 12, 2026Naïve Bayes is a probabilistic classifier.
It predicts a class label by computing:
February 22, 2026Probability distributions are the bridge between: real-world randomness and mathematical modelling.
A random experiment produces outcomes. A random variable turns those outcomes into numbers. A probability distribution tells you how likely each number (or range of numbers) is.
Key takeaway: A distribution is a complete “story” about uncertainty: what values are possible, how likely they are, and how we summarise them (mean, variance).
flowchart TD PD["Probability<br/>distributions"] --> RV["Random<br/>variables"] PD["Probability<br/>distributions"] --> DS["Common<br/>distributions"] style PD fill:#90CAF9,stroke:#1E88E5,color:#000 style RV fill:#90CAF9,stroke:#1E88E5,color:#000 style DS fill:#90CAF9,stroke:#1E88E5,color:#000
In practice: choosing a distribution is a modelling decision. It affects: prediction, uncertainty estimates, and what “rare” or “typical” means in your data.
July 4, 2024The AI pipeline is a continuous process where data is collected, prepared, used to train models, evaluated for performance, and continuously improved after deployment.
timeline
title AI Pipeline
Collect Data : Data Ingestion
: Data Understanding
Prepare Data : Cleaning
: Feature Engineering
: Sampling
Train Model : Model Training
: Validation & Metrics
Deploy Model : Deployment
: Monitoring & Retraining
A Markov Decision Process (MDP) is a mathematical framework for modelling sequential decisions. It describes the situations an agent may encounter, the actions it may take, how the environment may change, and the rewards produced by those changes.
Bandit problems ask which action is best in a single recurring situation. An MDP adds changing states: an action affects not only the immediate reward but also the situation faced next.
Parallel algorithms need hardware that can execute independent work efficiently. Modern systems therefore combine multiple CPU cores, memory hierarchies, threads, instruction pipelines, GPUs, clusters, and specialised matrix processors.
This page covers:
By the end of this page, you should be able to:
Linear Regression is a supervised ML method used to predict a numerical target by fitting a model that is linear in its parameters.
In ML , linear models are a core baseline: they’re fast, often surprisingly strong, and usually easy to interpret.
Key takeaway: Linear Regression learns parameters by minimising a squared-error cost. You can solve it directly (closed form) or iteratively (gradient descent), and you can extend it using basis functions and regularisation.
February 22, 2026A random variable is a way to attach numbers to outcomes of a random experiment.
It lets us move from: “what happened?” to: “what number should we analyse?”
Key takeaway: A random variable is a function from the sample space to real numbers. Once you define the random variable clearly, the rest (pmf/pdf/cdf, mean, variance) becomes systematic.
flowchart TD PD["Probability<br/>distributions"] --> RV["Random<br/>variables"] RV --> T["Types"] T --> RV1["Discrete<br/>RVs"] T --> RV2["Continuous<br/>RVs"] RV --> F["PMF / PDF / CDF"] RV --> S["Mean / Variance<br/>Covariance"] RV --> J["Joint & Marginal<br/>distributions"] RV --> X["Transformations"] style PD fill:#90CAF9,stroke:#1E88E5,color:#000 style RV fill:#90CAF9,stroke:#1E88E5,color:#000 style T fill:#CE93D8,stroke:#8E24AA,color:#000 style F fill:#CE93D8,stroke:#8E24AA,color:#000 style S fill:#CE93D8,stroke:#8E24AA,color:#000 style J fill:#CE93D8,stroke:#8E24AA,color:#000 style X fill:#CE93D8,stroke:#8E24AA,color:#000 style RV1 fill:#CE93D8,stroke:#8E24AA,color:#000 style RV2 fill:#CE93D8,stroke:#8E24AA,color:#000
Random variable: a rule that assigns a number to each outcome.
February 22, 2026Once you can describe a random variable using a pmf or pdf, the next step is to use named distributions that appear repeatedly in real data and in ML models.
Key takeaway: Named distributions give you ready-made probability models for common patterns: binary outcomes, counts, and measurement noise.
flowchart TD PD["Probability<br/>distributions"] --> DS["Common<br/>distributions"] DS --> DIS["Discrete"] DS --> CON["Continuous"] DIS --> D1["Bernoulli"] DIS --> D2["Binomial"] DIS --> D3["Poisson"] CON --> D4["Normal<br/>(Gaussian)"] CON --> D5["t / Chi-square / F<br/>(intro)"] style PD fill:#90CAF9,stroke:#1E88E5,color:#000 style DS fill:#90CAF9,stroke:#1E88E5,color:#000 style DIS fill:#CE93D8,stroke:#8E24AA,color:#000 style CON fill:#CE93D8,stroke:#8E24AA,color:#000 style D1 fill:#C8E6C9,stroke:#2E7D32,color:#000 style D2 fill:#C8E6C9,stroke:#2E7D32,color:#000 style D3 fill:#C8E6C9,stroke:#2E7D32,color:#000 style D4 fill:#C8E6C9,stroke:#2E7D32,color:#000 style D5 fill:#C8E6C9,stroke:#2E7D32,color:#000
Use when: one trial has two outcomes (success/failure).
February 21, 2026Revision:
OLS is the direct method for linear regression. It finds the best-fit line by minimising the sum of squared residuals without iterative updates.
Linear regression parameters can be found in two main ways.
| Method | Main idea | When used |
|---|---|---|
| Ordinary Least Squares | Compute the best parameters directly | Small or moderate datasets |
| Gradient Descent | Start with parameters and update repeatedly | Large datasets or many features |
flowchart LR
A["Linear Regression"] --> B["Direct Solution<br/>OLS"]
A --> C["Iterative Solution<br/>Gradient Descent"]
B --> B1["Normal Equation"]
B --> B2["No learning rate"]
B --> B3["One-shot solution"]
C --> C1["Learning rate"]
C --> C2["Repeated updates"]
C --> C3["Stops after convergence"]
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 B1 fill:#EDE7F6,stroke:#8a6fb3,color:#000
style B2 fill:#EDE7F6,stroke:#8a6fb3,color:#000
style B3 fill:#EDE7F6,stroke:#8a6fb3,color:#000
style C1 fill:#EDE7F6,stroke:#8a6fb3,color:#000
style C2 fill:#EDE7F6,stroke:#8a6fb3,color:#000
style C3 fill:#EDE7F6,stroke:#8a6fb3,color:#000
OLS is called least squares because it chooses parameters that make the squared residual errors as small as possible.
February 21, 2026Revision:
A cost function converts model error into a single number. Training means changing the model parameters until this number becomes as small as possible.
A machine learning model needs a way to decide whether one set of parameters is better than another.
For linear regression, every possible value of the parameters gives a different line. The cost function tells us which line is better by measuring how far the predictions are from the true values.