In this blog, we’ll explore how to use gradient descent to fit a line to three data points. Instead of diving into the theoretical aspects, we’ll take a hands-on approach by using a simple slope-intercept form. We’ll start with an initial slope and intercept of zero, then calculate the value of y using our hypothesis […]
Gradient descent step by step Read More »
The cost function J(θ)J(theta) is a mathematical measure of how well a machine learning model’s predictions match the actual target values. It evaluates the overall error between predicted outputs hθ(x)h_theta(x) and true outputs yy across the entire dataset. For example, in linear regression, the cost function is typically the Mean Squared Error (MSE): J(θ)=12m∑i=1m(hθ(x(i))−y(i))2 Where:
Matrix form of the closed-form solution for the hypothesis function Read More »
The progression from a simple linear equation to its matrix form and then to a hypothesis function is designed to make the relationship between inputs and outputs scalable and efficient. A basic linear equation describes how a single input influences an output, but in real-world problems, we often deal with multiple inputs and data
slope intercept to model parameters Read More »
Linear regression is one of the simplest and most powerful tools in data science. Let’s start with the classic equation you’ve likely seen in school and build up to a more generalized, multi-dimensional matrix representation. This transition will help us handle multiple features and datasets in an elegant way, which is key to applying machine
Linear regression from basic to matrix form Read More »
As we move from simple linear equations like y=mx+by = mx + b to models with multiple variables, things become more complex. To handle these higher-dimensional problems efficiently, we need matrix representation. Matrices allow us to perform calculations with multiple features simultaneously, making the process faster and more scalable. By using matrix form, we can
Transition from slope intercept to matrix form Read More »
Normal Distribution Key Idea: Bell-shaped curve; most values are around the mean, with fewer as you move away. Tip: Think of heights or test scores. Uniform Distribution Key Idea: All outcomes are equally likely; flat line from start to end. Tip: Think of a fair die or random number generator. Binomial Distribution Key Idea: Discrete
Types of distribution Read More »
Consider how input is correlated to output. It looks like a linear relationship The red dashed lines represent the residuals. A large residual means the point is far from the line, while a small residual means it’s close. How do you think we can find the “best” line that minimizes these residuals? 1. Cost Function
Sum of Squared Residuals: closed form Read More »
Introduction https://youtu.be/Z8mOZ-STNnQ Linear regression is one of the simplest and most commonly used methods for predicting outcomes or understanding relationships between two variables. For example: In a business setting, you might use it to predict sales based on advertising spending. In health care, you could predict a patient’s recovery time based on the dosage of
Introduction – Linear Regression Read More »