Equations
Understanding Equations in Simple Terms
An equation is like a balance scale ⚖️. It shows that two things are equal using the equals sign ==.
For example: 2 + 3 = 5
This equation tells us that 2 plus 3 is the same as 5.
Now, when equations have variables (like x and y), they show how different values relate to each other.
For example: y = 2x+3
This means:
– If \( x = 1 \), then \( y = 2(1) + 3 = 5 \).
– If \( x = 2 \), then \( y = 2(2) + 3 = 7 \).
So, equations describe relationships between numbers.
Here is detailed video on equations:
Tip: As you are watching the above video, make sure practice it with your hands.
How Equations Are Used in Machine Learning 🚀
Machine learning is all about finding equations that best describe data. Let’s break it down into different areas:
1️⃣ Linear Regression (Predicting Values)
– In ML, we often use equations like:
\[
y = mx + b
\]
– This helps us predict values. For example, if you want to predict a house price based on its size, ML will find the best equation that fits past data.
2️⃣Cost Function (Measuring Error)
– ML models learn by reducing errors, which is done using an equation called a cost function.
– Example:
\[
\text{Cost} = \frac{1}{n} \sum (y_{\text{actual}} – y_{\text{predicted}})^2
\]
– This equation helps the model adjust until predictions become accurate.
3️⃣ Neural Networks (Complex ML Models)
– Deep learning models use equations with many variables to detect patterns in images, text, and data.
– Example:
\[
y = \sigma ( w_1 x_1 + w_2 x_2 + b )
\]
– This is a basic **neuron equation**, where **weights \( w \)** adjust to improve learning.
4️⃣ Probability & Statistics (Decision Making)
– Equations in ML help calculate probabilities for decision-making.
– Example (Logistic Regression for classification):
\[
P(y=1) = \frac{1}{1 + e^{-(w_1 x_1 + w_2 x_2 + b)}}
\]
– This helps in things like **spam detection**, where ML predicts whether an email is spam or not.
In Simple Words:
- Equations are the language of ML—they describe patterns in data.
- ML algorithms find the best equations to make predictions.
- Without equations, ML wouldn’t exist—they are the foundation of learning!
Would you like me to show a real-world ML example where equations are used? 🚀
