Let's say you are standing at the top of a big mountain. Your goal is to get to the bottom of the mountain, where there is a treasure waiting for you. But the mountain is really foggy, so you can’t see far ahead.
- Step-by-Step: You start walking down carefully, one small step at a time. After every step, you check: "Am I going down or up?" If you're going down, you’re on the right path. If you start going up, you turn around because you want to keep going down.
- Learning from Mistakes: If you take a big step, you might trip or miss the way. So, you take smaller steps to be safe and check your progress often. This helps you get closer and closer to the treasure at the bottom.
- The Goal: In machine learning, the treasure at the bottom of the mountain is the best answer (or minimum error). Gradient Descent is just a fancy way for the computer to learn, step by step, how to make better guesses and get the best answer.
- Key Idea:
- The computer looks at the "mountain" (data or problem).
- It keeps checking if it’s getting closer to the answer (like going downhill).
- It learns to take smaller steps if it’s confused, so it doesn’t make big mistakes.
- Θj\Theta_jΘj → Your current position.
- α\alphaα → Step size (how big you want to move).
- 1m∑\frac{1}{m} \summ1∑ → Average over steps (here, simplified to individual steps).
- (hΘ(xi)?y)xj(h_{\Theta}(x_i) - y)x_j(hΘ(xi)?y)xj → Represents the slope of the hill (in machine learning terms, it's based on error).
