Explain Gradient Descent.
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🔹 What is Gradient Descent?
Gradient Descent is an optimization algorithm used to minimize a cost function (loss function) in machine learning and deep learning models.
The idea is to iteratively adjust parameters (weights) of a model in the direction that reduces the error, until we reach the lowest point of the cost function (the minimum).
Think of it like a person walking down a hill blindfolded:
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At each step, you feel the slope beneath your feet (the gradient).
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You move in the direction that goes downward (negative gradient).
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You keep stepping until you reach the bottom (minimum error).
🔹 How It Works
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Start with initial values for model parameters (weights & biases).
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Compute the cost function (how wrong the model is).
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Calculate the gradient (the slope of the cost function with respect to parameters).
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Gradient tells us the direction of steepest ascent.
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We move in the opposite direction (steepest descent).
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Update parameters:
Where:
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= model parameters (weights).
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= learning rate (step size).
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= gradient of cost function.
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Repeat until convergence (cost function stops decreasing).
🔹 Types of Gradient Descent
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Batch Gradient Descent
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Uses the whole dataset to compute gradients.
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More stable, but slow for large datasets.
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Stochastic Gradient Descent (SGD)
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Updates weights using one sample at a time.
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Faster but noisier (cost may zigzag).
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Mini-Batch Gradient Descent
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A compromise: uses small random batches of data.
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Faster than batch and smoother than SGD.
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Most commonly used in deep learning.
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🔹 Importance of Learning Rate (α)
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If α is too large → overshoot the minimum (never converge).
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If α is too small → very slow convergence.
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Choosing the right α is crucial.
🔹 Visual Intuition
Imagine a U-shaped curve (cost function):
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You start at some point on the curve.
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Each step, you move downwards along the slope.
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Eventually, you reach the lowest point (global minimum).
🔹 Advantages
✅ Simple and widely used.
✅ Works well for convex functions.
✅ Scales to large datasets (with mini-batch).
🔹 Limitations
❌ Can get stuck in local minima (especially in non-convex functions).
❌ Requires careful tuning of learning rate.
❌ Slow for very large-scale problems.
✅ Summary:
Gradient Descent is an optimization technique that updates model parameters step by step in the direction of the negative gradient to minimize the cost function. It’s the backbone of training algorithms in machine learning and deep learning.
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