Gradient descent and stochastic gradient descent (SGD) are optimization algorithms used to minimize a function, typically associated with minimizing the error in a model.
The primary differences between the two are the following:
Gradient Descent (GD)
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In standard gradient descent, the algorithm computes the gradient of the cost function using the entire training dataset.
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It updates the model parameters by taking steps proportional to the negative of the gradient of the entire dataset.
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This method guarantees convergence to the minimum (given certain conditions like convexity and appropriate learning rates) but can be computationally expensive for large datasets.
Stochastic Gradient Descent (SGD)
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In stochastic gradient descent, the algorithm updates the model parameters using the gradient of the cost function for each individual training example.
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It makes frequent updates based on single or small batches of training examples, making it much faster than gradient descent for large datasets.
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However, due to its noisy updates, SGD has more fluctuations and doesn't necessarily converge to the absolute minimum; it converges to an area close to the minimum, oscillating around it.
When to use one over the other:
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Gradient Descent (GD): It's suitable when the dataset is relatively small and can fit into memory. If the cost function is smooth and well-behaved, GD can efficiently converge to the minimum.
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Stochastic Gradient Descent (SGD): It's preferable when dealing with large datasets where computing gradients for the entire dataset becomes computationally expensive. It's also useful in scenarios where the cost function has many local minima, as SGD's noise in updates might help escape shallow local minima. Furthermore, SGD is commonly used in training neural networks due to their vast datasets and high-dimensional parameter spaces.
Moreover, variations such as mini-batch gradient descent, which balances the benefits of both GD and SGD by considering a subset of the data for each update, are often used in practice. The choice between these algorithms often depends on computational resources, dataset size, and the specific problem's characteristics.
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