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Statistical Machine Learning, Week 5: Loss Function Optimization using Gradient Descent
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#machinelearning #gradientdescent #optimization
Gradient descent is a fundamental optimization algorithm widely employed in machine learning to iteratively minimize a loss function. It operates by calculating the gradient of the loss function with respect to the model's parameters and then updating those parameters in the direction opposite to the gradient. This process continues until convergence, ideally reaching a point where the loss is minimized, signifying that the model has learned to make accurate predictions. A variant of this, stochastic gradient descent (SGD), introduces an element of randomness by computing the gradient and updating parameters based on a single randomly selected training example or a small batch of examples (mini-batch SGD) in each iteration. This approach can be computationally more efficient and even help escape local minima, though it might lead to a noisier optimization path.
Epochs represent the number of times the entire training dataset is passed forward and backward through the neural network. In the context of SGD, one epoch involves iterating over the entire training dataset, updating the model's parameters based on randomly selected examples or mini-batches. The SGDRegressor in scikit-learn implements stochastic gradient descent for linear regression problems. It leverages the concepts of epochs, learning rate, and other hyperparameters to optimize the model's coefficients and minimize the loss function. The max_iter parameter in SGDRegressor controls the maximum number of epochs. By understanding these concepts and tuning the hyperparameters appropriately, one can effectively train linear regression models using SGDRegressor.
Gradient descent is a fundamental optimization algorithm widely employed in machine learning to iteratively minimize a loss function. It operates by calculating the gradient of the loss function with respect to the model's parameters and then updating those parameters in the direction opposite to the gradient. This process continues until convergence, ideally reaching a point where the loss is minimized, signifying that the model has learned to make accurate predictions. A variant of this, stochastic gradient descent (SGD), introduces an element of randomness by computing the gradient and updating parameters based on a single randomly selected training example or a small batch of examples (mini-batch SGD) in each iteration. This approach can be computationally more efficient and even help escape local minima, though it might lead to a noisier optimization path.
Epochs represent the number of times the entire training dataset is passed forward and backward through the neural network. In the context of SGD, one epoch involves iterating over the entire training dataset, updating the model's parameters based on randomly selected examples or mini-batches. The SGDRegressor in scikit-learn implements stochastic gradient descent for linear regression problems. It leverages the concepts of epochs, learning rate, and other hyperparameters to optimize the model's coefficients and minimize the loss function. The max_iter parameter in SGDRegressor controls the maximum number of epochs. By understanding these concepts and tuning the hyperparameters appropriately, one can effectively train linear regression models using SGDRegressor.