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Monday, February 26, 2024

Two Common Approaches for Training Models — Part 1

Two Common Approaches for Training Models — Part 1

In machine learning, training models involves optimizing their parameters to minimize a cost or loss function. Two common approaches for training models are closed-form solutions and gradient descent.

1. Closed-Form Solutions:
* Description: Closed-form solutions, also known as analytical solutions, involve finding the optimal model parameters directly using mathematical equations. These solutions can provide a precise and immediate solution to the optimization problem.
>> Pros:
— Often faster for small to moderately sized datasets.
— Exact solutions when they exist, leading to a global minimum for the loss function.
>> Cons:
— Not applicable to all models or problems; closed-form solutions may not exist for complex models.
— May not scale well for very large datasets.
>> Example: Linear regression, when using the least squares method, has a closed-form solution to find the optimal coefficients.

2. Gradient Descent:
* Description: Gradient descent is an iterative optimization technique that adjusts model parameters to minimize the cost or loss function. It works by calculating the gradient of the loss function with respect to the parameters and adjusting the parameters in the direction of steepest descent.
>> Pros:
— Applicable to a wide range of models, including deep neural networks and complex non-linear models.
— Scales well to large datasets.
— Works well in high-dimensional spaces.
>> Cons:
— May converge to local minima rather than the global minimum.
— Requires careful tuning of hyperparameters like learning rate.
— Can be computationally expensive, especially for deep learning models.
>> Variants: There are variants of gradient descent, including stochastic gradient descent (SGD), mini-batch gradient descent, and advanced optimizers like Adam, RMSprop, and Adagrad, which are designed to overcome some of the limitations of basic gradient descent.
>> Example: Training deep neural networks often involves using stochastic gradient descent (or its variants) to iteratively update the network’s weights.

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