Linear SVMs have no hyperparameters that need to be set by cross-validation

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The correct answer is: FALSE.

Linear SVMs have a number of hyperparameters that need to be set, such as the regularization parameter $\lambda$, the kernel function, and the cost function. These hyperparameters can be set using cross-validation to find the values that give the best performance on the test set.

Here is a brief explanation of each of these hyperparameters:

  • The regularization parameter $\lambda$ controls the trade-off between the model’s fit to the training data and its complexity. A higher value of $\lambda$ will result in a more complex model that is less likely to overfit the training data, while a lower value of $\lambda$ will result in a simpler model that is more likely to overfit the training data.
  • The kernel function is a function that maps the data points into a higher-dimensional space. The choice of kernel function can have a significant impact on the performance of the SVM. Some common kernel functions include the linear kernel, the polynomial kernel, and the radial basis function kernel.
  • The cost function is a function that measures the error of the model. The choice of cost function can also have a significant impact on the performance of the SVM. Some common cost functions include the hinge loss and the quadratic loss.

Cross-validation is a technique that is used to estimate the performance of a model on unseen data. It works by dividing the data into a number of folds, and then training the model on a subset of the folds and evaluating it on the remaining folds. This process is repeated multiple times, and the average performance of the model on the test folds is used to estimate the model’s performance on unseen data.

Cross-validation can be used to find the optimal values for the hyperparameters of a model. To do this, you would first train the model on a number of different values of the hyperparameters, and then evaluate the model on the test set. The value of the hyperparameter that gives the best performance on the test set would then be used to train the final model.