# ▸ Support Vector Machines :

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1. Suppose you have trained an SVM classifier with a Gaussian kernel, and it learned the following decision boundary on the training set:

You suspect that the SVM is underfitting your dataset. Should you try increasing or decreasing $\inline&space;C$? Increasing or decreasing $\inline&space;\sigma&space;^2$?

1. Suppose you have trained an SVM classifier with a Gaussian kernel, and it learned the following decision boundary on the training set:

When you measure the SVM’s performance on a cross validation set, it does poorly. Should you try increasing or decreasing $\inline&space;C$? Increasing or decreasing $\inline&space;\sigma&space;^2$?

1. The formula for the Gaussian kernel is given by similarity
$\inline&space;(x,l^{(1)})=exp\left&space;(&space;-\frac{\left&space;\|&space;x-l^{(1)}\right&space;\|^2}{2\sigma^2&space;}\right&space;)$.
The figure below shows a plot of $\inline&space;f_1=smililarity(x,l^{(1)})$ when $\inline&space;\sigma^2$.

Which of the following is a plot of $\inline&space;f_1$ when $\inline&space;\sigma^2&space;=&space;0.25$?

1. The first term in the objective is:
$\inline&space;C\sum_{i=1}^m&space;y^{(i)}&space;cost_1(\theta^T&space;x^{(i)})+(1-y^{(i)})&space;cost_0(\theta^T&space;x^{(i)})$
This first term will be zero if two of the following four conditions hold true. Which are the two conditions that would guarantee that this term equals zero?

1. Suppose you have a dataset with n = 10 features and m = 5000 examples.

After training your logistic regression classifier with gradient descent, you find that it has underfit the training set and does not achieve the desired performance on the training or cross validation sets.

Which of the following might be promising steps to take? Check all that apply.

• Increase the regularization parameter Î».

• Use an SVM with a Gaussian Kernel.
By using a Gaussian kernel, your model will have greater complexity and can avoid underfitting the data.

• Create / add new polynomial features.
When you add more features, you increase the variance of your model, reducing the chances of underfitting.

• Use an SVM with a linear kernel, without introducing new features.

• Try using a neural network with a large number of hidden units.
A neural network with many hidden units is a more complex (higher variance) model than logistic regression, so it is less likely to underfit the data.

• Reduce the number of example in the training set.

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