What is the relation between primal and dual?

What is the relation between primal and dual?

The number of variables in the dual problem is equal to the number of constraints in the original (primal) problem. The number of constraints in the dual problem is equal to the number of variables in the original problem. 2.

What is slack variable in SVM?

Many datasets will not be linearly separable. One way to cope with such datasets and still learn useful classifiers is to loosen some of the constraints by introducing slack variables. Slack variables are introduced to allow certain constraints to be violated.

What if we set c parameter to infinite in SVM?

What would happen when you use very large value of C(C->infinity)? For large values of C, the penalty for misclassifying points is very high, so the decision boundary will perfectly separate the data if possible.

What is SVM loss?

In machine learning, the hinge loss is a loss function used for training classifiers. The hinge loss is used for “maximum-margin” classification, most notably for support vector machines (SVMs). For an intended output t = ±1 and a classifier score y, the hinge loss of the prediction y is defined as.

Why is SVM convex?

The SVM problem is not an LP if the norm (used in the objective function) is the Euclidean norm, which SVM problem usually assumes. When using the Euclidian norm, the SVM objective function (besided being convex) is quadratic because the Euclidian norm is equivalent to an inner product of w with itself.

What is convex function in machine learning?

Convexity in gradient descent optimization Our goal is to minimize this cost function in order to improve the accuracy of the model. MSE is a convex function (it is differentiable twice). This means there is no local minimum, but only the global minimum. Thus gradient descent would converge to the global minimum.

Is hinge loss convex?

Hinge loss is a convex upper bound on 0-1 loss.

Does SVM use gradient descent?

3. Optimizing the SVM with SGD. To use Stochastic Gradient Descent on Support Vector Machines, we must find the gradient of the hinge loss function.

How is hinge loss calculated?

From our SVM model, we know that hinge loss = [0, 1- yf(x)].

How do you make a hinge loss differentiable?

Hinge loss is not differentiable and cannot be used with methods which are differentiable like stochastic gradient descent(SGD). In this case Cross entropy(log loss) can be used. This function is convex like Hinge loss and can be minimised used SGD.

Which loss function is used for classification?

We use binary cross-entropy loss for classification models which output a probability p. The range of the sigmoid function is [0, 1] which makes it suitable for calculating probability.

What is squared hinge loss?

Squared hinge loss is nothing else but a square of the output of the hinge’s max(…) function. It generates a loss function as illustrated above, compared to regular hinge loss. With squared hinge, the function is smooth – but it is more sensitive to larger errors (outliers).

What is a loss function give example?

A simple, and very common, example of a loss function is the squared-error loss, a type of loss function that increases quadratically with the difference, used in estimators like linear regression, calculation of unbiased statistics, and many areas of machine learning.”

What is the best loss function?

Mean Squared Error Loss The Mean Squared Error, or MSE, loss is the default loss to use for regression problems. Mathematically, it is the preferred loss function under the inference framework of maximum likelihood if the distribution of the target variable is Gaussian.

Can cost function be zero?

Yes, the cost function could be zero. If it matches all the expected values, then the graph would end up with a line lying exactly on the expected values. In that case, the cost function could be zero.

What is the difference between cost function and loss function?

The loss function (or error) is for a single training example, while the cost function is over the entire training set (or mini-batch for mini-batch gradient descent). Generally cost and loss functions are synonymous but cost function can contain regularization terms in addition to loss function.

How does backpropagation algorithm work?

The backpropagation algorithm works by computing the gradient of the loss function with respect to each weight by the chain rule, computing the gradient one layer at a time, iterating backward from the last layer to avoid redundant calculations of intermediate terms in the chain rule; this is an example of dynamic …

What are the different activation functions?

Types of Activation Functions

• Sigmoid Function. In an ANN, the sigmoid function is a non-linear AF used primarily in feedforward neural networks.
• Hyperbolic Tangent Function (Tanh)
• Softmax Function.
• Softsign Function.
• Rectified Linear Unit (ReLU) Function.
• Exponential Linear Units (ELUs) Function.

Why do we use cost function?

In ML, cost functions are used to estimate how badly models are performing. Put simply, a cost function is a measure of how wrong the model is in terms of its ability to estimate the relationship between X and y. This is typically expressed as a difference or distance between the predicted value and the actual value.

How do you minimize a cost function?

Well, a cost function is something we want to minimize. For example, our cost function might be the sum of squared errors over the training set. Gradient descent is a method for finding the minimum of a function of multiple variables. So we can use gradient descent as a tool to minimize our cost function.