Why do we use Huber loss?

Why do we use Huber loss?

In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used.

Why is Huber loss more robust to outliers?

Indeed, for absolute errors smaller than α the corresponding distribution resembles the normal distribution, outside this region it coincides with the more heavy-tailed Laplace distribution. This is precisely the reason why this loss is robust against outliers.

What is modified Huber loss?

Modified Huber loss stems from Huber loss, which is used for regression problems. Looking at this plot, we see that Huber loss has a higher tolerance to outliers than squared loss. As you’ve noted, other loss functions are much more tolerant to outliers, with the exception of squared hinge loss.

Is Huber loss function differentiable?

Huber loss is less sensitive to outliers in data than the squared error loss. It’s also differentiable at 0. It’s basically absolute error, which becomes quadratic when error is small.

What is pseudo Huber loss?

Pseudo-Huber Loss Function Huber loss is, as Wikipedia defines it, “a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss [LSE]”. This loss function attempts to take the best of the L1 and L2 by being convex near the target and less steep for extreme values.

How is Huber loss calculated?

Defining a Custom Loss Function – Huber Loss

1. Huber loss is defined as:
2. abs(x) returns the positive value(absolute value) of x .
3. square(x) returns the squared value of x .
4. where(bool_array, x, y) returns the elements where condition is True in bool_array (multiplexing x and y ).

Why use cross entropy instead of MSE?

First, Cross-entropy (or softmax loss, but cross-entropy works better) is a better measure than MSE for classification, because the decision boundary in a classification task is large (in comparison with regression). For regression problems, you would almost always use the MSE.

What is Delta in Huber loss?

In Huber loss function, there is a hyperparameter (delta) to switch two error function.

When do you use the Huber loss function?

In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used. The Huber loss function describes the penalty incurred by an estimation procedure f. Huber (1964) defines the loss function piecewise by .

Which is the error measure proposed by Huber Huber?

Figure 1 Error measure proposed by Huber Huber (1973). The upper part above is the l1 norm, while the lower part is the l2 norm. The problem is this: given some observed data , we want to find the best model that explains the data via the operator .

Which is more robust Huber loss or MSE?

Huber loss is more robust to outliers than MSE. It is used in Robust Regression, M-estimation and Additive Modelling. A variant of Huber Loss is also used in classification. The name is pretty self-explanatory. Binary Classification refers to assigning an object into one of two classes.

How to minimize the Huber misfit function?

In the work reported here, I use a hybrid l1 – l2 error measure proposed by Huber Huber (1973) : I will call the Huber misfit function ,or Huber function for short (Figure 1 ). Note that the Huber function is smooth near zero residual, and weights small residuals by the mean square.