Loss Functions in Machine Learning: An Easy Overview(2021)

Ajay Ohri


By means of the loss function, machines learn. It is a method of determining how well the particular algorithm models the given data. In a project, if real outcomes deviate from the projections, then comes the loss function that will cough up a very large amount. Gradually, with the aid of any optimization function, the loss function in machine learning reduces the error in estimation. In this article, we will go over some loss functions, and their implementations in the area of machine or loss function deep learning.

There’s no option that fits all loss function of algorithms in machine learning. Many other considerations are involved in choosing a loss of function for a particular problem, such as the type of machine learning algorithm selected, ease of computing the derivatives, and the type of machine learning algorithm is selected at some degree of outliers percentage to set in the data. 

The loss function can be categorized into two main groups based upon the type of learning task, and those are :

  1. Regression Losses 
  2. Classification Losses

In classification, one can predict the output from a set of finite categorical values, i.e. categorizing a broad data set of handwritten digits into one of 0–9 digits.

Regression losses, on the other hand, deals with projecting a constant value, for example, given floor space, the size of rooms, the number of rooms and predicting the price of space.


        n – examples of the number of training.

        i – data set ith training example.

        y(i) – Training example for ith ground truth label

        y_hat(i) – ith training example predictions

1. Regression Losses 

  • Quadratic Loss/ L2 Loss /Mean Square Error

Mathematical formulation:-

MSE loss performs as outlined because of the average of absolute variations between the particular and also the foretold value. It’s the second most ordinarily used Regression loss function. The function value is the Mean of these Absolute Errors (MAE). The MAE Loss function is additional strong to outliers compared to the MSE Loss function. Therefore, it ought to be used if the information is liable to several outliers. The logistic loss function has nice mathematical properties, which make it simpler to measure the logistic regression loss function. 

  • Mean Absolute Error/L1 Loss 

Mathematical formulation:-

A mean absolute error also means the linear loss function, which is calculated as the average number of absolute variations between real measurements and forecasts. Like MSE, calculate the degree of error without considering their quality loss function. Unlike MSE, MAE needs more complex methods such as linear regression loss function to calculate the gradients. Here, MAE is more resistant to outliers because it does not use the square.

  • Mean Bias Error

This is less popular in the machine learning domain as opposed to its counterpart because it is the same as MSE, with the only exception that we do not take absolute values. In simple words, there is a need for caution as positive and negative errors could balance each other out. Since mean bias error is less reliable in practice, it could decide whether the model had a negative bias or positive bias.

Mathematical formulation:-

2. Classification Losses

  • Multi-class SVM Loss/ Hinge Loss

The score of all the incorrect categories should be lesser than the scores of the correct category by some safety margin. The most typical loss operates used for Classification issues, and another to Cross-Entropy loss function is Hinge Loss, primarily developed for Support Vector Machine (SVM) model evaluation.

Mathematical formulation:-

  • Cross-Entropy Loss / Negative Log-Likelihood

This is one of the common settings for classification problems. Cross-entropy loss rises from the actual label to the predicted probability diverge.

Mathematical formulation:-

  • Cross entropy loss

This is that the most typical Loss performs utilized in Classification problems. The cross-entropy loss decreases because the expected likelihood converges to the particular label. It measures the performance of a classification model whose predicted output could be a probability worth between zero and 1. The cross-entropy loss function penalizes the predictions that are right but proved to be wrong.

  • Quantile Loss 

A quantile is a value from which a percentage of samples in a group drop. Machine learning models work by reducing (or maximizing) an objective function. As the name suggests, the quantile regression loss function is applied to estimate quantiles. For a series of forecasts, the failure would be the average.

  • Log-Cosh Loss

The Log-Cosh loss is described as the number system of the hyperbolic trigonometric function of the prediction error. It is another function used in regression tasks and is much simpler than MSE Loss. It has all the advantages of Huber loss, and some Learning algorithms like XGBoost use Newton’s method to find the optimum.


Above, we have mentioned the various types of loss function example, which will give a clear understanding of What is a loss function in machine learning.

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