What is Cross-Entropy in Machine learning?
In recent years, machine learning has special scrutiny with respect to both industry and academia and proved its potential strength in extensive applications, like pattern analysis, data exploration, and development predictions. As acknowledged for this field, data resources are important in learning task that provides different formats and structures of data.
Where in small scale datasets, expert knowledge is acceptable to some extent for precise footnote and interpretation, and in large scale datasets, data analysis becomes a complicated task where accuracy and precise predictions matter a lot for unstructured or unlabeled data.
With the volume of the increasing datasets, their analysis tends to generalize better but the annotations cost in terms of money and time, adding more, different mathematical and statistical methods are highly deployed for successful annotations. The same tool is cross-entropy.
Let’s learn about cross-entropy, its extensions (Loss Function and KL Divergence) and their role in respect to machine learning.
Understanding Cross-Entropy
In order to understand cross-entropy, starting with the definition of the entropy, ‘
“Entropy is defined as the smallest average size of the encoding per transportation by which any source can send data efficiently to the destination without any loss of information.” Mathematically, the probability distribution is used to define entropy.
Back to cross-entropy, It is a measure of the degree of dissimilarities between two probability distribution, in the connection with supervised machine learning, one of the probability distributions shows the label ”true” for training samples and correct replies are indicated with the value hundred percent.
Cross-Entropy is expressed by the equation;
Where x represents the predicted results by ML algorithm, p(x) is the probability distribution of “true” label from training samples and q(x) depicts the estimation of the ML algorithm.
Cross-entropy is a distinction measurement between two possible distributions for a set of given random variables or events. It builds on the concept of data-entropy and finds the variety of bits needed to transform an event from one distribution to another distribution.
Cross-entropy examines the predictions of models with the true probability distribution. It goes down when predictions get more accurate and become zero when predictions tend to perfect.
KL Divergence (Relative Entropy)
The Kullback-Liebler Divergence or KL Divergence quantifies between two probability distribution, i.e measure the difference between two probability distributions, a KL Divergence having value zero indicates the identical probability distribution.
For probability distributions P and Q, KL Divergence is given by the equations,
For discrete distributions,
For continuous distributions,
In other words, from Machine Learning: A Probabilistic Perspective,2012,
The KL Divergence is the average number of extra bits needed to encode the data, due to the fact that we need distribution q to encode the data instead of the true distribution p.
Cross-Entropy as Loss Function
Cross entropy is extensively used as a Loss Function when optimizing classification models, e.g. logistics regression or ANN algorithms used for classification tasks.
In brief, classification tasks involve one or more input variables and prediction of a class label description, in addition, if the classification problems contain only two labels for the outcomes’ predictions refereed as a binary classification problem and if classification problems consist of more than two variables are termed as categorical or multi-class classification problems.
Cross-entropy loss measures the achievement of a classification model that gives output in terms of probability having values between 0 and 1. It increases as the estimated probability deviates from the actual class label.
E.g. A model contains a sample with a known class label having a probability of 1.0 and the probability of 0.0 for other class labels, this model can measure the probability of each class label, now the role of cross-entropy comes here, it is then used to find the difference between the probability distributions of different class labels. Also, cross-entropy enables one to choose the plausible split that reduces the uncertainty about the classification.
Conclusion
This tutorial covers the important concepts of entropy, cross-entropy, and its extensions in terms of a loss function and KL Divergence. I hope it gave you a significant understanding of these commonly used terms and their roles in a better understanding of machine learning and neural networks.
Although, you have learned Cross-Entropy can be applied as a Loss Function when optimizing classification models, and it is different from KL Divergence but can be determined using KL Divergence, and is separated from Log Loss but estimates the same quantity when practiced as a Loss Function.
