Question

What is Bayes Theorem in ML?

Answer 1

ML Bayes Theorem:

• One of the most recent developments in artificial intelligence is machine learning.
• The Bayes Theorem is the key idea in machine learning.
• The Bayes theorem is frequently referred to as the Bayes rule or Bayes Law.
• One of the most well-known theories in machine learning, the Bayes theorem helps determine the likelihood that one event will occur with unclear information while another has already happened.
• The mathematical formulation of the Bayes theorem is $P\left(\overline{)X}Y\right)=\frac{P\left(\overline{)Y}X\right)·P\left(X\right)}{P\left(Y\right)}$. Here,

1. Both occurrences $X$ and $Y$ are separate occurrences. This indicates that the likelihood of the two occurrences' outcomes is independent of one another.
2. $P\left(X\right|Y)$ is known as the posterior. It is described as a revised probability that takes the available data into account.
3. $P\left(Y\right|X)$ referred to as the likelihood. It is the likelihood that the theory will be supported by evidence.
4. $P\left(X\right)$ is referred to as the prior probability, or the probability of a hypothesis before taking the data into account.
5. $P\left(Y\right)$ referred to as marginal probability. It is described as the likelihood of the evidence taken into account.

• The Bayes theorem has a wide range of uses in machine learning, making it one of the most popular approaches among all algorithms for classification-related issues. So, it is safe to claim that the Bayes theorem plays a significant role in machine learning.

Hence, Bayes Theorem in ML is described.