Bayes Theorem for Machine Learning

What is Bayes theorem?

Using Bayes’s Theorem, you may calculate the conditional probability of an event occurring. The probability formula is typically used to calculate Bayes conditional probability, which includes calculating the joint probability of both events occurring concurrently and then dividing it by the chance of event two occurring. It is possible to calculate machine learning conditional probability by utilizing Bayes Theorem.

Use the following steps to calculate conditional probability using Bayes’ theorem:

  • Consider that condition A is true, then calculate the likelihood that condition B is also true.
  • Be able to calculate the likelihood of A occurring.
  • Double the two probabilities to get the final result.
  • Subtract event B’s probability from the total.

Making this calculation is especially beneficial when computing the conditional probability is straightforward.

  • Naive Bayes is used for solving a wide range of classification and regression problems in a variety of fields.

Implementations for Bayes Theorem

The Naive Bayes method is the most popular use of the Bayes theorem in machine learning. This theorem is frequently used in natural language processing or as bayesian analysis tools in machine learning.

As the name suggests, Naive Bayes assumes that the values assigned to the witness’s evidence/attributes – Bs in P(B1, B2, B3*A) – are independent of one another. Assuming these attributes have no impact on each other simplifies the model and makes computations possible, rather than attempting to calculate the intricate interactions between the attributes. When this assumption isn’t true (which is probably the case), the Naive Bayes theorem for classification tends to perform well.

  • Multinomial, Bernoulli, and Gaussian variations of the Naive Bayes classifier are also widely employed in classification.

There are a variety of methods for classifying texts, including the multinomial Naive Bayes algorithm, which is particularly useful for understanding the frequency of words inside documents.

Bernoulli Naive Bayes is a similar method to Multinomial Naive Bayes, but the predictions are boolean. Meaning that the values will be binary, no or yes when predicting a class. Using a Bernoulli Naive Bayes method, a text classification system would determine whether or not a word is included in the text.

Gaussian Naive Bayes can be employed if the values of the predictors/features aren’t discrete, but rather continuous. The values of the continuous features are considered to have been sampled from a Gaussian distribution.

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Bayes Theorem on practical application

Let’s look at an instance of the Bayes Theorem in machine learning to make this easier to understand. Let’s say you’re playing a guessing game in which numerous players tell you a slightly different story and you have to figure out which one of them is telling the truth to you. Now let’s fill in the variables in this guessing game scenario to complete the Bayesian learning in machine learning.

So if there are four other players besides you, categorical variables P1, P2, P3, and P4 can be used to predict whether each member in the game is lying or stating the truth. What they do is the proof that they are lying or telling the truth.

There are various ways to figure out if a certain person is lying, just like when you play poker. Any evidence that their story isn’t true would be helpful if you were able to interrogate them. A person’s lying proof can be represented as L.

Clarification: We want to forecast Probability. So we will say that person P# is lying based on their behavior. Our goal would therefore be to determine the probability of L given P, or the chance that their conduct would occur regardless of whether the person was lying or not. Try to figure out under what circumstances the behavior you’ve observed would make the most sense.

This computation would be done for each of the actions that you are watching if you were to observe three behaviors. As a result, you would have to repeat the process for each instance of person and for every player in the game other than yourself.

Our probabilistic model would be updated based on any new information we got about the actual chances in this equation. Your prior probabilities are updated, and this is what is referred to as updating your prior probabilities.