Why is the Bayes classifier optimal?

It can be shown that of all classifiers, the Optimal Bayes classifier is the one that will have the lowest probability of miss classifying an observation, i.e. the lowest probability of error. So if we know the posterior distribution, then using the Bayes classifier is as good as it gets.

What is Bayes optimal error rate?

In statistical classification, Bayes error rate is the lowest possible error rate for any classifier of a random outcome (into, for example, one of two categories) and is analogous to the irreducible error. The Bayes error rate finds important use in the study of patterns and machine learning techniques.

How do you optimize naive Bayes?

Better Naive Bayes: 12 Tips To Get The Most From The Naive Bayes Algorithm

1. Missing Data. Naive Bayes can handle missing data.
2. Use Log Probabilities.
3. Use Other Distributions.
4. Use Probabilities For Feature Selection.
5. Segment The Data.
6. Re-compute Probabilities.
7. Use as a Generative Model.
8. Remove Redundant Features.

What does Bayes Theorem describe?

Bayes’ theorem, named after 18th-century British mathematician Thomas Bayes, is a mathematical formula for determining conditional probability. Conditional probability is the likelihood of an outcome occurring, based on a previous outcome occurring.

What is meant by Bayesian classifier?

A Bayesian classifier is based on the idea that the role of a (natural) class is to predict the values of features for members of that class. A Bayesian classifier is a probabilistic model where the classification is a latent variable that is probabilistically related to the observed variables.

Why is Bayes error used?

The Bayes error rate gives a statistical lower bound on the error achievable for a given classification problem and associated choice of features. By reliably estimating this rate, one can assess the usefulness of the feature set that is being used for classification.

What is the difference between Naive Bayes and Gaussian Naive Bayes?

Summary. Naive Bayes is a generative model. (Gaussian) Naive Bayes assumes that each class follow a Gaussian distribution. The difference between QDA and (Gaussian) Naive Bayes is that Naive Bayes assumes independence of the features, which means the covariance matrices are diagonal matrices.

What is Bayes theorem and maximum posterior hypothesis?

Maximum a Posteriori or MAP for short is a Bayesian-based approach to estimating a distribution and model parameters that best explain an observed dataset. MAP involves calculating a conditional probability of observing the data given a model weighted by a prior probability or belief about the model.