Naive Bayes Flashcards
(30 cards)
What does Bayes’ Theorem compute?
The probability of a hypothesis given observed evidence.
What is the formula for Bayes’ Theorem?
P(A|B) = P(B|A) * P(A) / P(B)
What is P(A) in Bayes’ Theorem?
The prior probability of the hypothesis.
What is P(B|A) in Bayes’ Theorem?
The likelihood of the evidence given the hypothesis.
What is P(B) in Bayes’ Theorem?
The total probability of the evidence.
What is P(A|B) in Bayes’ Theorem?
The posterior probability of the hypothesis after seeing the evidence.
What does the Thomas (librarian vs. farmer) example illustrate?
The importance of including base rates (priors) in probability judgments.
What does the Naïve Bayes classifier assume?
That all features are conditionally independent given the class label.
What is the main benefit of the independence assumption in Naïve Bayes?
It simplifies the computation of class probabilities.
What is the goal of the Naïve Bayes classifier?
To find the most probable class label given a set of features.
Does Naïve Bayes calculate the denominator P(x1,…,xn) for classification?
No, it’s the same for all classes and can be ignored when comparing.
What type of output does Naïve Bayes provide?
Probabilistic class predictions.
What does ‘naïve’ refer to in Naïve Bayes?
The assumption that all features are independent given the class.
In the one-feature walking example, what was the predicted probability of walking on a sunny day?
0.75
What happens when Naïve Bayes is extended to multiple features?
It multiplies the conditional probabilities of all features for each class.
What is Gaussian Naïve Bayes used for?
Modeling continuous input features using normal distributions.
What distribution is assumed in Gaussian Naïve Bayes?
The normal (Gaussian) distribution.
What is the formula for the Gaussian probability density function?
P(x|μ,σ) = (1 / √(2πσ²)) * e^{-(x - μ)² / (2σ²)}
What parameters are estimated in Gaussian Naïve Bayes for each class?
Mean (μ) and standard deviation (σ) for each feature.
What is the role of priors in Naïve Bayes classification?
They adjust the likelihoods based on class frequencies in the data.
How does Naïve Bayes handle continuous and categorical data?
It models continuous features with Gaussians and categorical ones with frequencies.
What kind of features does Naïve Bayes assume are conditionally independent?
All features given the class label.
What is one limitation of Naïve Bayes?
It assumes all features are independent, which is often not true.
What is Laplace smoothing used for in Naïve Bayes?
To prevent zero probabilities for unseen feature-class combinations.
