4 votes

How is Bayes' Theorem used in artificial intelligence and machine learning?

Bayes theorem states the probability of some event B occurring provided the prior knowledge of another event(s) A, given that B is dependent on event A (even partially). A real-world application ...
  • 1,953
4 votes
Accepted

Why is the denominator ignored in the Bayes' rule?

The answer from @kiner_shah in the comments has solved it: They have eliminated it because in comparing probability for best outcome, it would just introduce additional division and the divisor p(x)...
  • 326
2 votes
Accepted

Bayesian Perceptron: How is it compatible to Bayes Theorem?

Thanks for asking the question. I'm the author of the paper. The key point is that the weights $w$ cannot be updated directly with the new data as $w$ is not directly related with the output $y$ (see ...
2 votes

What is Bayes' theorem?

Bayes' theorem relates conditional probabilities: $$P(A \mid B) = \frac{P(B \mid A) P(A)}{P(B)}$$
1 vote
Accepted

Why is $P(X_{t+1} \mid e_{1:t}, e_{t+1}) = \alpha P(e_{t+1} \mid X_{t+1}, e_{1:t}) P(X_{t+1} \mid e_{1:t})$ true in Norvig & Russell's book?

Let me denote the events with simpler symbols $A = X_{t+1}$ $C = e_{1:t} = e_1, \dots e_t$ $D = e_{t+1}$ So, we can rewrite $$ P(X_{t+1} \mid e_{1:t}, e_{t+1}) = \alpha P(e_{t+1} \mid X_{t+1}, e_{1:...
  • 35k
1 vote

Bayesian Perceptron: Why to marginalize over neuron's output instead of it's weights?

We want a distribution over $w$, don't we? Yes. You want to obtain a distribution over the parameters, which models the uncertainty about the parameters. This distribution over the parameters can ...
  • 35k
1 vote

What's the likelihood in Bayesian Neural Networks?

The likelihood depends on the task that you are solving, so this is similar to traditional neural networks (in fact, even these neural networks have a probabilistic/Bayesian interpretation!). For ...
  • 35k
1 vote
Accepted

Understanding how to calculate $P(x|c_k)$ for the Bernoulli naïve Bayes classifier

Bernoulli naïve Bayes $P(x \mid c_k) = \prod^{n}_{i=1} p^{x_i}_{ki} (1-p_{ki})^{(1-x_i)}$ Let's examine the example of document classification. Let K different text classes and n different terms that ...
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1 vote

How is Bayes' Theorem used in artificial intelligence and machine learning?

If you want to understand in one line how it's used in AI, I would say how you update your beliefs according to new data/information is calculated by Bayes' theorem. Bayes' theorem says it will ...
1 vote

How is Bayes' Theorem used in artificial intelligence and machine learning?

Since you are a highschool student I will try to express it easier. It is a problem for a machine to make a decision if you haven't given that information to it before. You should think of every cases ...
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