# Tag Info

### 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 ...
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### 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)...
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### 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 ...

### Doesn't every single machine learning classifier use conditional probability/Bayes in its underlying assumptions?

Conditional probability and Bayes rule are related but they are not the same thing, you can predict conditional probabilities without using Bayes rule. So no, not all machine learning classifiers use ...
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### What is Bayes' theorem?

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

### Doesn't every single machine learning classifier use conditional probability/Bayes in its underlying assumptions?

Probability is one way to solve classification problems. Still, there are other ways like clustering and K nearest neighbor approach where we tend to analyze the position of the current data point and ...
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### 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:...
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### What do we mean by "orderly opinions" in this sentence in the context of Bayes theorem?

That term exactly refers to the difference between two main paradigms in probability and statistics: Frequentism vs Bayesianism. You can find many texts for explaining the difference, for example [1] ...
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### 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 ...
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### 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 ...
• 40.5k
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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### 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 ...
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### 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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