Questions tagged [bayes-theorem]
For questions related to Bayes' theorem (or rule) used in the AI context.
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How can i cast this problem as an POMDP or an belief space MDP?
I am currently attempting to formulate my problem as either a Partially Observable Markov Decision Process (POMDP) or a Belief space MDP. My end goal is to gain insights into the proposed methods ...
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Doesn't every single machine learning classifier use conditional probability/Bayes in its underlying assumptions?
I'm reading about how Conditional Probability/ Bayes Theorem is used in Naive Bayes in Intro to Statistical Learning, but it seems like it isn't that "groundbreaking" as it is described?
If ...
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Why isn't the evidence $p(x) = 1$ if it's an observed variable?
Every explanation of variational inference starts with the same basic premise: given an observed variable $x$, and a latent variable $z$,
$$ p(z|x)=\frac{p(x,z)}{p(x)} $$
and then proceeds to expand $...
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Given A and B, C are independent of each other. Given A, B and C, D and E are independent of each other. What is the minimal number of parameters?
Assuming all variables $A, B, C, D,$ and $E$ are random binary variables. I come up with Bayes net: $D \rightarrow B \rightarrow A \leftarrow C \leftarrow E$ which has the minimal number of parameters ...
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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?
On page 572 of Norvig & Russell's AI book (edition 3)
Going from the first line to the second line in one shot like that, I am lost.
Can someone walk me through it step by step?
I tried but got:
$...
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What makes Sequential Bayesian Filtering and Smoothing tractable?
I'm currently diving into the Bayesian world and I find it pretty fascinating.
I've so far understood that applying the Bayes' Rule, i.e.
$$\text{posterior} = \frac{\text{likelihood}\times \text{prior}...
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What do we mean by "orderly opinions" in this sentence in the context of Bayes theorem?
In this page, it's written (emphasis mine)
If probabilities are thought to describe orderly opinions, Bayes theorem describes how the opinions should be updated in the light of new information
What ...
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Bayesian Perceptron: How is it compatible to Bayes Theorem?
I found a very interesting paper on the internet that tries to apply Bayesian inference with a gradient-free online-learning approach: [Bayesian Perceptron: Bayesian Perceptron: Towards fully Bayesian ...
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Bayesian Perceptron: Why to marginalize over neuron's output instead of it's weights?
I found a very interesting paper on the internet that tries to apply Bayesian inference with a gradient-free online-learning approach: Bayesian Perceptron: Towards fully Bayesian Neural Networks.
I ...
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What's the likelihood in Bayesian Neural Networks?
I'm trying to understand the concept behind BNN.
Their are based on the Bayes Theorem:
$$p(w \mid \text{data}) = \frac{p(\text{data} \mid w)*p(w)}{p(\text{data})}$$
which boils down to
$$\text{...
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Understanding how to calculate $P(x|c_k)$ for the Bernoulli naïve Bayes classifier
I'm looking at the Bernoulli naïve Bayes classifier on Wikipedia and I understand Bayes theorem along with Gaussian naïve Bayes. However, when looking at how $P(x|c_k)$ is calculated, I don't ...
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Why is the denominator ignored in the Bayes' rule?
The naïve Bayes' generative algorithm is often represented by the following formula:
$$\text{argmax}_{y} p(y|x) = \text{argmax}_y \frac{p(x|y)p(y)}{p(x)} \approx \text{argmax}_y p(x|y)p(y)$$
Why do we ...
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How is Bayes' Theorem used in artificial intelligence and machine learning?
How is Bayes' Theorem used in artificial intelligence and machine learning?
As a high school student, I will be writing an essay about it, and I want to be able to explain Bayes' Theorem, its general ...
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