All Questions
Tagged with bayes-rule or bayes-theorem
13 questions
3
votes
2
answers
535
views
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 ...
user65577
0
votes
1
answer
83
views
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 $...
- 1
-1
votes
1
answer
104
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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 ...
- 11
0
votes
1
answer
71
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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:
$...
- 115
0
votes
0
answers
60
views
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.
$$\text{posterior} = \frac{\text{likelihood}\times \text{prior}...
- 1
4
votes
1
answer
49
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What do we mean by "orderly opinions" in this sentence in the context of Bayes theorem?
In this page, it's written (emphasis mine)
If probabilities are thought to describe orderly opinions, Bayes theorem describes how the opinions should be updated in the light of new information
What ...
- 41
1
vote
2
answers
282
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Bayesian Perceptron: How is it compatible to Bayes Theorem?
I found a very interesting paper on the internet that tries to apply Bayesian inference with a gradient-free online-learning approach: [Bayesian Perceptron: Bayesian Perceptron: Towards fully Bayesian ...
- 99
0
votes
1
answer
233
views
Bayesian Perceptron: Why to marginalize over neuron's output instead of it's weights?
I found a very interesting paper on the internet that tries to apply Bayesian inference with a gradient-free online-learning approach: Bayesian Perceptron: Towards fully Bayesian Neural Networks.
I ...
- 99
1
vote
1
answer
794
views
What's the likelihood in Bayesian Neural Networks?
I'm trying to understand the concept behind BNN.
Their are based on the Bayes Theorem:
$$p(w \mid \text{data}) = \frac{p(\text{data} \mid w)*p(w)}{p(\text{data})}$$
which boils down to
$$\text{...
- 19
1
vote
1
answer
105
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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 ...
- 65
0
votes
1
answer
169
views
6
votes
1
answer
1k
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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 ...
- 366
11
votes
3
answers
10k
views
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 ...
- 111