# Questions tagged [probability-theory]

For questions related to probability theory in the context of artificial intelligence.

21 questions
Filter by
Sorted by
Tagged with
10 views

485 views

### Why don't we also need to approximate $p(x \mid z)$ in the VAE?

In the VAE, we approximate the probability distribution $p(z \mid x)$, where $z$ is the latent vector and $x$ is our data. The reason is that $p(z \mid x)$ becomes impossible to calculate for ...
• 175
1 vote
123 views

### Which formula of p(x, y) to use?

The probability distribution $p(x, y)$ can be calculated in two ways : $p(x, y) = p(y \mid x) p(x)$ $p(x, y) = p(x \mid y) p(y)$ But according to the book Deep Generative Modeling (page number 3 ...
• 175
1 vote
335 views

### Why are today's neural networks not modeled with probability theory?

In the paper The Perceptron: A probabilistic model for information storage and organization in the brain, Rosenblatt used the probability theory to model his perceptron. My professor told me that ...
• 11
48 views

### 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
158 views

### How would the probability of a document $P(d)$ be computed in the Naive Bayes classifier?

In naive Bayes classification, we estimate the class of a document as follows $$\hat{c} = \arg \max_{c \in C} P(c \mid d) = \arg \max_{c \in C} \dfrac{ P(d \mid c)P(c) }{P(d)}$$ It has been said in ...
• 3,890
443 views

1 vote
102 views

### 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
68 views

• 11
603 views

### What are the main benefits of using Bayesian networks?

I have some trouble understanding the benefits of Bayesian networks. Am I correct that the key benefit of the network is that one does not need to use the chain rule of probability in order to ...
1k views

### How do compute the table for $p(s',r|s,a)$ (exercise 3.5 in Sutton & Barto's book)?

I am trying to study the book Reinforcement Learning: An Introduction (Sutton & Barto, 2018). In chapter 3.1 the authors state the following exercise Exercise 3.5 Give a table analogous to that ...
• 255
### Why is the equation $r(s', a, s') =\sum_{r \in \mathcal{R}} r \frac{p\left(s^{\prime}, r \mid s, a\right)}{p\left(s^{\prime} \mid s, a\right)}$true?
I am referring to eq. 3.6 (page 49) based on Sutton's online book and can be found in an image below. I could not make sense of the final derivation of the equation $r(s, a, s')$. My question is ...