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16 votes
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Are softmax outputs of classifiers true probabilities?

The answer is both yes, and no. Or, to put it another way, the answer depends on what exactly you mean by "represent probabilities", and there is a valid sense in which the answer is yes, ...
D.W.'s user avatar
  • 307
12 votes

Are softmax outputs of classifiers true probabilities?

Excellent question. The simple answer is no. Softmax actually produces uncalibrated probabilities. That is, they do not really represent the probability of a prediction being correct. What usually ...
Dr. Snoopy's user avatar
  • 1,345
5 votes
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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?

No, the substitution you suggest based on Equation (3.4) is not correct because you forgot about the $\sum_{r \in \mathcal{R}}$ in the right-hand side Equation (3.4). Equation (3.4) says (leaving out ...
Dennis Soemers's user avatar
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3 votes
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Why don't we also need to approximate $p(x \mid z)$ in the VAE?

What I can guess here is that, in VAEs, we assume $p(z)$ (prior), so we are able to calculate $p(x \mid z)$, but for $p(x)$ we can't assume its distribution? Is it right? You could assume $p(x)$ is ...
nbro's user avatar
  • 40.9k
3 votes
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How is the formula for the Bayes error rate with an integral derived?

Bayes Error Rate For the general case of K different classes, the probability of classifing x instance correctly is: \begin{equation} \label{eq1} \begin{split} P(correct) & = \sum_{i=1}^{K} p(x \...
ddaedalus's user avatar
  • 919
3 votes

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

The function $r(s,a,s')$ gives the expected reward in each scenario, but not the distribution of rewards that lead to values $r_{search}$ and $r_{wait}$ The text explains that reward is $+1$ for ...
Neil Slater's user avatar
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2 votes

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

At first, like Neil Slater says, I thought this could only be solved using the expected rewards instead of actual rewards, or else there wasn't enough information to solve it. But now I think there ...
IssaRice's user avatar
  • 171
2 votes

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

In the book you mentioned, the author is dealing with classification, that is, inferring the label $y$ from a sample $x$. Let $X$ and $Y$ be the corresponding random variables. $p(y|x)$ can be ...
Eduardo Montesuma's user avatar
2 votes
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Why is the equation $\mathbb{E} \left[ (Y - \hat{Y})^2 \right] = \left(f(X) - \hat{f}(X) \right)^2 + \operatorname{Var} (\epsilon)$ true?

Let's say we have $a$ - constant and $\epsilon \sim \mathcal{N}(0,\sigma)$, then: $$\mathbb{E}\left[(a+\epsilon)^2\right] = \mathbb{E}\left[a^2\right] + 2 \mathbb{E}\left[a\right]\mathbb{E}\left[\...
Kostya's user avatar
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1 vote
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Book(s) recomendation for Probability Theory Foundations

This right here is the money shot. https://ocw.mit.edu/courses/18-05-introduction-to-probability-and-statistics-spring-2022/pages/classes-reading-and-in-class-materials/ That's essentially what you're ...
Joseph's user avatar
  • 51
1 vote

Independence of random variable in Gaussian Process context

It is not saying that the $t_n$ are independent of one another but that $t_n|y_n$ are independent. The only variation in the target values $t_n$ once you've supplied the $y_n$ is given by $\epsilon_n$....
Eponymous's user avatar
  • 146
1 vote

Why is the equation $\mathbb{E} \left[ (Y - \hat{Y})^2 \right] = \left(f(X) - \hat{f}(X) \right)^2 + \operatorname{Var} (\epsilon)$ true?

Let me try to show this. The only (non-constant) random variable here is $\epsilon$, while $f(X)$ and $\hat{Y} = \hat{f}(X)$ are constant random variables (so their expectations is equal to their only ...
nbro's user avatar
  • 40.9k
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 ...
nbro's user avatar
  • 40.9k
1 vote

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

Your professor is wrong (or maybe you misunderstood what he wanted to say, or he did not explain correctly what he wanted to say). It may be a good idea to ask your professor for some clarification ...
nbro's user avatar
  • 40.9k
1 vote

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] ...
OmG's user avatar
  • 1,826
1 vote
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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 ...
ddaedalus's user avatar
  • 919
1 vote

Is it possible to compute $P( F \mid S )$ given $P(F \mid S,A)$ and $P(F \mid S, \lnot A)$ in Bayesian network?

This is a bit of a puzzle but you can compute a reasonable narrow limit even without knowing whether or not $P(S,A) = P(S) P(A)$. Start with the contingency table relating $P(S, A)$, $P(S,\neg A)$, $...
Sextus Empiricus's user avatar
1 vote

What are the main benefits of using Bayesian networks?

Yes, you are correct that one of the key benefits of Bayesian networks is that they allow you to calculate joint probability distributions without directly using the chain rule of probability. ...
Hans-Peter Schrei's user avatar
1 vote

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

This means that the reward set is actually R={0,1,−3} (we assume that in each timestep, the robot can only collect one can). @riceissa While I agree with the rest of your demonstration, I wouldn't ...
Etienne Kintzler's user avatar
1 vote

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

In the announced problem, most of the transitions aren't possible, so most the terms of equations (3.3) and (3.4) from the book will end up being 0. In my understanding, $$ \begin{align} p(s'= high |...
Gigi's user avatar
  • 111

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