Questions tagged [probability-theory]

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

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How to understand the phrase “conditioning on an input” for a neural network?

Suppose I have a dataset $D_1$ with size $n$ and each training sample has $m$ attributes/features. So, my neural network has $m$ neurons at input layer, i.e., $D_1$ has $n$ samples of size $m$. ...
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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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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 ...