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# Questions tagged [random-variable]

For questions related to the mathematical concept of a random variable (in the context of AI).

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### Independence of random variable in Gaussian Process context

From Bishop's Pattern Recognition and Machine Learning: $t_n = y_n + \epsilon_n$, where $\epsilon_n$ is a random noise variable whose value is chosen independently for each observation $n$. Consider ...
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### Trouble understanding Variational Inference objective

I was reading the Meta Temporal Point Processes paper and was having trouble understading the training objective presented. The authors state that it is the ELBO used in Variational Inference ...
1 vote
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### How to compute an estimate of the expected value of a stochastic random variable in Reinforcement Learning?

In the section on LSTD in SuttonBarto's book on RL, there is a proof on convergence of semi-gradient TD(0) using a linear function approximator. Later on they estimated A and b as I was under the ...
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### What should be taken as random variables in the distributions of datasets?

Consider the following two paragraphs taken from the paper titles Generative Adversarial Nets by Ian J. Goodfellow et.al #1: Abstract We propose a new framework for estimating generative models via ...
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### Is there any advantage in viewing weights of a neural network as random variables?

In artificial intelligence, especially in machine learning, the inputs and outputs of neurons in a neural network can be viewed as random variables. And this view is highly useful in many ways. The ...
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### For the VAE, should the input, output and latent variable code be random variables?

For a variational autoencoder, we have input $x$ (assume 1 data point for now, like an image), a latent code sampled from the decoder, $z$, and an output $\hat{x}$. If I were to draw a diagram for the ...
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### When can we call a feature "hierarchical"?

Features in machine learning are the attributes of the elements of a data set. They are considered as random variables in probability. Consider the following excerpt from 1.1: The deep learning ...
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### What are the different possible usages of the word "i.i.d" in machine learning?

The acronym "iid" stands for "independent and identically distributed". It is a property of a sequence of random variables. You can read here for more details. This question is ...
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### Is knowing underlying probability distribution mandatory for deciding iid property of random variables?

Consider the following information regarding iid random variables The acronym IID stands for "Independent and Identically Distributed". A sequence of random variables (or random vectors) is ...
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### What does the notation $\mathcal{N}(z; \mu, \sigma)$ stand for in statistics?

I know that the notation $\mathcal{N}(\mu, \sigma)$ stands for a normal distribution. But I'm reading the book "An Introduction to Variational Autoencoders" and in it, there is this notation:...
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1 vote
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### Why is this variable in equation 2 of the SQAIR paper a random vector of $n$ ones followed by a zero?

I've been reading the SQAIR paper lately, and the mathematics involved seems a bit complicated. Some background, about the paper: SQAIR stands for Sequential Attend, Infer, Repeat - the paper does ...
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### Should the biases be zero or randomly initialised?

I'm initialising DNN of shape [2 inputs, 2 hiddens, 1 output] with these weights and biases: ...
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1 vote
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### What is the point of converting conditional probability to factor for Variable Elimination?

I have this slide from my AI class on using a Bayes network to compute a conditional probability. I don't really understand the point of converting the conditional probabilities to factors (besides ...
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### Is learning possible without random thoughts and actions?

In my view intelligence begins once the thoughts/actions are logical rather than purely randomn based. The learning environments can be random but the logic seems to obey some elusive rules. There is ...
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If we take the vanilla variational auto-encoder (VAE), we $p(z)$ is a Gaussian distribution with zero mean and unit variance and we approximate $p(z|x) \approx q(z|x)$ to be a Gaussian distribution as ...