Questions tagged [random-variable]

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

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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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46 views

Which of the following probability distribution is generating an iid dataset?

Let $X_1, X_2$ be two discrete random variables. Each random variable takes two values: $1, 2$ The probability distribution $p_1$ over $X_1, X_2$ is given by $$p_1(X_1=1, X_2 = 1) = \dfrac{1}{4}$$ $$...
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1answer
32 views

Can I always interpret features as random variables in machine learning safely?

Consider the following statements from Chapter 5: Machine Learning Basics from the book titled Deep Learning (by Aaron Courville et al.) Machine learning tasks are usually described in terms of how ...
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1answer
37 views

What are the iid random variables for a dataset in the GAN framework?

I am trying to understand why mean is used for expectation in training Generative Adversarial Networks. The answer tells that it is due to the law of large numbers which is based on the assumption ...
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1answer
145 views

Is it abuse of notation to use tilde operator in this context?

The following is a way to use tilde (∼) in context of random variables or random vectors. In statistics, the tilde is frequently used to mean "has the distribution (of)," for instance, $X∼N(...
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Is it possible to use (infinite cardinal) random variables during implementation?

Random variables can be classified into three types: random variables whose range is finite, random variable whose range is countably infinite and random variables whose range is uncountable. Random ...
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24 views

What machine learning model should I use for a random dice-based game?

Consider a game like Pig (https://en.wikipedia.org/wiki/Pig_(dice_game)), but with a few additions: namely functions of both player's score and turn number that have unique impacts on scoring. What ...
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1answer
67 views

In the definition of the state-action value function, what is the random variable we take the expectation of?

I know that $$\mathbb{E}[g(X) \mid A] = \sum\limits_{x} g(x) p_{X \mid A}(x)$$ for any random variable $X$. Now, consider the following expression. $$\mathbb{E}_{\pi} \left[ \sum \limits_{k=0}^{\infty}...
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1answer
144 views

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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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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1answer
55 views

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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49 views

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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146 views

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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What kind of distributions can be used to model discrete latent variables?

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 ...