Questions tagged [random-variable]
For questions related to the mathematical concept of a random variable (in the context of AI).
22 questions
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Why neural networks model statistical patterns
I've tried to come up with a simple connection between statistics and deep learning. One question is:
In very simplified terms, why do neural networks model probability distributions?
What I expect ...
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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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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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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
$$p_1(X_1=1, X_2 = 1) = \dfrac{1}{4}$$
$$...
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Can I always interpret features as random variables in machine learning safely?
Consider the following statements from Chapter 5: Machine Learning Basics from the book titled Deep Learning (by Aaron Courville et al.)
Machine learning tasks are usually described in terms of how ...
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What are the iid random variables for a dataset in the GAN framework?
I am trying to understand why mean is used for expectation in training Generative Adversarial Networks.
The answer tells that it is due to the law of large numbers which is based on the assumption ...
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Is it abuse of notation to use tilde operator in this context?
The following is a way to use tilde (∼) in context of random variables or random vectors.
In statistics, the tilde is frequently used to mean "has the
distribution (of)," for instance, $X∼N(...
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Is it possible to use (infinite cardinal) random variables during implementation?
Random variables can be broadly classified into three types:
random variables whose range is finite,
random variable whose range is countably infinite and
random variables whose range is uncountable.
...
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What machine learning model should I use for a random dice-based game?
Consider a game like Pig (https://en.wikipedia.org/wiki/Pig_(dice_game)), but with a few additions: namely functions of both player's score and turn number that have unique impacts on scoring.
What ...
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In the definition of the state-action value function, what is the random variable we take the expectation of?
I know that
$$\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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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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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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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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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 ...
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