7 votes
Accepted

What does the notation $\mathcal{N}(z; \mu, \sigma)$ stand for in statistics?

It means that $z$ has a (multivariate) normal distribution with 0 mean and identity covariance matrix. This essentially means each individual element of the vector $z$ has a standard normal ...
David's user avatar
  • 4,900
2 votes
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Is it abuse of notation to use tilde operator in this context?

The notation $p(x)$ is widely used in machine learning (e.g. here) and even statistics (e.g. here). People often use $p(x)$ to refer to a probability distribution (either pmf, pdf, or cdf) rather than ...
nbro's user avatar
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2 votes
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In the definition of the state-action value function, what is the random variable we take the expectation of?

I am using the convention of uppercase $X$ for random variable and lowercase $x$ for an individual observation. It is possible your source material did not do this, which might be causing your ...
Neil Slater's user avatar
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2 votes
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Should the biases be zero or randomly initialised?

From the stanford CNN class (http://cs231n.github.io/neural-networks-2/): Blockquote Initializing the biases. It is possible and common to initialize the biases to be zero, since the asymmetry ...
RonsenbergVI's user avatar
2 votes
Accepted

Is learning possible without random thoughts and actions?

Learning is possible without random thoughts and actions. Knowledge can be encapsulated in predetermined forms and passed through predetermined knowledge transfer mechanisms. Much of civilization is ...
Douglas Daseeco's user avatar
2 votes

Is knowing underlying probability distribution mandatory for deciding iid property of random variables?

The point is even you know the distribution, sometimes you can't prove that the sampled data is i.i.d. or not! (more details in https://stats.stackexchange.com/q/130381/144441). Hence, without ...
OmG's user avatar
  • 1,816
2 votes
Accepted

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

A sequence of $n$ random variables $z_{1:n} = z_1, z_2, \dots, z_n$ is i.i.d. if they are identically distributed, i.e. each random variable $z_i$ has the same distribution the joint distribution of ...
nbro's user avatar
  • 40.5k
2 votes
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Can I always interpret features as random variables in machine learning safely?

In general terms yes. Because what the ML algorithms do in general is to learn the hidden probability density function of the target examples (cats, dogs..). And that is done by learning the ...
JVGD's user avatar
  • 1,108
2 votes

Is there any advantage in viewing weights of a neural network as random variables?

In Bayesian statistics, as opposed to frequentist statistics, you can model the parameters as random variables. Bayesian machine learning is the application of Bayesian statistics in the context of ...
nbro's user avatar
  • 40.5k
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
Accepted

For the VAE, should the input, output and latent variable code be random variables?

The VAE attempts to model a specific probabilistic (directed) graphical model (Bayesian network) So, in this PGM, $\mathbf{z}$ and $\mathbf{x}$ are random variables. In principle, I think you could ...
nbro's user avatar
  • 40.5k
1 vote

When can we call a feature "hierarchical"?

You can find a brief explanation of hierarchical feature selection in the following from "An Empirical Evaluation of Hierarchical Feature Selection Methods for Classification in Bioinformatics ...
OmG's user avatar
  • 1,816
1 vote

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

Independent and identically distributed random variables share the same probability distribution and each item doesn’t influence or provide insight about the value of the next item you measure. The ...
Aray Karjauv's user avatar

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