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Short answer Check out the paper of Shuman et al. [1], it provides some background on Graph Signal Processing, including answers to your questions in sections II.C and III.A Long Answer Question 1 Yes, the filter $g_{\theta}$ is analogous to CNN's filter. You have a diagonal matrix with $\theta_{i}$ in its diagonal mainly for matrix-multiplication purposes (...


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When it comes to notation/terminology, often, people in machine learning are (a bit?) sloppy, which causes a lot of confusion, especially for newcomers to the field or people not very math-savvy. I was also confused about this notation at some point (see my last questions here, which are all about this confusing topic). See also this answer. In the VAE paper,...


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It's an uppercase "J" from the math calligraphy alphabet, i.e. \mathcal{J} in latex. $\mathcal{J}$


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I don't think there's any rationale behind the usage of the letter $z$ to denote the noise (which sometimes is also denoted by $\epsilon$ in other contexts), apart from the fact that $x$ and $y$ are already being used and that the letters $x$, $y$, $z$ and $w$ are often used to denote variables in mathematics. In particular, in machine learning, $x$ and $y$ ...


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Whilst you're right that for any continuous distribution $P(X = x) = 0 \;; \forall x \in \mathcal{X}$ where $\mathcal{X}$ is there support of the distribution, they are not referring to probabilities here, rather they are referring to density functions (though this should really be denoted with a lower case $p$ to avoid confusion such as this). $p(x|z)$ is a ...


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It takes a little bit of time to fully understand the 2D convolution/cross-correlation and to relate it to the usual diagrams of the convolution operation, so, before addressing your questions, let me first try to break the definition of the 2D cross-correlation down, from the left to right. $$S(i,j) =(K*I)(i,j) = \sum_m \sum_n I(i+m, j+n)K(m,n) \label{1}\...


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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 just $p$. There is also the notation $p_x$ (or things like $p_{x \mid y}$ for conditional p.d.s), which you will find in some statistics books. Of course, if ...


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Machine learning papers are often somewhat confused about the distinction between a distribution and its probability density. I would rewrite this The process consists of two steps: (1) a value $\mathbf{z}^{(i)}$ is generated from some prior distribution $p_{\boldsymbol{\theta}^{*}}(\mathbf{z})$; (2) a value $\mathbf{x}^{(i)}$ is generated from some ...


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You can read $X=\{x^{(i)}\}_{i=1}^N$ as $X$ represents the sequence of all values of $x$ from $x_i$ to $x_N$ where $i$ is all values from 1 to $N$. To me, the notation is confusing since my experience tells me that curly braces are used for sets, but this seems to be the best interpretation.


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The issue doesn't come up terribly often. If you are only dealing with vectors, everything is either a row or column vector. It makes no difference which it is. A more relevant issue is whether one uses the so-called "numerator layout" or "denominator layout". In the numerator layout, $\partial f / \partial x$ is $\mathbb{R}^{n\times m}$, ...


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The following link satisfied my inquiries: https://www.mdpi.com/1999-4907/12/2/131/htm I hope this is useful for someone else! Justin


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I don't see where it's implied that G is a probability distribution. G is a function, whose output conditioned on one variable has a probability distribution, but it isn't one. z is random noise which is G's source of randomness. y is something that isn't random. We call G over and over with the same y and different random z's and look at the distribution of ...


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The bandit problem is an MDP. You can make the same argument about needing data to learn in the stateful MDP setting. The thing is, the data you need (the past rewards in this case) was drawn iid (conditioned on the arm) and is not actually a trajectory. For instance, once you learn an optimal policy, you no longer need to gather data and the sequence of ...


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Based on my experience, I would say that the standard notation is just to have a regular function, and specify that it applies element wise. For example, a common notation for activation functions is $\sigma$, so e.g. you could represent the activations of a regular dense layer as $\sigma(W x + b)$ where $x, b$ are vectors and $W$ is a matrix. I've never ...


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The mathematical notation for complex tensorial expressions always tries to balance complexity and precision. More precise notation - the one that explicitly spells all the indices - becomes extremely convoluted very quickly. My favorite example illustrating it is from physics -- the Standard Model Lagrangian is written shortly on T-shirts and coffee mugs as:...


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If we use $T$ as the notation for the terminal state, then the last action is $a_{T-1}$. This is because when you reach state $s_T$ you don't take another action, which would be $a_T$, because the episode is finished upon reaching the terminal state.


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You are right, it is sloppy notation by the authors. However, the target network is not necessarily linked to the behaviour policy $\beta$ either. Essentially when they take the expectation with respect to $\rho^\beta$ they are taking expectation with respect to a state distribution induced by some policy $\beta$ that is not necessarily the same as our ...


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That notation should mean to go from time step $T$ to time step $1$ by a negative step $-1$, i.e. backward, so $T$, then $T-1$, then $T-2$, and so on until $1$. If you know Python, this should be familiar. However, note that this is just a guess, because I am not familiar with this algorithm.


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