Questions tagged [convolution]
Convolution is a function-valued operation on two functions $f$ and $g$: $\int _{-\infty }^{\infty }f(\tau )g(t-\tau )d\tau$. Often used for obtaining the density of a sum of independent random variables. This tag should also be used for the inverse operation of deconvolution. DO NOT use this tag for convolutional neural networks.
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the Detailed Architecture of EfficientNetV2-B2
I'm currently studying different neural network architectures and I'm particularly interested in EfficientNetV2-B2. I understand that this model is an improved version of the original EfficientNet, ...
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How should I go about completely decorrelating a digital signal?
So I'm working on real time signal compression, and I need to come up with the best convolution to minimize the entropy of incoming data (which I will then compress), which I understand is achieved by ...
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Uniform distribution over a triangle
Problem
Consider a triangle $T$ with vertices $V_1,V_2,V_3 \in \mathbb{R}^2$ and let
\begin{equation*}\begin{aligned}
y&=z+v\\
v&\sim\mathcal{N}(0, R)\\
z&\sim\mathcal{U}(T)
\end{aligned}\...
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Uniform density over 2 segments [duplicate]
Background
Let $V_1, V_2 \in \mathbb{R}^2$ be the vertices of a segment and let $z$ be uniformly distributed over that segment. Now consider the random vector
\begin{equation*}
\begin{aligned}
y&=...
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Convolution with a pathological distribution
Problem definition
Consider the following random bivariate vector
\begin{equation}
\begin{aligned}
y&=z+v \\
z&\sim p_z(z;c) \\
v&\sim p_v(v)
\end{aligned}
\end{equation}
where $p_z$ ...
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Why does GAP at the end of FCN for MTSC work?
I have a binary MTSC (Multivariate Time Series Classification) problem where i train a CNN, namely a FCN (or Fully Convolutional Network) to predict class 0 or class 1 based on a multivariate time ...
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1
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Percentiles of a distribution of weighted summary statistics
Suppose I have a collection of different independent probability distributions, $\{ P_i(X)\}_{i=1}^N$, each with their own support $I_i$. I know that the $10^{th}$ percentile of a given distribution ...
- 149
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What is the variance of convolution of two random variables?
Consider two random variables $Z$ and $W$. Given the variances of $Z$ and $W$, how can we compute the variance of their convolution $Z \circledast W $?
As an example, please consider the case of noise ...
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PDF of difference of uniform distributions [duplicate]
Main questions are in bold but feel free to correct me if I'm wrong somewhere else. As far as possible, I need both intuition and formal explanation.
Let $X \sim Uniform(a,b)$ and $Y \sim Uniform(c,d)$...
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4
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Probability that sum of binary variables is even
Let $S_i \in \{0,1\}$, $i=1,\dots,N$ be $N$ independent random binary variables, each taking the value 1 with probability $0 \le p_i \le 1$ (and the value 0 with probability $1-p_i$).
I am interested ...
- 4,440
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What is the distribution of a RV with the constant random variable? [duplicate]
For random variables (rv) $X$ and $Y$ on a space $\Omega$:
Assume the rv $X\sim f_0$ distributed and $Y(t)=c$ is a constant rv, i.e. $Y\sim \delta(t-c)$ using the $\delta$-distribution as a short ...
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Why is the maximum path length for convolutional layer $O(n/k)$ in attention is all you need paper?
In the table-1 third row it is being mentioned. Why is it $O(n/k)$? Take for example 1d convolution of 2 over 9 tokens with stride $1$. It won't be $n/k$ or $9/2=4.5$ rather it would be roughly $n-1$ ...
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Inference on latent variable with observation of its convolution with itself
Problem
I have an inference problem where the data observed are univariate random numbers whose distribution is obtained as follows. A latent random variable X is first sampled from a parametric ...
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43
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Weighted Average of Uniformly Distributed RV [duplicate]
Let $x \sim U[0,1]$ and $y\sim U[0,1]$. Let $z= \omega\, x+ (1-\omega)\,y$, where $\omega\in[0,1]$. The pdf of $z$ is a trapezoidal distribution over $[0,1]$:
\begin{equation*}
\begin{aligned}
f(z)&...
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1
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Convolutional Neural Networks - Flattening with multiple feature maps
I have a very simple question about CNNs, which I unfortunately couldn't find an explanation for.
Imagine we have a CNN, that has four filters (eg right, left, top, bottom edges) each of those outputs ...
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