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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Convolution problem [closed]
If the sum of coefficients of a filter h is zero, then for what padding will the sum of elements of a resultant convolved image also be zero after performing convolution with an image f(m,n) ?
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Why does convolutional neural network use a 2d Filter
Given an input of C,H,W where C is channels the filter is of size X,Y and slides across each channel individually. Why isn't the filter of size C,X,Y and slides across the entire 3d shape?
I know of ...
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Deriving the pdf of noisy signal: sum of pdf f(s)=1/2+s/2 and a uniformly distributed noise [duplicate]
I am having a hard time to find the pdf of $\widetilde{s}=s+x$.
$s$ has a pdf $f(s)=1/2+s/2$ where $s\in(-1,1)$. $x$ is uniformly distributed over $[-\epsilon, \epsilon]$. I am trying to use the ...
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1
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Sampling line segments within a box
I'm at a bit of a loss for where to start with a sampling problem I'm having so any and all direction would be helpful. I essentially want to sample line segments of identical length within a bounding ...
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3
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Distribution after Combining Two Sets of Normal Distribution Samples
Suppose I draw $N1$ samples from distribution $N(\mu_1,\sigma_1^2)$, $N2$ samples from distribution $N(\mu_2,\sigma_2^2)$. These two distributions are independent.
Can the combined sample of $N1+N2$ ...
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Positional Invariance missing after max pooling operation in custom CNN
I am an early career researcher in computational neuroscience, and I am currently trying to model a robust object recognition model.
My model takes a dataset (binary images; where each object is ...
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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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4
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1
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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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1
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51
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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 ...
- 159
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1
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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 ...
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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)&...
1
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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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3
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1
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How to obtain the last convolutional layer of a model in torchvision for applying grad cam?
I'm using efficient net b0 from torchvision for training a classifier for cifar10. I would like to apply grad cam for generating saliency maps for explaining the predictions. However, I'm not sure ...
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23
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Computing an integral that reduces to $\mathbb{P}[X>Y]$
Problem
Evaluate $$I=\int_{-\infty}^\infty \frac{e^{-\frac{1}{2}\left(\frac{x-\mu)}{\sigma} \right)^2}}{\sigma \sqrt{2 \pi}}\frac{1}{1+e^{-x}}\, \mathrm{d}x$$
My attempt
Now the first part of the ...
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Exact Successor State Distribution for a Pendulum
I want to solve the following problem. Suppose we have a simple pendulum, which follows the differential equation
\begin{equation}
\dot{x} = f(x) = [x_2, -\sin(x_1)]^T, \text{with } x=[x_1, x_2]^T.
\...
- 307
2
votes
1
answer
41
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No activation function between two convolutional layers in MUNIT?
I'm reading the code of NVIDIA's MUNIT, the code of the resnet is as follows:
...
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1
vote
1
answer
205
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Is it wrong to view convolution as template matching?
I am reading about the convolution operation but I can't see how it can be seen as template matching.
Suppose that we convolve the input $\mathbf{X}$:
$$
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 ...
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1
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278
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Why convolving a function with a Gaussian kernel is the same as adding a Gaussian noise to the input? [duplicate]
I am implementing accelerated Langevin Dynamics (LD) for posterior estimation with prior presented with deep autoregressive network from paper [1]. I have a question about the prior smoothing ...
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1
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149
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Probability Density of the Sum of Two Un-identical Uniform Random Variables
Let $X$ ~ Uniform$[a,b]$ and $Y$ ~ Uniform$[c,d],$ where $a\le b\le c\le d.$ Find the probability density of $Z = X + Y.$
I know I have to use the convolution formula
$$f_Z(z) = \int_{-\infty}^\...
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Cannot apply simple OLS model in the case of low resolution devices resulting in Fourier space convolution
There's a problem which often comes up within my field and doesn't seem to be approachable analytically. Any suggestions or direction towards the class of problems this falls under would be helpful.
...
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1
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184
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When is a conditional hazard rate increasing?
Cross posted from Mathoverflow
Let $X$ and $Y$ be two random variables such that $X\sim Exp(\lambda)$ and $Y$ have positive support and (strictly) increasing hazard rate $h_Y$. $X$ and $Y$ are ...
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3
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2
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134
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Convolution of two functions doesn't fit my data as I thought it would
I have simulated a Gaussian curve in 50 bins of data. I have then repeated this many times, drawing the amplitude of the Gaussian from a log-normal distribution. Here are a 10 realizations:
(IMAGE 1)
...
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Estimating the distribution of a sum of two random variables if the family of one of the variables is known
Assume I have a random variable $Y=X_1+X_2$. I want to estimate the distribution $f$ of $Y$ given a sample $y_1,\ldots,y_N$. If this was all that is known about $Y$ the best way would probably be to ...
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Calculating convolution in R [closed]
I am struggling to get the correct answer for the simple calculation of convolution in R.
The convolution of $f(t) = e^{-t}$ and $g(t) = \sin(t)$ is:
$$
(f * g)(t) = 1/2 \left( e^{-t} + \sin(t) - \cos(...
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How to backpropagate transposed convolution?
I'm currently learning Convolutional Neural Networks and am stuck on trying to figure out how to compute gradients in a layer that uses transposed convolution. Also, how do I calculate the gradients ...
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3
votes
4
answers
668
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Probability of a given result with multiples of mixed dice with different number of faces
What is the formula to calculate the probability of getting 41 when I throw two 10-sided dice and four 8-sided dice? I’m looking for an algorithm for the general case of throwing multiples of two sets ...
- 275
3
votes
2
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369
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Calculating the distribution of $X-Y$
One can find the distribution of $X+Y$ where $X$ and $Y$ are independent random variables using this formula
$$f_{X+Y}(a)=\int_{-\infty}^\infty f_X(a-y) f_Y(y) dy$$
I'm wondering how to adapt this ...
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votes
1
answer
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what are the differences between receptive field (RF) and field-of-views (FOV) in DeepLab papers?
I am learning the deeplab models. However, some concepts in the papers made me confused. Receptive field (RF) and field-of-views (FOV) are two concepts mentioned in the Deeplabv1 paper. I know that ...
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Density of $|t_1 - t_2|$ where $t_1$ and $t_2$ are iid with $P(t) = \alpha e^{-t\alpha}$
I am trying to answer the following question from my quantum mechanics textbook and my probability theory is admittedly rusty (this is not schoolwork as should be clear from my post history on Phys ...
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Order Statistics - Percentile Range of Normal Mixture of Normals
Say I have draw N values from a normal distribution [$\mu_1$, $\sigma_1$]. Below are 10 sampled points compared to the normal distribution they're sampled from
I then create a normal mixture of ...
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3
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118
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Distribution closed under convolution and truncation followed by convolution
Let $D(\theta)$ denote an absolutely continuous distribution on $\mathbb{R}$. (The finite dimensional vector $\theta$ collects the parameters of the distribution.) Assume that the p.d.f. of $D(\theta)$...
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How can I build a 6D Convolution Layer in a CNN, using R or Python? [closed]
As stated in the title, I would like to build an N-dimensional Convolutional Layer as part of a Convolution Neural Network, without doing dimensionality reduction on my data; because I have multiple ...
- 113
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0
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26
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Unclear Architecture of MNIST Neural Network
I am trying to reproduce a Neural Network trained to detect whether there is a 0-3 digit in an image with another confounding image. The paper I am following lists the corresponding architecture:
A ...
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1
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93
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What "Convolution filters along the time axis" means?
Suppose that I have a tensor of height:25 and width:50. Height is my temporal axis, therefore I have a window of 25 time steps. Therefore my input tensor is:
I want to extract temporal features / ...
- 233
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Relationship between convolutions in neural nets and probabilistic convolution
In probability theory, convolution extends to produce the distribution of the sum of two independent random variables. I've only ever seen this in the context of univariate random variables.
However, ...
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Are Class Activated Maps an example of backpropagated Explainable AI?
Class Activated Maps (NOT GradCAM) is listed in van der Velden et al as a back-propagation approach in table 1, but that is not actually true, is it?
CAM doesn't use back-propagation in the method, ...
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23
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How to calculate how much each error source contributes to an overall accuracy metric?
I am building a model of overall accuracy for a robotic system, I have various error sources from assembly, calibrations, measurements, imaging, for each error I have a PDF of the error it induces on ...
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2
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114
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How to average multiple non-normal distributions?
I have the following statistics of two independent random variables:
First random variable:
...
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42
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Mean conditional on sum
Let $X$ and $Y$ be two random variables. I am interested in how $\mathrm{E}[X | X + Y = z]$ changes as $z$ changes.
Intuitively, if $X$ and $Y$ are independent, the conditional mean should be ...
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4
votes
3
answers
4k
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How to determine the no of multiplication operations in convolution operation?
Let's say We have an input of size 28×28×192. We apply 32, 5×5 convolution filters with padding "same". How many multiplication operations will be there in total?
I know there will be ...
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0
answers
68
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How to take 1000 samples from distribution X and then use MLE to prove they came from distribution X?
I am trying to do:
find 1000 points that represent samples from distribution X with parameters $(a,b,c,\ldots, d)$
be guaranteed that the MLEs for those 1000 points are $(a,b,c,\ldots, d)$ with $99\%$...
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