# 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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### Find pdf of X+Y [duplicate]

Let X ∼ Exp(λ) and Y ∼ Exp(μ) be two independent exponential random variables, where λ, μ > 0. Find the probability density function of X + Y if λ ̸= μ. I have successfully find ans if λ = μ, but ...
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### When does the sum of two $t$-distributed random variables follow a $t$ distribution?

In the scope of a project, I need to find the sum of two independent $t$-distributions. I know that in the general case, the sum of two $t$-distributed random variables is not $t$-distributed. However,...
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### How general is this property about correlation and the sum of two normal RVs?

(Cross-posted from math stack exchange as I didn't get any responses there) Given a random vector $(X_1,X_2)$ that is jointly normal with means / sd's $\mu_1,\mu_2, \sigma_1,\sigma_2$ and correlation ...
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### Covariance of a convolution between a gaussian random walk and white noise [closed]

I want to compute the covariance of $$U_t:=\sum_{l=-L}^{l=L} (X_l-X_{l-1})X_{l-t}$$ with $X_t$ defined as : \begin{align*} X_0&=0 \\ X_t&=X_{t-1}+\epsilon_t \end{align*} $t=1,2,...$...
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### Discrete convolution with circular matrices

Cross-correlation (read convolution) is the process of sliding a kernel across the input image and each step multiplying the elements and summing the results (i.e. matrix multiplication). PyTorch has ...
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### Conditional expectation of X given X+Y [duplicate]

X and Y are two independent variables, X ~ exp(a), Y ~ exp(a). I need to find E(X|X+Y). I tried to calculate by definition, but it did not lead to success. Maybe there is another, more convenient way ...
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### How doesn't a dilated convolution lose information?

In the example below (source), we see the difference between stride and dilation in CNNs. The explanation as quoted: "Using a dilated convolution increases the size of the receptive field ...
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### How could I downsize CNN?

Let's take a CNN with an input of size (512, 512) and an output of the same size. Now imagine I want to feed an image of size (256, 256) to the network. Would it be possible to do so without upscaling ...
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### Are convolutional autoencoders required to have symmetric encoders and decoders?

I am a newer to deep learning. Recently I am studying the convolutional autoencoder (CAE). I found the architectures built with keras and matlab are a little different. In particular, the architecture ...
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### Make output of a sequential model self-consistent

I'm training a sequential model on the following type of sequence (just showing the target labels here): ...
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### Mathematical representation of 1D convolution

How does one write the mathematical formula for conv1d used in PyTorch, including parameters like stride length and padding? For instance, I can write ...
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### Spectral Graph Convolutions: What are the spectral filters functions

I am trying to understand the mathematical meaning of one of the steps that appear in the Convolution Theorem (Step 4 here). To give some context, this is related to applying the convolution theorem ...
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### When is $\sum Z_i \sim \sqrt{n} Z_i$?

If $X_i$ are independently and identically distributed $N(0,\sigma^2)$ then $Y=\sum X_i \sim N(0,n\sigma^2)$, i.e. $\sum X_i \sim \sqrt{n}X_i$. That raises two questions: Is a zero-mean normal ...
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### if i need a kernel to detect cones shape.. how to do so?

i'm working on a project of cones detection from lidar point cloud, I have got an idea to use Hough transform and I'm using convolution for voting principle for cone detection and I already ...
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### A question about Convolutional Neural Networks, equivariance and parameter sharing

I have a couple of questions acbout Convolutional Neural Networks and I'm struggling to give an answer. Q1 Let's say I have $[3 \times 32 \times 32]$ image (with three channels) and I apply a first ...
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### What is the best way to feed IMU data to CNN?

I took the Introduction to Embedded Machine Learning course, which is provided by Shawn Hymel, on Coursera. While talking about sensor fusion, he made the following statement for the following diagram:...
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### Why CNN is suitable for time-series data? [duplicate]

I am confused by the statements that I came across in two different papers. The statement from the paper titled as "Detecting Cyber Attacks in Industrial Control Systems Using Convolutional ...
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### Successor to Densenet, and Why Would My Resnet Model Peform Better Than My Densenet Model?

Currently, I'm modifying PoseNet, for use with camera localizaiton, with Resnet and Densenet. I modified both to have 2048 output classes, which feeds into dense layers to get the camera pose(like the ...
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### Why does my loss decrease very slowing at the start of training, but picks up in the middle

I'm training S3D on my own dataset and uses a cosine learning rate decay. But the training loss doesn't decrease in the first 40 epochs, and than starts to decrease quickly, while the loss increased ...
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### Do Convolutional Layers Pool data?

Sorry for the trivial question but considering this example in the image attached doesn't the conv layer pool data by summing them? What I am asking is if this images describes a subset where a conv ...
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### Neural network to read short strings - translational invariance in CNNs

I have a series of short strings that each describe some item (one item per string). The people who write these strings can get pretty creative when it comes to spelling. For each string, I also have ...
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### Recovering weights between neurons in a convolutional layer

Given a convolutional layer, I am interested in recovering the weight matrix $W$, where $w_{i,j}$ is the weight between neuron $i$ in the input layer and neuron $j$ in the output layer. I know that ...
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### Calculating Convolution Only for a Certain Interval Using "conv()" in MATLAB

Below you can see the code for convolution of two continuous functions. There is a function called fx which I took as the square root of a Gaussian distribution. ...
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### Convolution between two random variables

Given $X$ is a random variable which distributed uniformly in $[1,3]$ and $Y$ distributed uniformly in $[0,a]$. I need to calculate the value of the density function of: $$Z=X+Y,$$ at a point $b$ (i....
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### CNN for images with different channel sizes

Assuming the channels of an image have different sizes. E.g.: red: 128x128, blue: 128x128, green: 256x256 Is it better to resize the green channel to a lower size, or would It be better to add a conv ...
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### Does the sum of squared "dependent" Gaussian variables still exhibit a Chi-squared distribution?

Suppose we have $x_1,\cdots,x_n$, such that $x_i$ are i.i.d according to $x_i\sim N(0,1)$ for $i=1,\cdots,n$. Then we know that $Y=\sum_{i=1}^nx_i^2$ $$Y\sim \chi^2(n)$$ ...
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I have a log-normal distribution: $\frac{1}{x} Ae^{-\frac{(ln(x)-\mu)^2}{2\sigma^2}}$ And I draw from it (1000 times) and plot the draws in a histogram: The log-normal function from which the draws ...