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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Issue about both results in agreement with 2 different ways to compute variance of a random variable : weighted chisquared vs Gamma distributions

1.) I am interested in computing the variance of this observable $O$ involving the coefficients of spherical harmonics $a_{\ell m}$ and the $C_{\ell}$ which is the variance of an $a_{\ell m}$ : $$O=\...
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3D convolutions and jitter

I want to process a sequence of cropped and aligned face images from a video with a neural network. I am considering a use of 3D convolutions in order to capture the spatiotemporal dependency. However,...
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Why does MobileNet Architecture start with a Standard Convolution?

I am trying to understand the design choices behind the MobileNet architecture. (pdf available on the right). The authors use Depthwise Separable Convolutions as a replacement for Classical ...
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How to count the parameters in a convolution layer?

I'm preparing for an exam in Computer Vision. I came across with the following question from one of the exams: What is the number of parameters of a convolution layer in a neural network, when the ...
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How to obtain the density of a sum of independent discrete random variables?

Let's $X_1, X_2, ..., X_n$, $n=1,2,...$ are independent discrete random variables. It is necessary to find the distribution law of the their sum: $p(k) =P(X_1 + X_2 + ... + X_n = k), k=0, 1, 2, ... $ ...
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Recovering the distribution of an independent variable of a probit model

I have the following model: $$ y_i^* = \beta_0 + \beta_1 x_i + \epsilon_i,$$ where I assume that $\epsilon \sim N(0,1)$ and $x \sim N(\mu, \sigma^2)$. I dont observe $y^*$, only $y_i=1 \text{ if } y_i^...
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CNN model accuracy is increasing really slowly [duplicate]

I am training a CNN model from scratch on the Caltech101 dataset. The accuracy of the model is increasing very slowly after the 5th epoch. Shown below is the accuracy and loss curves of the model for ...
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Why my cdf of the convolution of n exponential distribution is not in the range(0,1)?

I assume that there are n exponential distribution that $x_i$ ~ $Exp(\lambda_i)$, i=1..n, and I want to calculate the cumulative distribution of $S=x_1+x_2+...+x_n$, the convolution of n exponential ...
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Training accuracy growing way faster than validation accuracy?

i've been trying to solve this classification problem using a convolutional neural network for some days but no matter what I do I can't seem to find the correct hyperparameters and configuration to ...
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What prevents my PyTorch convolutional auto-encoder to converge on some initializations? [duplicate]

I built a small auto-encoder for greyscale images. It is there to make some tests, so I train it often, and I have a strange behavior. On some initialisations, it does not converge. I mean, the MSE ...
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Convolution of a conditional PDF with itself [duplicate]

Let's say that $x$ is a random variable which follows a conditional probability density function $f(x|N)$, where $N$ is an integer parameter. If the functional form of $f(x|N=1)$ is known, then one ...
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convolving a conditional pdf with itself

Let's say that x is a random variable which follows a conditional probability density function $f(x|N)$, where $N$ is an integer parameter. If the functional form of $f(x|N=1)$ is known, then one can ...
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Is there an explanation for a classifier achieving high F1 scores, but having still high CrossEntropyLoss?

I am training a CNN classifier on a balanced dataset (around 35k examples for each label) with 13 classes. The model seems to achieve high F1 scores from the first batches; The F1 score for each class ...
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How is it ensured that a CNN does not learn the same filter multiple times?

Let's say we have a dataset of pictures displaying straight vertical lines with different translations or nothing (just an example), and we apply a CNN to that. We choose that the CNN should learn N ...
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How is derivative calculated for Grad-CAM if the final output is multidimensional?

For Grad-CAM, the derivative of the final output is found with respect to the elements of the channel considered Selvaraju et al. 2019. But if the output is a multidimensional matrix how is the ...
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Kernel_size for rgb images in cnn?

I came across a cnn code of rgb images where kernel_size was mentioned only 3 not 3,3,3. So does 3 means 3,3,3. and for greyscale images kernel size was mentioned 3,3 so for grey scale images 3,3 I ...
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Complexity of 1D CNN and 2D CNN

Are the computational complexity of 1D CNN and 2D CNN the same? If not what are their computational complexity and what is the best way to compute them? Considering both forward and backward ...
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Working with modalities (sensor data) with different frequencies

Accelerometer data: 119 Hz. Gyroscope data: 119 Hz. Magnetometer data: 20 Hz. I would like to build a 2D-CNN. I have sensors with different sampling rates. Rather than extracting a feature, how I can ...
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Can we recover joint distribution from a continuous range of convolutions?

Given a correct model of the joint distribution of a random vector $(X,Y)$, we can derive (though not necessarily in closed form) the correct distribution model for $pX+(1-p)Y$ for any $p\in[0,1]$. ...
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How does max pooling reduce the number of parameters to be learnt in a CNN if we already have parameter sharing?

I've been a bit confused about max pooling for a little while but I've finally understood why it provides more generalisation since you're essentially getting rid of less useful information and ...
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Convolution of Binomial and Poisson Distributions?

I am currently working through the paper Estimation of Probability of Defaults (PD) for Low-Default Portfolios: An Actuarial Approach In Section 2 of this paper, the author provides the following ...
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Computing an Exponential Moving Average

According to the Wikipedia page on moving averages, "This is also why sometimes an EMA is referred to as an $N$-day EMA. Despite the name suggesting there are $N$ periods, the terminology only ...
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Guessing filters from responses to step signals

Consider a signal $X$ filtered by a kernel $p$ with finite support $[t_0,t_1]$ and $\int_{t_0}^{t_1}p(t)\,\text{d}t = 1$, yielding the response function $$\overline{X}(T) = \int_{t_0}^{t_1} X(T + t)\ ...
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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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4 votes
2 answers
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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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3 votes
2 answers
121 views

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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6 votes
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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 $Y=\sum_{i=1}^nx_i^2$ \begin{equation} Y\sim \chi^2(n) \end{equation} ...
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What is the resulting function to describe a log-normal function with Gaussian noise added?

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 ...
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