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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27 views

When (if ever) is the sum of two dependent geometric RVs negative binominal?

Imagine you have two random variables $X $ and $Y$, you know $$ X \sim \text{Geometric}(p) \\ X + Y \sim \text{Negative Binomial}(2, p) $$ I am interested in what if anything can be said about the ...
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Convolutional roots of mixture of exponential distributions

In the reference book on infinite divisibility and generalised gamma convolution, BONDESSON, Lennart. Generalized gamma convolutions and related classes of distributions and densities. Springer ...
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Estimation of generalized gamma convolutions

How can i estimate on a data sample parameters of a generalised gamma convolution ? To be more specific, if my estimation gives me only a gamma convolution and not a generalised gamma convolution i'll ...
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29 views

Neural networks assume continuity, what does this mean?

I encountered the following paragraph by Pedro Domingos (mentioned in Gary F. Marcus paper): ANNs assume continuity, graphical models assume conditional independence, and instance-based learning ...
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Cropping input images Neural Networks

I'm creating a simple neural network for image classification,I had some doubts about the input images. Let's suppose i'm trying to classify (for example) a bear and i have an input image like this: ...
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How do I learn one time signal given another?

I conducted an experiment which led me to believe that two sensors were time correlated somehow. Their signals do not show any obvious correlation, however their spectrograms show a strong similarity ...
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59 views

Does replacing a random variable in a sum with it's expectation shift the mass of the expectation towards the mean?

Assume any two positive, independent random variables $X$, $Y$ with pmf's $f_X$ and $f_Y$, as well as a third (degenerate) random variable $Z$ that is defined to be equal to the expectation of $Y$, i....
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More efficient way to calculate convolution of Weibull distribution

Hi I was trying to compute the convolution of Weibull distribution as follows with parameter t, lambda(scale parameter) and k: ...
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Convolution of two indicator functions [duplicate]

I am experiencing difficulties understanding the concept of convolution and especially convolution of 2 independent indicator functions. I would be really thankful if someone can help understand the ...
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Convolutions of joint random variables

I have two discrete dependent random variables $X,Y$, where both $X$ and $Y$ can take values either $0$ or $1$. Furthermore, I know their joint distribution $f_{X,Y}(X,Y)$. Now let's say I have an ...
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What is the purpose of the last 1x1 convolution layer in segmentation networks providing a linear transformation of the features?

Semantic segmentation networks make use of a final 1x1 convolution layer at the very end of their network which brings the feature maps equal to the number of classes in the dataset. Since this 1x1 ...
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ResNet Reduce Block

I am building a ResNet. I have two separate blocks: Cnn block, Reduce block. Cnn block - 1 cnn layer, activation, Batch Normal -> 1 cnn, activation, Batch Normal, so 2 CNN in this block. In Reduce ...
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CNN models comparison [duplicate]

I coded a 38 layer CNN and 8 layer CNN but there's something wrong in my 38 layer CNN, which doesn't learn anything. Not able to fugure out what's wrong. They were trained on CIFAR.
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Does max-pooling increase the receptive field? [duplicate]

I'm new in deep learning. when applying convolution on the image , the receptive field is increased but when applying max pooling on the image, I don't know the receptive field is increasing or keep ...
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Visualine Node Importance in Graph Convolution

I am quite new to the concept of attention. I am working with graph data and running graph convolution on it to learn node level embedding first. Then an attention layer to aggregate the nodes to ...
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1answer
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How many input pixels influence output pixel in an FCN type architecture?

Let's say I have 8 back to back convolutional layers with zero padding such that the input and output dimensions are the same. There are no max-pooling layers between the layers. All the layers use a ...
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How can a Keras convolutional network be defined such that it outputs images of the same dimensions as the input?

I wanna train a convolutional neural network to convert an input image to an output image, where the input and output images are of the same dimensions (50 pixels wide, 300 pixels high and greyscale). ...
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Question about the log-normal distribution

The main object of my question is this: if $X$ has a log-normal distribution, $Y = X + Z$ and $Y$ has the same distribution as that of $Z^2$ (in other words, $F_{Z^2} = F_{X+Z}$) and $X, Z$ are ...
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AutoEncoder Reconstruction error for Anomaly Detection

I'm building a convolutional autoencoder as a means of Anomaly Detection for semiconductor machine sensor data - so every wafer processed is treated like an image (rows are time series values, columns ...
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What is the difference between 1x1 convolutions and convolutions with “SAME” padding?

In general, 1x1 convolutions are used to reduce the dimensionality of filter space. I referred this answer. But we can also reduce the dimensionality of filter ...
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Deleting and repairing a Convolution Neural Network

Let's say that I have a convolutional neural network with multiple blocks, each consisting of multiple filters. If we have something along the lines of Input -> Block1 -> Block2 -> Block3 -> Max ...
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1answer
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Cannot overfit Mobilenet with one example

I am trying to do a single object detection. Since the problem is much simpler than multibox object localization I decided to try using a simple CNN that predicts the object class and its location. ...
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CNN Feature Extraction Time

I have a dataset consist of 260 thousands images that are extracted from several videos. I want to extract features of these images and use them for frame retrieval. I used VGG16 (pretrained on ...
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1answer
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What is E[X|X+Y < z] with X, Y independent Normals?

Let $X\sim N(\mu_X,\sigma_X^2)$ and $Y\sim N(\mu_Y,\sigma_Y^2)$ and $Cov(X,Y)=\sigma_{XY}$. Define $Z=X+Y$. I know that $E[X|Z=z]=\mu_X + \frac{\sigma_X^2+\sigma_{XY}}{\sigma_X^2+2\sigma_{XY}+\...
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How does the weight affect the sum of two Normals?

Question Take two independent, non-degenerate Normals, $X\sim N(\mu_X,\sigma_X^2)$ and $Y\sim N(\mu_Y,\sigma_Y^2)$. Define $Z=aX + Y$ with $a>0$. This implies $Z \sim N(a\mu_X+\mu_Y,a^2\sigma_X^...
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Why do we connect convolution layers in sequence instead of applying them separately on input image?

I am already aware of the convolution function, CNN and all. I have already implemented a few. But this question strucks my mind every time. Most of the networks I have seen, use a stack of ...
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Does the model architecture of a CNN depend on the dimension of your input images?

By model architecture, I'm interested in knowing the following: Number of nodes in input layer Number of nodes in subsequent layers Number of layers in the architecture Number of filters and ...
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591 views

How to implement 1D Convolutional Autoencoder with multiple channels? [closed]

I want to build a 1D convolution autoencoder with 4 channels in Keras. Instead of images with RGB channels, I am working with triaxial sensor data + magnitude which calls for 4 channels. I haven't ...
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Convolving non-square kernel on matrix vertically and horizontally along axis

I need clarification and verification to better help me understand convolving non-square kernel on matrices along axises. If I have a 1x3 kernel of [-1, 0, 1] and need to convolve a 3x3 matrix of [[...
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Are Fully Convolutional Neural Network (FCN) just normal ConvNets?

I was reading the paper Fully Convolutional Networks for Semantic Segmentation and on section 3 they introduce the notation for what they call a Fully Convolutional Neural Network (FCN). Are they just ...
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Computing derivatives for backpropagation across a convolution step

This will be a long post, but I hope it'll be instructive to anyone else in my position. I'm trying to find how the derivatives of the loss function are calculated with respect to the kernels and ...
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How do spectral neural networks for learning on graphs work?

I've been reading this paper "Spectral Networks and Locally Connected Networks on Graphs" but for the full understanding of this paper it requires the reader to be knowledgeable about harmonic ...
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Solving discrete convolution linear functions

Consider we have samples $\mathbf{X} \in \mathcal{R}^{n\times p}$ and we aim to find a "regression" coefficients $\beta \in \mathcal{R}^{q \times 1}$ ($q>p$), but the regression is defined as a ...
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1answer
152 views

Optimizing parameters for CNN autoencoder based on training and validation loss

I have designed an autoencoder with a encoder and decoder consiting of 2D convolutational layers (the input are 40'000 2D images). I train the autoencoder using adam optimizer. The autoencoders has ...
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1answer
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Using one neural network for each image type

I have been reading about Convolutional neural networks and its use in image recognition. Most of the examples I have seen so far train one single network to classify an image into one label or class. ...
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1answer
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Making sense of indices in 2D convolution operations in convolutional neural networks

Referring to the answer here: https://www.quora.com/Why-are-convolutional-nets-called-so-when-they-are-actually-doing-correlations, the equation for a discrete 2D convolution is specified as: $$C(x,y)...
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Difference between the convolution and correlation backpropagation

In the article about the convolution backpropagation, the computation of gradients to the input needs to rotate the weight and the computation of gradients to the weight also needs to rotate the input....
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Convolution with multiple input channel and multiple filters which have depth

How does the convolution work for an input which has multiple channels convolving with filters that also have depth. For example, assume somewhere in the network we have a ...
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Separable kernel vs depthwise separable convolution

I would like to compare separable kernel with depthwise separable convolution. In the first case (eg for 2D) we have: $y[m, n] = h[m, n] * x[m, n] = (h_1[m] \cdot h_2[n]) * x[m, n] = \\ h_1[m] * (h_2[...
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207 views

Does the sum of two independent exponentially distributed random variables with different rate parameters follow a gamma distribution?

short question. Suppose we have two independent exponentially distributed random variables with means $400$ and $200$, so that their respective rate parameters are $1/400$ and $1/200$. Do these ...
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Confusion about the average of two non-normal distributions and expected values

I don't really come from a stats heavy background and am having trouble understanding what the right approach to this question is: A question states that 'a company is trying to increase the ...
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1answer
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How to get the generative counterpart of a discriminative CNN

Say we train a (discriminative) CNN to predict age from images of faces. Is there a direct way of obtaining the homologous generative network (ie, from a scalar age to an image of a face) ? The ...
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R: Calculating the convolution of two (multivariate) functions using FFT

I'm looking for a way to calculate: $$(f\ast g)(x) = \int_{\mathbb{R}^d}f(y)g(x-y)dy$$ in R. I have solved this problem using Monte-Carlo integration. However, ...
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1answer
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Force sum of random varables to equal to 1 [duplicate]

Suppose I have 3 random variables, $X1, X2,X3$. Define $Z$ as: $Z=X1+X2+X3$ I want to force $Z$ to equal 1 for every "realization" of $X1,X2,X3$ ($X_i \sim Beta(a_i,b_i))$. As an example, let $X_i$ ...
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41 views

CNN, “squared” or "non-squared image?

I'm working on a project about image recognition. In my dataset I have images of different size, all rectangular image (the most 640x480 and 1280x640). I would like to build my classifier to ...
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What is Supremal/Infimal Convolution

I'm currently reading a paper which mentions supremal and infimal convolutions. As I understood, they are upper and lower bounds for a joint distribution. One of the formulas in that paper is as ...
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1answer
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Back propagation is done with each batch in a convolutional net, but is it also done with the validation set?

It's my understanding that the weights are updated in a convolutional neural network with each evaluation of a batch. But when the training data has been processed and it comes to predicting ...
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1answer
42 views

Convolution of two dependent distributions in MATLAB

Assume that I have two discrete random variables $X$ and $Y$. $X ∈ \{1,3,3,5,7,7,7,9,9,9,9,9\}$ and $Y ∈ \{5,5,9,9,10,12,13\}$ Where their empirical CDFs are given as: $F_x(1) = 0.0833, F_x(3) = ...
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26 views

is there a relationship between the determinant and the convolution

A long time ago, perhaps 13 or 16 years, I took a course called linear algebra. It has been a little while,so in parts that I don't use as much I was rusty. I possibly incorrectly remember having to ...
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53 views

Meaning of kernel size 1 for 1-D convolution in Keras

The kernel size is the window size for 1D convolution. Can anyone explain what is meant by kernel size $1$ in Keras/TensorFlow?